Branches History Index

Index: By Building Blocks

Mathematical Language

Axioms (34)
- Algebra (5)
  - Axiom: Axiom of Distributivity
  - Axiom: Axioms of Group
  - Axiom: Axioms of Magma
  - Axiom: Axioms of Monoid
  - Axiom: Axioms of Semigroup
- Geometry (7)
  - Elements Euclid (5)
    - Book 1 Plane Geometry (5)
      - Axiom: 1.1: Straight Line Determined by Two Distinct Points
      - Axiom: 1.2: Segment Extension
      - Axiom: 1.3: Circle Determined by its Center and its Radius
      - Axiom: 1.4: Equality of all Right Angles
      - Axiom: 1.5: Parallel Postulate
  - Euclidean Geometry (2)
    - Axiom: "Between" Relation, Axioms of Order
    - Axiom: Axioms of Connection
- Logic (1)
  - Axiom: Bivalence of Truth
- Number Systems Arithmetics (2)
  - Axiom: Archimedean Axiom
  - Axiom: Peano Axioms
- Probability Theory And Statistics (3)
  - Axiom: Addition of the Probability of Mutually Exclusive Events
  - Axiom: Probability as a Non-Negative Number
  - Axiom: Probability of the Certain Event
- Set Theory (12)
  - Axiom: Axiom of Choice
  - Axiom: Axiom of Empty Set
  - Axiom: Axiom of Existence
  - Axiom: Axiom of Extensionality
  - Axiom: Axiom of Foundation
  - Axiom: Axiom of Infinity
  - Axiom: Axiom of Pairing
  - Axiom: Axiom of Power Set
  - Axiom: Axiom of Replacement (Schema)
  - Axiom: Axiom of Union
  - Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension)
  - Axiom: Zermelo-Fraenkel Axioms
- Theoretical Physics (2)
  - Special Relativity (2)
    - Axiom: Principle of Relativity
    - Axiom: Principle of the Constancy of Light Speed
- Topology (2)
  - Axiom: Filter
  - Axiom: Separation Axioms
Definitions (759)
- Algebra (138)
  - Definition: (Unit) Ring
  - Definition: Absolute Values and Non-Archimedean Absolute Values of Fields
  - Definition: Addition of Ideals
  - Definition: Affine Basis, Affine Coordinate System
  - Definition: Affine Space
  - Definition: Affine Subspace
  - Definition: Affinely Dependent and Affinely Independent Points
  - Definition: Algebra over a Ring
  - Definition: Algebraic Element
  - Definition: Algebraic Structure (Algebra)
  - Definition: Alternating Multilinear Map
  - Definition: Associate
  - Definition: Associativity
  - Definition: Automorphism
  - Definition: Basis, Coordinate System
  - Definition: Bilinear Form
  - Definition: Binary Operation
  - Definition: Bounded Affine Set
  - Definition: Cancellation Property
  - Definition: Characteristic of a Field
  - Definition: Characteristic of a Ring
  - Definition: Closure
  - Definition: Coefficient Matrix
  - Definition: Column Vectors and Row Vectors
  - Definition: Commutative (Abelian) Group
  - Definition: Commutative (Unit) Ring
  - Definition: Commutativity
  - Definition: Complete Ordered Field
  - Definition: Conjugate Elements of a Group
  - Definition: Continued Fractions
  - Definition: Convex Affine Set
  - Definition: Convex Hull
  - Definition: Cosets
  - Definition: Cyclic Group, Order of an Element
  - Definition: Dependent and Independent Absolute Values
  - Definition: Diagonal Matrix
  - Definition: Dimension of a Vector Space
  - Definition: Dimension of an Affine Space
  - Definition: Direct Product of Groups
  - Definition: Direct Sum of Vector Spaces
  - Definition: Divisibility of Ideals
  - Definition: Dot Product, Inner Product, Scalar Product (Complex Case)
  - Definition: Dot Product, Inner Product, Scalar Product (General Field Case)
  - Definition: Eigenvalue
  - Definition: Eigenvector
  - Definition: Elementary Gaussian Operations
  - Definition: Elementary Symmetric Functions
  - Definition: Endomorphism
  - Definition: Epimorphism
  - Definition: Euclidean Affine Space
  - Definition: Euclidean Ring, Generalization of Division With Quotient and Remainder
  - Definition: Existence of a Neutral Element
  - Definition: Exponentiation in a Group
  - Definition: Exponentiation in a Monoid
  - Definition: Exterior Algebra, Alternating Product, Universal Alternating Map
  - Definition: Factorial Ring, Generalization of Factorization
  - Definition: Field
  - Definition: Field Extension
  - Definition: Field Homomorphism
  - Definition: Finite Field
  - Definition: Finite Field Extension
  - Definition: Gaussian Method to Solve Systems of Linear Equations, Rank of a Matrix
  - Definition: Generalization of Divisor and Multiple
  - Definition: Generalization of the Greatest Common Divisor
  - Definition: Generalization of the Least Common Multiple
  - Definition: Generating Set of a Group
  - Definition: Generating Set of an Ideal
  - Definition: Generating Systems
  - Definition: Group
  - Definition: Group Homomorphism
  - Definition: Group Operation
  - Definition: Group Order
  - Definition: Homomorphism
  - Definition: Ideal
  - Definition: Identity Matrix
  - Definition: Integral Closure
  - Definition: Integral Element
  - Definition: Inverse Element
  - Definition: Invertible and Inverse Matrix
  - Definition: Irreducible Polynomial
  - Definition: Irreducible, Prime
  - Definition: Isomorphism
  - Definition: Linear Combination
  - Definition: Linear Equations with many Unknowns
  - Definition: Linear Map
  - Definition: Linear Span
  - Definition: Linearly Dependent and Linearly Independent Vectors, Zero Vector
  - Definition: Magma
  - Definition: Matrix Multiplication
  - Definition: Matrix and Vector Addition
  - Definition: Matrix, Set of Matrices over a Field
  - Definition: Maximal Ideal
  - Definition: Minimal Polynomial
  - Definition: Module
  - Definition: Monoid
  - Definition: Monomorphism
  - Definition: Multilinear Map
  - Definition: Multiplicative System
  - Definition: Multiplicity of a Root of a Polynomial
  - Definition: Normal Subgroups
  - Definition: Ordered Field
  - Definition: Points, Lines, Planes, Hyperplanes
  - Definition: Polynomial Ring
  - Definition: Polynomial over a Ring, Degree, Variable
  - Definition: Prime Field
  - Definition: Prime Ideal
  - Definition: Principal Ideal
  - Definition: Principal Ideal Domain
  - Definition: Principal Ideal Ring
  - Definition: Recursive Definition of the Determinant
  - Definition: Reduction of an Integer Polynomial Modulo a Prime Number
  - Definition: Ring Homomorphism
  - Definition: Ring of Integers
  - Definition: Semigroup
  - Definition: Signum Function in An Ordered Field
  - Definition: Solution to a Lower Triangular SLE - Forward Substitution
  - Definition: Solution to an Upper Triangular SLE - Backward Substitution
  - Definition: Spectrum of a Commutative Ring
  - Definition: Square Matrix
  - Definition: Subadditive Function
  - Definition: Subfield
  - Definition: Subgroup
  - Definition: Subring
  - Definition: Subspace
  - Definition: Substructure
  - Definition: Symmetric Bilinear Form
  - Definition: Symmetric Matrix
  - Definition: Systems of Linear Equations with many Unknowns
  - Definition: Transcendental Element
  - Definition: Transposed Matrix
  - Definition: Unit
  - Definition: Unitary Affine Space
  - Definition: Upper and Lower Triangular Matrix
  - Definition: Vector Space
  - Definition: Zariski Topology of a Commutative Ring
  - Definition: Zero Divisor and Integral Domain
  - Definition: Zero Matrix, Zero Vector
  - Definition: Zero Ring
- Analysis (115)
  - Definition: (Weighted) Arithmetic Mean
  - Definition: Absolutely Convergent Complex Series
  - Definition: Absolutely Convergent Series
  - Definition: Accumulation Point (Real Numbers)
  - Definition: Accumulation Points (Complex Numbers)
  - Definition: Asymptotical Approximation
  - Definition: Banach Space
  - Definition: Bounded Complex Sequences
  - Definition: Bounded Complex Sets
  - Definition: Bounded Real Sequences, Upper and Lower Bounds for a Real Sequence
  - Definition: Bounded and Unbounded Functions
  - Definition: Closed Curve, Open Curve
  - Definition: Closed and Open Regions of the Complex Plane
  - Definition: Complete Metric Space
  - Definition: Complex Cauchy Sequence
  - Definition: Complex Infinite Series
  - Definition: Complex Polynomials
  - Definition: Complex Sequence
  - Definition: Constant Function Real Case
  - Definition: Continuous Complex Functions
  - Definition: Continuous Functions at Single Complex Numbers
  - Definition: Continuous Functions at Single Real Numbers
  - Definition: Continuous Real Functions
  - Definition: Continuously Differentiable Functions
  - Definition: Convergent Complex Sequence
  - Definition: Convergent Complex Series
  - Definition: Convergent Real Sequence
  - Definition: Convergent Real Series
  - Definition: Convex and Concave Functions
  - Definition: Cosine of a Real Variable
  - Definition: Curves In the Multidimensional Space `\(\mathbb R^n\)`
  - Definition: Decimal Representation of Real Numbers
  - Definition: Derivative of an n-Dimensional Curve
  - Definition: Derivative, Differentiable Functions
  - Definition: Difference Quotient
  - Definition: Directional Derivative
  - Definition: Divergent Sequences
  - Definition: Divergent Series
  - Definition: Even Complex Sequence
  - Definition: Even and Odd Complex Functions
  - Definition: Even and Odd Functions
  - Definition: Exponential Function of General Base
  - Definition: Extended Real Numbers
  - Definition: Finite and Sigma-Finite Measure
  - Definition: Finite and Sigma-Finite Pre-measure
  - Definition: First-Order Ordinary Differential Equation (ODE)
  - Definition: Functional
  - Definition: Functional Equation
  - Definition: Generalized Polynomial Function
  - Definition: Geometric Mean
  - Definition: Heine-Borel Property Defines Compact Subsets
  - Definition: Higher Order Directional Derivative
  - Definition: Higher-Order Derivatives
  - Definition: Hilbert Space
  - Definition: Hyperbolic Cosine
  - Definition: Hyperbolic Sine
  - Definition: Improper Integral
  - Definition: Infimum of Extended Real Numbers
  - Definition: Infimum, Greatest Lower Bound
  - Definition: Infinite Series, Partial Sums
  - Definition: Interior, Boundary, and Closures of a Region in the Complex Plane
  - Definition: Isolated Point (Real Numbers)
  - Definition: Jordan Arc (Simple Curve)
  - Definition: Limit Inferior
  - Definition: Limit Superior
  - Definition: Limits of Complex Functions
  - Definition: Limits of Real Functions
  - Definition: Linear Function
  - Definition: Local Extremum
  - Definition: Logarithmically Convex and Concave Functions
  - Definition: Maximum (Real Numbers)
  - Definition: Measurable Set
  - Definition: Measurable Space
  - Definition: Measure
  - Definition: Measureable Function
  - Definition: Minimum (Real Numbers)
  - Definition: Monotonic Functions
  - Definition: Monotonic Sequences
  - Definition: Nested Real Intervals
  - Definition: Odd Complex Sequence
  - Definition: One-sided Derivative, Right-Differentiability and Left-Differentiability
  - Definition: Open and Closed Discs
  - Definition: Order Relation for Step Functions
  - Definition: Periodic Functions
  - Definition: Pointwise and Uniformly Convergent Sequences of Functions
  - Definition: Polynomials
  - Definition: Positive and Negative Parts of a Real-Valued Function
  - Definition: Pre-measure
  - Definition: Rational Functions
  - Definition: Real Absolute Value Function
  - Definition: Real Cauchy Sequence
  - Definition: Real Identity Function
  - Definition: Real Intervals
  - Definition: Real Sequence
  - Definition: Real Subsequence
  - Definition: Rearrangement of Infinite Series
  - Definition: Reciprocal Function
  - Definition: Riemann Sum With Respect to a Partition
  - Definition: Riemann-Integrable Functions
  - Definition: Ring of Sets (measure-theoretic definition)
  - Definition: Sequences Tending To Infinity
  - Definition: Sigma-Algebra
  - Definition: Sine of a Real Variable
  - Definition: Solution of Ordinary DE
  - Definition: Step Functions
  - Definition: Supremum Norm for Functions
  - Definition: Supremum of Extended Real Numbers
  - Definition: Supremum, Least Upper Bound
  - Definition: Tangent of a Real Variable
  - Definition: Totally Differentiable Functions, Total Derivative
  - Definition: Uniformly Continuous Functions (Real Case)
  - Definition: Vector Field
  - Definition: `\(b\)`-Adic Fractions
  - Definition: `\(n\)` times Continuously Differentiable Functions
  - Definition: n-Periodical Complex Sequence
- Combinatorics (10)
  - Definition: Binomial Coefficients
  - Definition: Combinations
  - Definition: Cycles
  - Definition: Difference Operator
  - Definition: Factorial Polynomials
  - Definition: Falling And Rising Factorial Powers
  - Definition: Falling and Rising Factorial Powers of Functions
  - Definition: Indefinite Sum, Antidifference
  - Definition: Permutations
  - Definition: Stirling Numbers of First and Second Kind
- Geometry (160)
  - Analytic Geometry (4)
    - Definition: Describing a Straight Line Using Two Vectors
    - Definition: Hyperplane of a Number Space
    - Definition: Points in a Coordinate System - Number Spaces
    - Definition: Points vs. Vectors in a Number Space
  - Elements Euclid (144)
    - Book 1 Plane Geometry (35)
      - Definition: 1.01: Point
      - Definition: 1.02: Line, Curve
      - Definition: 1.03: Intersections of Lines
      - Definition: 1.04: Straight Line, Segment and Ray
      - Definition: 1.05: Surface
      - Definition: 1.06: Intersections of Surfaces
      - Definition: 1.07: Plane
      - Definition: 1.08: Plane Angle
      - Definition: 1.09: Angle, Rectilinear, Vertex, Legs
      - Definition: 1.10: Right Angle, Perpendicular Straight Lines
      - Definition: 1.11: Obtuse Angle
      - Definition: 1.12: Acute Angle
      - Definition: 1.13: Boundary
      - Definition: 1.14: Plane Figure
      - Definition: 1.15: Circle, Circumference, Radius
      - Definition: 1.16: Center of the Circle
      - Definition: 1.17: Diameter of the Circle
      - Definition: 1.18: Semicircle
      - Definition: 1.19: Rectilinear Figure, Sides, n-Sided Figure
      - Definition: 1.20: Equilateral Triangle, Isosceles Triangle, Scalene Triangle
      - Definition: 1.21: Right Triangle, Obtuse Triangle, Acute Triangle
      - Definition: 1.22: Square, Rectangle, Rhombus, Rhomboid, Trapezium
      - Definition: 1.23: Parallel Straight Lines
      - Definition: Altitude of a Triangle
      - Definition: Collinear Points, Segments, Rays
      - Definition: Concentric Circles
      - Definition: Decagon
      - Definition: Diagonal
      - Definition: Exterior, Interior, Alternate and Corresponding Angles
      - Definition: Hexagon
      - Definition: Parallelogram - Defining Property III
      - Definition: Pentagon
      - Definition: Sum of Angles
      - Definition: Supplemental Angles
      - Definition: Triangle
    - Book 2 Geometric Algebra (3)
      - Definition: 2.1: Area of Rectangle, Rectangle Contained by Adjacent Sides
      - Definition: 2.2: Gnomon
      - Definition: Point of Division, Point of External Division
    - Book 3 Circles (11)
      - Definition: 3.01: Congruent Circles
      - Definition: 3.02: Tangent to the Circle, Straight Line Touching The Circle
      - Definition: 3.03: Circles Touching One Another
      - Definition: 3.04: Chords Equally Far From the Center of a Circle
      - Definition: 3.05: Chords Being Further from the Center of a Circle
      - Definition: 3.06: Segment of a Circle, Arc
      - Definition: 3.07: Angle of a Segment
      - Definition: 3.08: Angle in the Segment (Inscribed Angle)
      - Definition: 3.09: Angle Standing Upon An Arc
      - Definition: 3.10: Circular Sector, Central Angle
      - Definition: 3.11: Similar Circular Segments
    - Book 4 Inscription And Circumscription (7)
      - Definition: 4.1: Rectilinear Figure Inscribed in Another Rectilinear Figure
      - Definition: 4.2: Rectilinear Figure Circumscribed about Another Rectilinear Figure
      - Definition: 4.3: Inscribing Rectilinear Figures in Circles
      - Definition: 4.4: Circumscribing Rectilinear Figures about Circles
      - Definition: 4.5: Inscribing Circles in Rectilinear Figures
      - Definition: 4.6: Circumscribing Circles about Rectilinear Figures
      - Definition: 4.7: Chord and Secant
    - Book 5 Proportion (19)
      - Definition: 5.01: Magnitude is Aliquot Part
      - Definition: 5.02: Multiple of a Real Number
      - Definition: 5.03: Ratio
      - Definition: 5.04: Having a Ratio
      - Definition: 5.05: Having the Same Ratio
      - Definition: 5.06: Proportional Magnitudes
      - Definition: 5.07: Having a Greater Ratio
      - Definition: 5.08: Proportion in Three Terms
      - Definition: 5.09: Squared Ratio
      - Definition: 5.10: Cubed Ratio
      - Definition: 5.11: Corresponding Magnitudes
      - Definition: 5.12: Alternate Ratio
      - Definition: 5.13: Inverse Ratio
      - Definition: 5.14: Composition of a Ratio
      - Definition: 5.15: Separation of a Ratio
      - Definition: 5.16: Conversion of a Ratio
      - Definition: 5.17: Ratio ex Aequali
      - Definition: 5.18: Perturbed Proportion
      - Definition: Geometric Progression, Continued Proportion
    - Book 6 Similar Figures (3)
      - Definition: 6.01: Similar Rectilinear Figures
      - Definition: 6.02: Cut in Extreme and Mean Ratio
      - Definition: 6.03: Height of a Figure
    - Book 7 Elementary Number Theory (22)
      - Definition: 7.01: Unit
      - Definition: 7.02: Number
      - Definition: 7.03: Proper Divisor
      - Definition: 7.04: Aliquant Part, a Number Being Not a Divisor of Another Number
      - Definition: 7.05: Multiple, Number Multiplying another Number
      - Definition: 7.06: Even Number
      - Definition: 7.07: Odd Number
      - Definition: 7.08: Even-Times-Even Number
      - Definition: 7.09: Even-Times-Odd Number
      - Definition: 7.10: Odd-Times-Odd Number
      - Definition: 7.11: Prime Number
      - Definition: 7.12: Co-prime (Relatively Prime) Numbers
      - Definition: 7.13: Composite Number
      - Definition: 7.14: Not Co-prime Numbers
      - Definition: 7.15: Multiplication of Numbers
      - Definition: 7.16: Rectangular Number, Plane Number
      - Definition: 7.17: Cuboidal Number, Solid Number
      - Definition: 7.18: Square Number
      - Definition: 7.19: Cubic Number, Cube Number
      - Definition: 7.20: Proportional Numbers
      - Definition: 7.21: Similar Rectangles and Similar Cuboids, Similar Plane and Solid Numbers
      - Definition: 7.22: Perfect Number
    - Book 10 Incommensurable Magnitudes (16)
      - Definition: 10.02: Magnitudes Commensurable and Incommensurable in Square
      - Definition: Def. 10.01: Magnitudes Commensurable and Incommensurable in Length
      - Definition: Def. 10.03: Rational and Irrational Magnitudes
      - Definition: Def. 10.04: Rational and Irrational Magnitudes in Square
      - Definition: Def. 10.05: First Binomial
      - Definition: Def. 10.06: Second Binomial
      - Definition: Def. 10.07: Third Binomial
      - Definition: Def. 10.08: Fourth Binomial
      - Definition: Def. 10.09: Fifth Binomial
      - Definition: Def. 10.10: Sixth Binomial
      - Definition: Def. 10.11: First Apotome
      - Definition: Def. 10.12: Second Apotome
      - Definition: Def. 10.13: Third Apotome
      - Definition: Def. 10.14: Fourth Apotome
      - Definition: Def. 10.15: Fifth Apotome
      - Definition: Def. 10.16: Sixth Apotome
    - Book 11 Elementary Stereometry (28)
      - Definition: Def. 11.01: Solid Figures, Three-Dimensional Polyhedra
      - Definition: Def. 11.02: Surface of a Solid Figure
      - Definition: Def. 11.03: Straight Line at Right Angles To a Plane
      - Definition: Def. 11.04: Plane at Right Angles to a Plane
      - Definition: Def. 11.05: Inclination of a Straight Line to a Plane
      - Definition: Def. 11.06: Inclination of a Plane to a Plane
      - Definition: Def. 11.07: Similarly Inclined Planes
      - Definition: Def. 11.08: Parallel Planes
      - Definition: Def. 11.09: Similar Solid Figures
      - Definition: Def. 11.10: Equal Solid Figures
      - Definition: Def. 11.11: Solid Angle
      - Definition: Def. 11.12: Pyramid, Tetrahedron
      - Definition: Def. 11.13: Prism, Parallelepiped
      - Definition: Def. 11.14: Sphere
      - Definition: Def. 11.15: Axis of a Sphere
      - Definition: Def. 11.16: Center of a Sphere
      - Definition: Def. 11.17: Diameter of a Sphere
      - Definition: Def. 11.18: Cone
      - Definition: Def. 11.19: Axis of a Cone
      - Definition: Def. 11.20: Base of a Cone
      - Definition: Def. 11.21: Cylinder
      - Definition: Def. 11.22: Axis of a Cylinder
      - Definition: Def. 11.23: Bases of a Cylinder
      - Definition: Def. 11.24: Similar Cones, Similar Cylinders
      - Definition: Def. 11.25: Cube
      - Definition: Def. 11.26: Octahedron
      - Definition: Def. 11.27: Icosahedron
      - Definition: Def. 11.28: Dodecahedron
  - Euclidean Geometry (6)
    - Definition: "Lies on" Relation
    - Definition: Congruence
    - Definition: Ellipse
    - Definition: Euclidean Movement - Isometry
    - Definition: Points, Straight Lines, and Planes
    - Definition: Similarity
  - Projective Geometry (6)
    - Definition: Collinear Points
    - Definition: Concurrent Straight Lines
    - Definition: Coplanar Points and Straight Lines
    - Definition: Incidence
    - Definition: Perspectivities
    - Definition: Projectivities, Ranges and Pencils
- Graph Theory (57)
  - Definition: Adjacency List Representation
  - Definition: Adjacency Matrix
  - Definition: Biconnected Graphs, `\(k\)`-Connected Graphs
  - Definition: Bipartite Graph
  - Definition: Chromatic Number and `$k$`-Coloring of a Graph
  - Definition: Closed Walks, Closed Trails, and Cycles
  - Definition: Complement Graph
  - Definition: Complete Bipartite Graph
  - Definition: Complete Graph
  - Definition: Connected Vertices
  - Definition: Connected and Disconnected Graphs, Bridges and Cutvertices
  - Definition: Cycle Graph
  - Definition: Cyclic, Acyclic Graph
  - Definition: Degree Sequence
  - Definition: Digraph, Initial and Terminal Vertices, Loops, Parallel and Inverse Edges, Simple Digraph
  - Definition: Dual Planar Graph
  - Definition: Eulerian Graph
  - Definition: Eulerian Tour
  - Definition: Face Degree
  - Definition: Face, Infinite Face
  - Definition: Finite and Infinite Graphs
  - Definition: Girth and Circumference
  - Definition: Graph Decomposable Into `\(k\)` Trees
  - Definition: Hamiltonian Cycle
  - Definition: Hamiltonian Graph
  - Definition: Incidence, Adjacency, Neighbours
  - Definition: Incidence, Adjacency, Predecessor and Successor Vertices, Neighbours
  - Definition: Interlacing Pieces with Respect to a Cycle, Interlacement Graph
  - Definition: Isomorphic Digraphs
  - Definition: Isomorphic Undirected Graphs
  - Definition: Leaf
  - Definition: Minimal Tree Decomposability
  - Definition: Null Graph
  - Definition: Order of a Graph
  - Definition: Pieces of a Graph With Respect to A Cycle
  - Definition: Planar Drawing (Embedding)
  - Definition: Planar Graph
  - Definition: Regular Graph
  - Definition: Root, Degree of a Tree, Subtree, Height
  - Definition: Semi-Eulerian Graph
  - Definition: Semi-Eulerian Tour, Open Trail
  - Definition: Semi-Hamiltonian Graph
  - Definition: Semi-Hamiltonian Path
  - Definition: Separating and Non-Separating Cycles
  - Definition: Size of a Graph
  - Definition: Spanning Subgraph
  - Definition: Spanning Tree
  - Definition: Subdigraphs and Superdigraphs; Induced Subdigraph
  - Definition: Subdivision of a Graph
  - Definition: Subgraphs and Supergraphs; Induced Subgraph
  - Definition: Suppressing Vertices, Suppressed Multigraph
  - Definition: Trees and Forests
  - Definition: Undirected Graph, Vertices, Edges, Simple Graph
  - Definition: Vertex Degrees for Digraphs
  - Definition: Vertex Degrees for Undirected Graphs
  - Definition: Walks, Trails, and Paths
  - Definition: Weakly and Strongly Connected Digraphs
- Knot Theory (4)
  - Definition: Knot
  - Definition: Knot Diagram, Classical Crossing, Virtual Crossing
  - Definition: Reidemeister Moves, Planar Isotopy Moves, Diagrammatic Moves
  - Definition: Unknot
- Logic (45)
  - Definition: Atomic Formulae in Predicate Logic
  - Definition: Axioms
  - Definition: Boolean Algebra
  - Definition: Canonical Normal Form
  - Definition: Concatenation of Languages
  - Definition: Conjunction
  - Definition: Conjunctive and Disjunctive Canonical Normal Forms
  - Definition: Consistency and Negation-Completeness of a Logical Calculus
  - Definition: Contrapositive
  - Definition: Derivability Property
  - Definition: Disjunction
  - Definition: Domain of Discourse
  - Definition: Equivalence
  - Definition: Exclusive Disjunction
  - Definition: Formal Languages Generated From a Grammar
  - Definition: Function, Arity and Constant
  - Definition: Grammar (Syntax)
  - Definition: Implication
  - Definition: Interpretation of Propositions - the Law of the Excluded Middle
  - Definition: Interpretation of Strings of a Formal Language and Their Truth Function
  - Definition: Iteration of Languages, Kleene Star, Kleene Plus
  - Definition: Language
  - Definition: Literals, Minterms, and Maxterms
  - Definition: Logical Arguments
  - Definition: Logical Calculus
  - Definition: Negation
  - Definition: Negation of a String
  - Definition: Paradox
  - Definition: Predicate of a Logical Calculus
  - Definition: Proofs and Theorems in a Logical Calculus
  - Definition: Quantifier, Bound Variables, Free Variables
  - Definition: Rules of Inference
  - Definition: Satisfaction Relation, Model, Tautology, Contradiction
  - Definition: Semantics of PL0
  - Definition: Semantics of a Formal Language
  - Definition: Set of Truth Values (True and False)
  - Definition: Signature
  - Definition: Signature of Propositional Logic - PL0
  - Definition: Soundness and Completeness of a Logical Calculus
  - Definition: Strings (words) over an Alphabet
  - Definition: Syntax of PL0 - Propositions as Boolean Terms
  - Definition: Terms in Predicate Logic
  - Definition: Truth Table
  - Definition: Variable in a Logical Calculus
  - Definition: `$k$`-nary Connectives, Prime and Compound Propositions
- Number Systems Arithmetics (33)
  - Definition: Absolute Value of Complex Numbers
  - Definition: Absolute Value of Integers
  - Definition: Absolute Value of Rational Numbers
  - Definition: Absolute Value of Real Numbers (Modulus)
  - Definition: Addition of Complex Numbers
  - Definition: Argument of a Complex Number
  - Definition: Complex Conjugate
  - Definition: Convergent Rational Sequence
  - Definition: Definition of Complex Numbers
  - Definition: Definition of Irrational Numbers
  - Definition: Division of Real Numbers
  - Definition: Dot Product of Complex Numbers
  - Definition: Euler's Constant
  - Definition: Multiplication of Complex Numbers
  - Definition: Multiplication of Natural Numbers
  - Definition: Number `$\pi$`
  - Definition: Order Relation for Integers - Positive and Negative Integers
  - Definition: Order Relation for Natural Numbers
  - Definition: Order Relation for Rational Numbers - Positive and Negative Rational Numbers
  - Definition: Order Relation of Real Numbers
  - Definition: Products
  - Definition: Ratio of Two Real Numbers
  - Definition: Rational Cauchy Sequence
  - Definition: Rational Sequence
  - Definition: Set of Natural Numbers (Peano)
  - Definition: Set-theoretic Definition of Order Relation for Natural Numbers
  - Definition: Set-theoretic Definitions of Natural Numbers
  - Definition: Subtraction of Complex Numbers
  - Definition: Subtraction of Integers
  - Definition: Subtraction of Rational Numbers
  - Definition: Subtraction of Real Numbers
  - Definition: Sums
  - Definition: Triangle Numbers
- Number Theory (33)
  - Definition: Arithmetic Function
  - Definition: Canonical Representation of Natural Numbers, Factorization
  - Definition: Canonical Representation of Positive Rational Numbers
  - Definition: Co-prime Numbers
  - Definition: Complete Residue System
  - Definition: Composite Number
  - Definition: Congruent, Residue
  - Definition: Diophantine Equations
  - Definition: Divisor, Complementary Divisor, Multiple
  - Definition: Divisor-Closed Sets
  - Definition: Euler function
  - Definition: Even and Odd Numbers
  - Definition: Floor and Ceiling Functions
  - Definition: Harmonic Series
  - Definition: Jacobi Symbol
  - Definition: Legendre Symbol
  - Definition: Modulo Operation for Real Numbers
  - Definition: Multiplicative Functions
  - Definition: Möbius Function, Square-free
  - Definition: Number of Divisors
  - Definition: Perfect Number
  - Definition: Perfect Square
  - Definition: Prime Numbers
  - Definition: Prime-Counting Function
  - Definition: Quadratic Residue, Quadratic Nonresidue
  - Definition: Reduced Residue System
  - Definition: Sets of Integers Co-Prime To a Given Integer
  - Definition: Subsets of Prime Numbers Not Dividing a Natural Number
  - Definition: Sum of Divisors
  - Definition: Twin Prime Numbers
  - Definition: Von Mangoldt Function
  - Sieve Methods (2)
    - Definition: Sieve of Eratosthenes
    - Definition: Sieve, Sieve Problem
- Probability Theory And Statistics (17)
  - Definition: Bernoulli Experiment
  - Definition: Certain and Impossible Event
  - Definition: Conditional Probability
  - Definition: Continuous Random Variables
  - Definition: Discrete Random Variables
  - Definition: Geometric Probability
  - Definition: Independent Events
  - Definition: Laplace Experiments and Elementary Events
  - Definition: Mutually Exclusive and Collectively Exhaustive Events
  - Definition: Mutually Independent Events
  - Definition: Pairwise Independent Events
  - Definition: Probability Distribution
  - Definition: Probability Mass Function
  - Definition: Probability and its Axioms
  - Definition: Random Experiments and Random Events
  - Definition: Random Variable, Realization, Population and Sample
  - Definition: Relative and Absolute Frequency
- Set Theory (63)
  - Definition: Bijective Function
  - Definition: Bounded Subsets of Ordered Sets
  - Definition: Bounded Subsets of Unordered Sets
  - Definition: Canonical Projection
  - Definition: Cartesian Product
  - Definition: Comparing the Elements of Posets and Chains
  - Definition: Comparison of Cardinal Numbers
  - Definition: Complete System of Representatives
  - Definition: Composition of Binary Relations
  - Definition: Constant Function
  - Definition: Contained Relation "`$\in_X$`"
  - Definition: Countable Set, Uncountable Set
  - Definition: Disjoint Sets
  - Definition: Embedding, Inclusion Map
  - Definition: Equipotent Sets
  - Definition: Equivalence Class
  - Definition: Equivalence Relation
  - Definition: Extensional Relation
  - Definition: Finite Set, Infinite Set
  - Definition: Fixed Point, Fixed Point Property
  - Definition: Generalized Union of Sets
  - Definition: Graph of a Function
  - Definition: Identity Function
  - Definition: Index Set and Set Family
  - Definition: Indicator (Characteristic) Function, Carrier
  - Definition: Inductive Set
  - Definition: Injective Function
  - Definition: Inverse Relation
  - Definition: Invertible Functions, Inverse Functions
  - Definition: Irreflexive, Asymmetric and Antisymmetric Binary Relations
  - Definition: Limit Ordinal
  - Definition: Minimal Inductive Set
  - Definition: Mostowski Function and Collapse
  - Definition: Mutually Disjoint Sets
  - Definition: Order Embedding
  - Definition: Ordered Pair, n-Tuple
  - Definition: Ordinal Number
  - Definition: Partial and Total Maps (Functions)
  - Definition: Power Set
  - Definition: Preorder, Partial Order and Poset
  - Definition: Quotient Set, Partition
  - Definition: Reflexive, Symmetric and Transitive Binary Relations
  - Definition: Relation
  - Definition: Restriction
  - Definition: Set Complement
  - Definition: Set Difference
  - Definition: Set Intersection
  - Definition: Set Partition
  - Definition: Set Union
  - Definition: Set, Set Element, Empty Set
  - Definition: Singleton
  - Definition: Special Elements of Ordered Sets
  - Definition: Strict Total Order, Strictly-ordered Set
  - Definition: Subset and Superset
  - Definition: Surjective Function
  - Definition: The Class of all Ordinals `$\Omega$`
  - Definition: Total Order and Chain
  - Definition: Total and Unique Binary Relations
  - Definition: Transitive Set
  - Definition: Universal Set
  - Definition: Well-founded Relation
  - Definition: Well-order, Well-ordered Set
  - Definition: Zero of a Function
- Theoretical Computer Science (22)
  - Complexity Theory (1)
    - Definition: Big O Notation
  - Computability (10)
    - Definition: Algorithm (Effective Procedure)
    - Definition: Computational Problem, Solution
    - Definition: GOTO Command, GOTO Program, Index
    - Definition: GOTO-Computable Functions
    - Definition: LOOP Command, LOOP Program
    - Definition: LOOP-Computable Functions
    - Definition: Unit-Cost Random Access Machine
    - Definition: WHILE Command, WHILE Program
    - Definition: WHILE-Computable Functions
    - Definition: `$\mathcal P$`-Computable and `$\mathcal P$`-Decidable Problems
  - Data Structures (1)
    - Definition: Linked List, List Nodes
  - Formal Languages (10)
    - Definition: Abstract Syntax Tree
    - Definition: Ambiguous and Unambiguous Grammars
    - Definition: Deterministic Finite Automaton (DFA)
    - Definition: Epsilon Non-Deteriministic Finite Automaton (`$\epsilon$`-NFA)
    - Definition: Equivalent Grammars
    - Definition: Non-deterministic Finite Automaton (NFA)
    - Definition: Type-0 (Phrase Structure) Grammars and Recursively Enumerable Languages
    - Definition: Type-1 (cs) Grammars and Context-sensitive Languages
    - Definition: Type-2 (cf) Grammars and Context-free Languages
    - Definition: Type-3 (Linear) Grammars and Regular Languages
- Theoretical Physics (7)
  - Classical Physics (2)
    - Definition: Average Velocity
    - Definition: Instantaneous Velocity
  - Special Relativity (5)
    - Definition: Frame of Reference
    - Definition: Inertial and Noninertial Frames of Reference
    - Definition: Meter
    - Definition: Second
    - Definition: Spacetime Diagram
- Topology (55)
  - Definition: Boundary Points, Closures, Interiors, and Exteriors
  - Definition: Bounded Sequence
  - Definition: Bounded Subset of a Metric Space
  - Definition: Carrier Set
  - Definition: Cauchy Sequence
  - Definition: Comparison of Filters, Finer and Coarser Filters
  - Definition: Continuous Function
  - Definition: Continuous Functions in Metric Spaces
  - Definition: Convergent Sequences and Limits
  - Definition: Cotangent Bundle
  - Definition: Dense Sets, Nowhere Dense Sets
  - Definition: Derived, Dense-in-itself, and Perfect Sets
  - Definition: Diameter In Metric Spaces
  - Definition: Differentiable Manifold, Atlas
  - Definition: Differential Form of Degree k
  - Definition: Discrete and Indiscrete Topology
  - Definition: First and Second Category Sets
  - Definition: Hereditary and Weakly Hereditary Properties
  - Definition: Homeomorphism, Homeomorphic Spaces
  - Definition: Isolated, Adherent, Limit, `$\omega$`-Accumulation and Condensation Points
  - Definition: Isometry
  - Definition: Limit of a Function
  - Definition: Limits and Accumulation Points of Sequences
  - Definition: Manifold
  - Definition: Metric (Distance)
  - Definition: Metric Space
  - Definition: Modulus of Continuity of a Continuous Function
  - Definition: Neighborhood
  - Definition: Norm, Normed Vector Space
  - Definition: Open Ball, Neighborhood
  - Definition: Open Cover
  - Definition: Open Function, Closed Function
  - Definition: Open Sets in Metric Spaces
  - Definition: Open and Closed Functions
  - Definition: Open, Closed, Clopen
  - Definition: Ordering of Topologies
  - Definition: Pointwise and Uniform Convergence
  - Definition: Regular Open, Regular Closed
  - Definition: Section over a Base Space
  - Definition: Sequence
  - Definition: Simplex
  - Definition: Subbasis and Basis of Topology
  - Definition: Subsequence
  - Definition: Tangent Bundle
  - Definition: Topological Chart
  - Definition: Topological Product, Product Topology
  - Definition: Topological Space, Topology
  - Definition: Topological Subspaces and Subspace Topologies
  - Definition: Topological Sum, Disjoint Union
  - Definition: Topological, Continuous, Open, and Closed Invariants
  - Definition: Transition Map
  - Definition: Ultrafilter
  - Definition: Uniformly Continuous Functions (General Metric Spaces Case)
  - Definition: `\(C^n\)` Differentiable Function
  - Definition: `\(C^{n}\)`-Diffeomorphism
Theorems (90)
- Algebra (12)
  - Theorem: Classification of Cyclic Groups
  - Theorem: Classification of Finite Groups with the Order of a Prime Number
  - Theorem: Connection between Rings, Ideals, and Fields
  - Theorem: Construction of Fields from Integral Domains
  - Theorem: Construction of Groups from Commutative and Cancellative Semigroups
  - Theorem: Finite Basis Theorem
  - Theorem: Finite Integral Domains are Fields
  - Theorem: First Isomorphism Theorem for Groups
  - Theorem: Isomorphism of Rings
  - Theorem: Order of Cyclic Group (Fermat's Little Theorem)
  - Theorem: Order of Subgroup Divides Order of Finite Group
  - Theorem: Relationship Between the Solutions of Homogeneous and Inhomogeneous SLEs
- Analysis (28)
  - Theorem: Bernoulli's Inequality
  - Theorem: Completeness Principle for Complex Numbers
  - Theorem: Completeness Principle for Real Numbers
  - Theorem: Continuous Functions Mapping Compact Domains to Real Numbers Take Maximum and Minimum Values on these Domains
  - Theorem: Continuous Real Functions on Closed Intervals are Uniformly Continuous
  - Theorem: Darboux's Theorem
  - Theorem: De Moivre's Identity, Complex Powers
  - Theorem: Defining Properties of the Field of Real Numbers
  - Theorem: Every Bounded Monotonic Sequence Is Convergent
  - Theorem: Every Bounded Real Sequence has a Convergent Subsequence
  - Theorem: Fundamental Theorem of Calculus
  - Theorem: Heine-Borel Theorem
  - Theorem: Indefinite Integral, Antiderivative
  - Theorem: Inequality Between the Geometric and the Arithmetic Mean
  - Theorem: Inequality of Weighted Arithmetic Mean
  - Theorem: Inequality of the Arithmetic Mean
  - Theorem: Integration by Substitution
  - Theorem: Intermediate Root Value Theorem
  - Theorem: Intermediate Value Theorem
  - Theorem: Mean Value Theorem For Riemann Integrals
  - Theorem: Nested Closed Subset Theorem
  - Theorem: Partial Integration
  - Theorem: Reverse Triangle Inequalities
  - Theorem: Rolle's Theorem
  - Theorem: Squeezing Theorem for Functions
  - Theorem: Supremum Property, Infimum Property
  - Theorem: Taylor's Formula
  - Theorem: Triangle Inequality
- Combinatorics (6)
  - Theorem: Approximation of Factorials Using the Stirling Formula
  - Theorem: Binomial Theorem
  - Theorem: Fundamental Theorem of the Difference Calculus
  - Theorem: Inclusion-Exclusion Principle (Sylvester's Formula)
  - Theorem: Multinomial Theorem
  - Theorem: Taylor's Formula Using the Difference Operator
- Geometry (2)
  - Analytic Geometry (1)
    - Theorem: Existence and Uniqueness of a Straight Line Through Two Points
  - Elements Euclid (1)
    - Book 9 Number Theory Applications (1)
      - Theorem: Prop. 9.14: Fundamental Theorem of Arithmetic
- Graph Theory (13)
  - Theorem: Brooks' Theorem
  - Theorem: Characterization of Biconnected Planar Graphs
  - Theorem: Characterization of Bipartite Graphs
  - Theorem: Characterization of Eulerian Graphs
  - Theorem: Characterization of Planar Graphs
  - Theorem: Characterization of Planar Hamiltonian Graphs
  - Theorem: Characterization of Semi-Eulerian Graphs
  - Theorem: Euler Characteristic for Planar Graphs
  - Theorem: Five Color Theorem for Planar Graphs
  - Theorem: Four Color Theorem for Planar Graphs
  - Theorem: Four Color Theorem for Planar Graphs With a Dual Hamiltonian Graph
  - Theorem: Number of Labeled Spanning Trees
  - Theorem: Six Color Theorem for Planar Graphs
- Number Theory (12)
  - Theorem: Chinese Remainder Theorem
  - Theorem: Commutative Group of Multiplicative Functions
  - Theorem: Euler-Fermat Theorem
  - Theorem: Fermat's Last Theorem
  - Theorem: First Supplementary Law to the Quadratic Reciprocity Law
  - Theorem: Fundamental Theorem of Arithmetic
  - Theorem: Infinite Set of Prime Numbers
  - Theorem: Möbius Inversion Formula
  - Theorem: Number of Multiples of a Prime Number Less Than Factorial
  - Theorem: Properties of the Jacobi Symbol
  - Theorem: Quadratic Reciprocity Law
  - Theorem: Second Supplementary Law to the Quadratic Reciprocity Law
- Probability Theory And Statistics (3)
  - Theorem: Bayes' Theorem
  - Theorem: Law of Total Probability
  - Theorem: Theorem of Large Numbers for Relative Frequencies
- Set Theory (4)
  - Theorem: Distinction Between Finite and Infinite Sets Using Subsets
  - Theorem: Mostowski's Theorem
  - Theorem: Schröder-Bernstein Theorem
  - Theorem: Trichotomy of Ordinals
- Theoretical Computer Science (5)
  - Computability (2)
    - Theorem: Simulating LOOP Programs Using WHILE Programs
    - Theorem: Simulating WHILE Programs Using GOTO Programs (and vice versa)
  - Formal Languages (3)
    - Theorem: Deterministic Finite Automata Describe Regular Languages
    - Theorem: Reduction of NFA to DFA (Rabin-Scott Theorem)
    - Theorem: Reduction of `$\epsilon$`-NFA to NFA
- Theoretical Physics (3)
  - Classical Physics (3)
    - Theorem: First Law of Planetary Motion
    - Theorem: Second Law of Planetary Motion
    - Theorem: Third Law of Planetary Motion
- Topology (2)
  - Theorem: Continuous Functions on Compact Domains are Uniformly Continuous
  - Theorem: Theorem of Bolzano-Weierstrass
Lemmas (124)
- Algebra (22)
  - Lemma: A Criterion for Associates
  - Lemma: Any Positive Characteristic Is a Prime Number
  - Lemma: Continuants and Convergents
  - Lemma: Cyclic Groups are Abelian
  - Lemma: Divisibility of Principal Ideals
  - Lemma: Elementary Gaussian Operations Do Not Change the Solutions of an SLE
  - Lemma: Equivalency of Vectors in Vector Space If their Difference Forms a Subspace
  - Lemma: Factor Groups
  - Lemma: Factor Rings, Generalization of Congruence Classes
  - Lemma: Fiber of Maximal Ideals
  - Lemma: Fiber of Prime Ideals
  - Lemma: Fiber of Prime Ideals Under a Spectrum Function
  - Lemma: Fundamental Lemma of Homogeneous Systems of Linear Equations
  - Lemma: Greatest Common Divisor and Least Common Multiple of Ideals
  - Lemma: Group Homomorphisms and Normal Subgroups
  - Lemma: Kernel and Image of Group Homomorphism
  - Lemma: Kernel and Image of a Group Homomorphism are Subgroups
  - Lemma: One-to-one Correspondence of Ideals in the Factor Ring and a Commutative Ring
  - Lemma: Prime Ideals of Multiplicative Systems in Integral Domains
  - Lemma: Subgroups and Their Cosets are Equipotent
  - Lemma: Subgroups of Cyclic Groups
  - Lemma: Uniqueness Lemma of a Finite Basis
- Analysis (14)
  - Lemma: Abel's Lemma for Testing Convergence
  - Lemma: Addition and Scalar Multiplication of Riemann Upper and Lower Integrals
  - Lemma: Approximability of Continuous Real Functions On Closed Intervals By Step Functions
  - Lemma: Convergence Test for Telescoping Series
  - Lemma: Decreasing Sequence of Suprema of Extended Real Numbers
  - Lemma: Euler's Identity
  - Lemma: Functions Continuous at a Point and Non-Zero at this Point are Non-Zero in a Neighborhood of This Point
  - Lemma: Increasing Sequence of Infima of Extended Real Numbers
  - Lemma: Invertible Functions on Real Intervals
  - Lemma: Riemann Integral of a Product of Continuously Differentiable Functions with Sine
  - Lemma: Sum of Roots Of Unity in Complete Residue Systems
  - Lemma: Trapezoid Rule
  - Lemma: Unit Circle
  - Lemma: Upper Bound for the Product of General Powers
- Combinatorics (1)
  - Lemma: Stirling Numbers and Rising Factorial Powers
- Geometry (16)
  - Analytic Geometry (1)
    - Lemma: Equivalence of Different Descriptions of a Straight Line Using Two Vectors
  - Elements Euclid (15)
    - Book 10 Incommensurable Magnitudes (9)
    - Book 11 Elementary Stereometry (1)
      - Lemma: Lem. 11.23: Making a Square Area Equal to the Difference Of Areas of Two Other Incongruent Squares
    - Book 12 Proportional Stereometry (2)
      - Lemma: Lem. 12.02: Areas of Circles are as Squares on Diameters
      - Lemma: Lem. 12.04: Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms
    - Book 13 Platonic Solids (3)
- Graph Theory (11)
- Logic (26)
  - Lemma: A Criterion for Valid Logical Arguments
  - Lemma: A proposition cannot be both, true and false
  - Lemma: A proposition cannot be equivalent to its negation
  - Lemma: Affirming the Consequent of an Implication
  - Lemma: Boolean Algebra of Propositional Logic
  - Lemma: Boolean Function
  - Lemma: Construction of Conjunctive and Disjunctive Canonical Normal Forms
  - Lemma: De Morgan's Laws (Logic)
  - Lemma: Denying the Antecedent of an Implication
  - Lemma: Disjunctive Syllogism
  - Lemma: Distributivity of Conjunction and Disjunction
  - Lemma: Every Contraposition to a Proposition is a Tautology to this Proposition
  - Lemma: Every Proposition Implies Itself
  - Lemma: Hypothetical Syllogism
  - Lemma: Implication as a Disjunction
  - Lemma: It is true that something can be (either) true or false
  - Lemma: Mixing-up the Inclusive and Exclusive Disjunction
  - Lemma: Mixing-up the Sufficient and Necessary Conditions
  - Lemma: Modus Ponens
  - Lemma: Modus Tollens
  - Lemma: Negation of an Implication
  - Lemma: The Proving Principle By Contraposition, Contrapositive
  - Lemma: The Proving Principle by Complete Induction
  - Lemma: The Proving Principle by Contradiction
  - Lemma: The Proving Principle by Transfinite Induction
  - Lemma: Unique Valuation of Minterms and Maxterms
- Number Systems Arithmetics (8)
- Number Theory (11)
  - Lemma: Coprimality and Congruence Classes
  - Lemma: Division with Quotient and Remainder
  - Lemma: Gaussian Lemma (Number Theory)
  - Lemma: Generalized Euclidean Lemma
  - Lemma: Möbius and Floor Functions Combined
  - Lemma: Reciprocity Law for Floor Functions
  - Lemma: Sets of Integers Co-Prime to a given Integer are Divisor-Closed
  - Lemma: Sum of Möbius Function Over Divisors With Division
  - Lemma: Sums of Floors
  - Lemma: Upper Bound of Harmonic Series Times Möbius Function
  - Sieve Methods (1)
    - Lemma: Sieve for Twin Primes
- Set Theory (11)
  - Lemma: Any Set is Subset of Some Transitive Set - Its Transitive Hull
  - Lemma: Behavior of Functions with Set Operations
  - Lemma: Comparing the Elements of Strictly Ordered Sets
  - Lemma: Composition of Functions
  - Lemma: Composition of Relations (Sometimes) Preserves Their Left-Total Property
  - Lemma: Composition of Relations Preserves Their Right-Uniqueness Property
  - Lemma: Equivalence of Set Inclusion and Element Inclusion of Ordinals
  - Lemma: Finite Cardinal Numbers and Set Operations
  - Lemma: Properties of Ordinal Numbers
  - Lemma: Successor of Ordinal
  - Lemma: Zorn's Lemma
- Theoretical Computer Science (1)
  - Computability (1)
    - Lemma: LOOP-Computable Functions are Total
- Topology (3)
Propositions (1063)
- Algebra (32)
  - Proposition: A Field with an Absolute Value is a Metric Space
  - Proposition: Abelian Group of Matrices Under Addition
  - Proposition: Additive Subgroups of Integers
  - Proposition: Cancellation Law
  - Proposition: Characterization of Dependent Absolute Values
  - Proposition: Characterization of Non-Archimedean Absolute Values
  - Proposition: Criteria for Subgroups
  - Proposition: Criterions for Equality of Principal Ideals
  - Proposition: Finite Order of an Element Equals Order Of Generated Group
  - Proposition: Generalization of Cancellative Multiplication of Integers
  - Proposition: Group Homomorphisms with Cyclic Groups
  - Proposition: Group of Units
  - Proposition: In a Field, `$0$` Is Unequal `$1$`
  - Proposition: Open and Closed Subsets of a Zariski Topology
  - Proposition: Principal Ideal Generated by A Unit
  - Proposition: Principal Ideals being Maximal Ideals
  - Proposition: Principal Ideals being Prime Ideals
  - Proposition: Properties of Cosets
  - Proposition: Properties of a Complex Scalar Product
  - Proposition: Properties of a Group Homomorphism
  - Proposition: Quadratic Formula
  - Proposition: Quotient Space
  - Proposition: Simple Calculations Rules in a Group
  - Proposition: Simple Consequences from the Definition of a Vector Space
  - Proposition: Spectrum Function of Commutative Rings
  - Proposition: Square of a Non-Zero Element is Positive in Ordered Fields
  - Proposition: Subgroups of Finite Cyclic Groups
  - Proposition: Subset of Powers is a Submonoid
  - Proposition: Unique Solvability of `$a\ast x=b$` in Groups
  - Proposition: Uniqueness of Inverse Elements
  - Proposition: Uniqueness of the Neutral Element
  - Proposition: `$0$` Is Less Than `$1$` In Ordered Fields
- Analysis (222)
  - Proposition: A General Criterion for the Convergence of Infinite Complex Series
  - Proposition: A Necessary and a Sufficient Condition for Riemann Integrable Functions
  - Proposition: Abel's Test
  - Proposition: Additivity Theorem of Tangent
  - Proposition: Additivity Theorems of Cosine and Sine
  - Proposition: Antiderivatives are Uniquely Defined Up to a Constant
  - Proposition: Approximation of Functions by Taylor's Formula
  - Proposition: Arithmetic of Functions with Limits - Difference
  - Proposition: Arithmetic of Functions with Limits - Division
  - Proposition: Arithmetic of Functions with Limits - Product
  - Proposition: Arithmetic of Functions with Limits - Sums
  - Proposition: Basis Arithmetic Operations Involving Differentiable Functions, Product Rule, Quotient Rule
  - Proposition: Bounds for Partial Sums of Exponential Series
  - Proposition: Calculation Rules for General Powers
  - Proposition: Calculations with Uniformly Convergent Functions
  - Proposition: Cauchy Condensation Criterion
  - Proposition: Cauchy Criterion
  - Proposition: Cauchy Product of Absolutely Convergent Complex Series
  - Proposition: Cauchy Product of Absolutely Convergent Series
  - Proposition: Cauchy Product of Convergent Series Is Not Necessarily Convergent
  - Proposition: Cauchy-Schwarz Inequality for Integral p-norms
  - Proposition: Cauchy-Schwarz Test
  - Proposition: Cauchy–Schwarz Inequality
  - Proposition: Chain Rule
  - Proposition: Characterization of Monotonic Functions via Derivatives
  - Proposition: Closed Formula for the Maximum and Minimum of Two Numbers
  - Proposition: Closed Subsets of Compact Sets are Compact
  - Proposition: Closed n-Dimensional Cuboids Are Compact
  - Proposition: Compact Subset of Real Numbers Contains its Maximum and its Minimum
  - Proposition: Compact Subsets of Metric Spaces Are Bounded and Closed
  - Proposition: Comparison of Functional Equations For Linear, Logarithmic and Exponential Growth
  - Proposition: Complex Cauchy Sequences Vs. Real Cauchy Sequences
  - Proposition: Complex Conjugate of Complex Exponential Function
  - Proposition: Complex Convergent Sequences are Bounded
  - Proposition: Complex Exponential Function
  - Proposition: Composition of Continuous Functions at a Single Point
  - Proposition: Compositions of Continuous Functions on a Whole Domain
  - Proposition: Continuity of Complex Exponential Function
  - Proposition: Continuity of Cosine and Sine
  - Proposition: Continuity of Exponential Function
  - Proposition: Continuity of Exponential Function of General Base
  - Proposition: Continuous Real Functions on Closed Intervals Take Maximum and Minimum Values within these Intervals
  - Proposition: Continuous Real Functions on Closed Intervals are Riemann-Integrable
  - Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Infinity
  - Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Zero
  - Proposition: Convergence Behavior of the Sequence `\((b^n)\)`
  - Proposition: Convergence Behaviour of Absolutely Convergent Series
  - Proposition: Convergence of Series Implies Sequence of Terms Converges to Zero
  - Proposition: Convergent Complex Sequences Are Bounded
  - Proposition: Convergent Complex Sequences Are Cauchy Sequences
  - Proposition: Convergent Complex Sequences Vs. Convergent Real Sequences
  - Proposition: Convergent Real Sequences Are Cauchy Sequences
  - Proposition: Convergent Real Sequences are Bounded
  - Proposition: Convergent Sequence together with Limit is a Compact Subset of Metric Space
  - Proposition: Convergent Sequence without Limit Is Not a Compact Subset of Metric Space
  - Proposition: Convergent Sequences are Bounded
  - Proposition: Convex Functions on Open Intervals are Continuous
  - Proposition: Convexity and Concaveness Test
  - Proposition: Definition of the Metric Space `\(\mathbb R^n\)`, Euclidean Norm
  - Proposition: Derivate of Absolute Value Function Does Not Exist at `\(0\)`
  - Proposition: Derivative of Cosine
  - Proposition: Derivative of General Powers of Positive Numbers
  - Proposition: Derivative of Sine
  - Proposition: Derivative of Tangent
  - Proposition: Derivative of an Invertible Function on Real Invervals
  - Proposition: Derivative of the Exponential Function
  - Proposition: Derivative of the Inverse Sine
  - Proposition: Derivative of the Inverse Tangent
  - Proposition: Derivative of the Natural Logarithm
  - Proposition: Derivative of the Reciprocal Function
  - Proposition: Derivative of the n-th Power Function
  - Proposition: Derivatives of Even and Odd Functions
  - Proposition: Difference of Convergent Complex Sequences
  - Proposition: Difference of Convergent Real Sequences
  - Proposition: Difference of Convergent Real Series
  - Proposition: Difference of Squares of Hyperbolic Cosine and Hyperbolic Sine
  - Proposition: Differentiable Functions and Tangent-Linear Approximation
  - Proposition: Differential Equation of the Exponential Function
  - Proposition: Direct Comparison Test For Absolutely Convergent Complex Series
  - Proposition: Direct Comparison Test For Absolutely Convergent Series
  - Proposition: Direct Comparison Test For Divergent Series
  - Proposition: Dirichlet's Test
  - Proposition: Estimate for the Remainder Term of Complex Exponential Function
  - Proposition: Estimate for the Remainder Term of Exponential Function
  - Proposition: Estimates for the Remainder Terms of the Infinite Series of Cosine and Sine
  - Proposition: Euler's Formula
  - Proposition: Eveness (Oddness) of Polynomials
  - Proposition: Eveness of the Cosine of a Real Variable
  - Proposition: Exponential Function
  - Proposition: Exponential Function of General Base With Integer Exponents
  - Proposition: Exponential Function of General Base With Natural Exponents
  - Proposition: Fixed-Point Property of Continuous Functions on Closed Intervals
  - Proposition: Functional Equation of the Complex Exponential Function
  - Proposition: Functional Equation of the Exponential Function
  - Proposition: Functional Equation of the Exponential Function of General Base
  - Proposition: Functional Equation of the Exponential Function of General Base (Revised)
  - Proposition: Functional Equation of the Natural Logarithm
  - Proposition: Gamma Function
  - Proposition: Gamma Function Interpolates the Factorial
  - Proposition: General Powers of Positive Numbers
  - Proposition: Generalized Bernoulli's Inequality
  - Proposition: Generalized Product Rule
  - Proposition: Generalized Triangle Inequality
  - Proposition: How Convergence Preserves Upper and Lower Bounds For Sequence Members
  - Proposition: How Convergence Preserves the Order Relation of Sequence Members
  - Proposition: Hölder's Inequality
  - Proposition: Hölder's Inequality for Integral p-norms
  - Proposition: Identity Function is Continuous
  - Proposition: Image of a Compact Set Under a Continuous Function
  - Proposition: Inequality between Binomial Coefficients and Reciprocals of Factorials
  - Proposition: Inequality between Powers of `$2$` and Factorials
  - Proposition: Inequality between Square Numbers and Powers of `$2$`
  - Proposition: Infinite Geometric Series
  - Proposition: Infinite Series for Cosine and Sine
  - Proposition: Infinitesimal Exponential Growth is the Growth of the Identity Function
  - Proposition: Infinitesimal Growth of Sine is the Growth of the Identity Function
  - Proposition: Integral Test for Convergence
  - Proposition: Integral of Cosine
  - Proposition: Integral of General Powers
  - Proposition: Integral of Inverse Sine
  - Proposition: Integral of Sine
  - Proposition: Integral of the Exponential Function
  - Proposition: Integral of the Inverse Tangent
  - Proposition: Integral of the Natural Logarithm
  - Proposition: Integral of the Reciprocal Function
  - Proposition: Integrals on Adjacent Intervals
  - Proposition: Inverse Cosine of a Real Variable
  - Proposition: Inverse Hyperbolic Cosine
  - Proposition: Inverse Hyperbolic Sine
  - Proposition: Inverse Sine of a Real Variable
  - Proposition: Inverse Tangent and Complex Exponential Function
  - Proposition: Inverse Tangent of a Real Variable
  - Proposition: Legendre Polynomials and Legendre Differential Equations
  - Proposition: Leibniz Criterion for Alternating Series
  - Proposition: Limit Comparizon Test
  - Proposition: Limit Inferior is the Infimum of Accumulation Points of a Bounded Real Sequence
  - Proposition: Limit Superior is the Supremum of Accumulation Points of a Bounded Real Sequence
  - Proposition: Limit Test for Roots or Ratios
  - Proposition: Limit of 1/n
  - Proposition: Limit of Exponential Growth as Compared to Polynomial Growth
  - Proposition: Limit of Logarithmic Growth as Compared to Positive Power Growth
  - Proposition: Limit of Nested Real Intervals
  - Proposition: Limit of Nth Powers
  - Proposition: Limit of Nth Root of N
  - Proposition: Limit of Nth Root of a Positive Constant
  - Proposition: Limit of a Function is Unique If It Exists
  - Proposition: Limit of a Polynomial
  - Proposition: Limit of a Rational Function
  - Proposition: Limit of the Constant Function
  - Proposition: Limit of the Identity Function
  - Proposition: Limits of General Powers
  - Proposition: Limits of Logarithm in `$[0,+\infty]$`
  - Proposition: Limits of Polynomials at Infinity
  - Proposition: Linearity and Monotony of the Riemann Integral
  - Proposition: Linearity and Monotony of the Riemann Integral for Step Functions
  - Proposition: Logarithm to a General Base
  - Proposition: Minkowski's Inequality
  - Proposition: Minkowski's Inequality for Integral p-norms
  - Proposition: Monotonic Real Functions on Closed Intervals are Riemann-Integrable
  - Proposition: Monotony Criterion
  - Proposition: Natural Logarithm
  - Proposition: Not all Cauchy Sequences Converge in the set of Rational Numbers
  - Proposition: Not all Continuous Functions are also Uniformly Continuous
  - Proposition: Nth Powers
  - Proposition: Nth Roots of Positive Numbers
  - Proposition: Oddness of the Sine of a Real Variable
  - Proposition: Only the Uniform Convergence Preserves Continuity
  - Proposition: Open Intervals Contain Uncountably Many Irrational Numbers
  - Proposition: Open Real Intervals are Uncountable
  - Proposition: Positive and Negative Parts of a Riemann-Integrable Functions are Riemann-Integrable
  - Proposition: Preservation of Continuity with Arithmetic Operations on Continuous Functions
  - Proposition: Preservation of Continuity with Arithmetic Operations on Continuous Functions on a Whole Domain
  - Proposition: Preservation of Inequalities for Limits of Functions
  - Proposition: Product of Convegent Complex Sequences
  - Proposition: Product of Convegent Real Sequences
  - Proposition: Product of Riemann-integrable Functions is Riemann-integrable
  - Proposition: Product of a Complex Number and a Convergent Complex Sequence
  - Proposition: Product of a Convergent Real Sequence and a Real Sequence Tending to Infinity
  - Proposition: Product of a Real Number and a Convergent Real Sequence
  - Proposition: Product of a Real Number and a Convergent Real Series
  - Proposition: Pythagorean Identity
  - Proposition: Quotient of Convergent Complex Sequences
  - Proposition: Quotient of Convergent Real Sequences
  - Proposition: Raabe's Test
  - Proposition: Ratio Test
  - Proposition: Ratio Test For Absolutely Convergent Complex Series
  - Proposition: Rational Functions are Continuous
  - Proposition: Rational Numbers are Dense in Real Numbers
  - Proposition: Rational Powers of Positive Numbers
  - Proposition: Real Sequences Contain Monotonic Subsequences
  - Proposition: Rearrangement of Absolutely Convergent Series
  - Proposition: Rearrangement of Convergent Series
  - Proposition: Relationship between Limit, Limit Superior, and Limit Inferior of a Real Sequence
  - Proposition: Riemann Integral for Step Functions
  - Proposition: Riemann Sum Converging To the Riemann Integral
  - Proposition: Riemann Upper and Riemann Lower Integrals for Bounded Real Functions
  - Proposition: Root Test
  - Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function
  - Proposition: Square Roots
  - Proposition: Step Function on Closed Intervals are Riemann-Integrable
  - Proposition: Step Functions as a Subspace of all Functions on a Closed Real Interval
  - Proposition: Sufficient Condition for a Local Extremum
  - Proposition: Sum of Arguments of Hyperbolic Cosine
  - Proposition: Sum of Arguments of Hyperbolic Sine
  - Proposition: Sum of Convergent Complex Sequences
  - Proposition: Sum of Convergent Real Sequences
  - Proposition: Sum of Convergent Real Series
  - Proposition: Sum of a Convergent Real Sequence and a Real Sequence Tending to Infininty
  - Proposition: Supremum Norm and Uniform Convergence
  - Proposition: Taylor's Formula with Remainder Term of Lagrange
  - Proposition: The distance of complex numbers makes complex numbers a metric space.
  - Proposition: The distance of real numbers makes real numbers a metric space.
  - Proposition: Uniform Convergence Criterion of Cauchy
  - Proposition: Uniform Convergence Criterion of Weierstrass for Infinite Series
  - Proposition: Unique Representation of Real Numbers as `\(b\)`-adic Fractions
  - Proposition: Uniqueness Of the Limit of a Sequence
  - Proposition: Zero of Cosine
  - Proposition: Zero-Derivative as a Necessary Condition for a Local Extremum
  - Proposition: `\(\exp(0)=1\)`
  - Proposition: `\(\exp(0)=1\)` (Complex Case)
  - Proposition: `\(b\)`-Adic Fractions Are Real Cauchy Sequences
  - Proposition: n-th Roots of Unity
- Combinatorics (26)
  - Proposition: Antidifferences are Unique Up to a Periodic Constant
  - Proposition: Antidifferences of Some Functions
  - Proposition: Basic Calculations Involving Indefinite Sums
  - Proposition: Basic Calculations Involving the Difference Operator
  - Proposition: Closed Formula For Binomial Coefficients
  - Proposition: Comparison between the Stirling numbers of the First and Second Kind
  - Proposition: Difference Operator of Falling Factorial Powers
  - Proposition: Difference Operator of Powers
  - Proposition: Factorial
  - Proposition: Factorial Polynomials have a Unique Representation
  - Proposition: Factorial Polynomials vs. Polynomials
  - Proposition: Factorials and Stirling Numbers of the First Kind
  - Proposition: Fundamental Counting Principle
  - Proposition: Indicator Function and Set Operations
  - Proposition: Inversion Formulas For Stirling Numbers
  - Proposition: Multinomial Coefficient
  - Proposition: Nth Difference Operator
  - Proposition: Number of Ordered n-Tuples in a Set
  - Proposition: Number of Relations on a Finite Set
  - Proposition: Number of Strings With a Fixed Length Over an Alphabet with k Letters
  - Proposition: Number of Subsets of a Finite Set
  - Proposition: Recursive Formula for Binomial Coefficients
  - Proposition: Recursive Formula for the Stirling Numbers of the First Kind
  - Proposition: Recursive Formula for the Stirling Numbers of the Second Kind
  - Proposition: Recursively Defined Arithmetic Functions, Recursion
  - Proposition: Simple Binomial Identities
- Geometry (469)
  - Analytic Geometry (1)
    - Proposition: Presentation of a Straight Line in a Plane as a Linear Equation
  - Elements Euclid (464)
    - Book 1 Plane Geometry (48)
      - Proposition: 1.01: Constructing an Equilateral Triangle
      - Proposition: 1.02: Constructing a Segment Equal to an Arbitrary Segment
      - Proposition: 1.03: Cutting a Segment at a Given Size
      - Proposition: 1.04: "Side-Angle-Side" Theorem for the Congruence of Triangle
      - Proposition: 1.05: Isosceles Triangles I
      - Proposition: 1.06: Isosceles Triagles II
      - Proposition: 1.07: Uniqueness of Triangles
      - Proposition: 1.08: "Side-Side-Side" Theorem for the Congruence of Triangles
      - Proposition: 1.09: Bisecting an Angle
      - Proposition: 1.10: Bisecting a Segment
      - Proposition: 1.11: Constructing a Perpendicular Segment to a Straight Line From a Given Point On the Straight Line
      - Proposition: 1.12: Constructing a Perpendicular Segment to a Straight Line From a Given Point Not On the Straight Line
      - Proposition: 1.13: Angles at Intersections of Straight Lines
      - Proposition: 1.14: Combining Rays to Straight Lines
      - Proposition: 1.15: Opposite Angles on Intersecting Straight Lines
      - Proposition: 1.16: The Exterior Angle Is Greater Than Either of the Non-Adjacent Interior Angles
      - Proposition: 1.17: The Sum of Two Angles of a Triangle
      - Proposition: 1.18: Angles and Sides in a Triangle I
      - Proposition: 1.19: Angles and Sides in a Triangle II
      - Proposition: 1.20: The Sum of the Lengths of Any Pair of Sides of a Triangle (Triangle Inequality)
      - Proposition: 1.21: Triangles within Triangles
      - Proposition: 1.22: Construction of Triangles From Arbitrary Segments
      - Proposition: 1.23: Constructing an Angle Equal to an Arbitrary Rectilinear Angle
      - Proposition: 1.24: Angles and Sides in a Triangle III
      - Proposition: 1.25: Angles and Sides in a Triangle IV
      - Proposition: 1.26: "Angle-Side-Angle" and "Angle-Angle-Side" Theorems for the Congruence of Triangles
      - Proposition: 1.27: Parallel Lines I
      - Proposition: 1.28: Parallel Lines II
      - Proposition: 1.29: Parallel Lines III
      - Proposition: 1.30: Transitivity of Parallel Lines
      - Proposition: 1.31: Constructing a Parallel Line from a Line and a Point
      - Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle
      - Proposition: 1.33: Parallel Equal Segments Determine a Parallelogram
      - Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms
      - Proposition: 1.35: Parallelograms On the Same Base and On the Same Parallels
      - Proposition: 1.36: Parallelograms on Equal Bases and on the Same Parallels
      - Proposition: 1.37: Triangles of Equal Area I
      - Proposition: 1.38: Triangles of Equal Area II
      - Proposition: 1.39: Triangles of Equal Area III
      - Proposition: 1.40: Triangles of Equal Area IV
      - Proposition: 1.41: Parallelograms and Triagles
      - Proposition: 1.42: Construction of Parallelograms I
      - Proposition: 1.43: Complementary Segments of Parallelograms
      - Proposition: 1.44: Construction of Parallelograms II
      - Proposition: 1.45: Construction of Parallelograms III
      - Proposition: 1.46: Construction of a Square on a Given Segment
      - Proposition: 1.47: Pythagorean Theorem
      - Proposition: 1.48: The Converse of the Pythagorean Theorem
    - Book 2 Geometric Algebra (14)
      - Proposition: 2.01: Summing Areas or Rectangles
      - Proposition: 2.02: Square is Sum of Two Rectangles
      - Proposition: 2.03: Rectangle is Sum of Square and Rectangle
      - Proposition: 2.04: Square of Sum
      - Proposition: 2.05: Rectangle is Difference of Two Squares
      - Proposition: 2.06: Square of Sum with One Halved Summand
      - Proposition: 2.07: Sum of Squares
      - Proposition: 2.08: Square of Sum with One Doubled Summand
      - Proposition: 2.09: Sum of Squares of Sum and Difference
      - Proposition: 2.10: Sum of Squares (Half)
      - Proposition: 2.11: Constructing the Golden Ratio of a Segment
      - Proposition: 2.12: Law of Cosines (for Obtuse Angles)
      - Proposition: 2.13: Law of Cosines (for Acute Angles)
      - Proposition: 2.14: Constructing a Square from a Rectilinear Figure
    - Book 3 Circles (37)
      - Proposition: 3.01: Finding the Center of a given Circle
      - Proposition: 3.02: Chord Lies Inside its Circle
      - Proposition: 3.03: Conditions for Diameter to be a Perpendicular Bisector
      - Proposition: 3.04: Chords do not Bisect Each Other
      - Proposition: 3.05: Intersecting Circles have Different Centers
      - Proposition: 3.06: Touching Circles have Different Centers
      - Proposition: 3.07: Relative Lengths of Lines Inside Circle
      - Proposition: 3.08: Relative Lengths of Lines Outside Circle
      - Proposition: 3.09: Condition for Point to be Center of Circle
      - Proposition: 3.10: Two Circles have at most Two Points of Intersection
      - Proposition: 3.11: Line Joining Centers of Two Circles Touching Internally
      - Proposition: 3.12: Line Joining Centers of Two Circles Touching Externally
      - Proposition: 3.13: Circles Touch at One Point at Most
      - Proposition: 3.14: Equal Chords in Circle
      - Proposition: 3.15: Relative Lengths of Chords of Circles
      - Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle
      - Proposition: 3.17: Construction of Tangent from Point to Circle
      - Proposition: 3.18: Radius at Right Angle to Tangent
      - Proposition: 3.19: Right Angle to Tangent of Circle Goes Through Center
      - Proposition: 3.20: Inscribed Angle Theorem
      - Proposition: 3.21: Angles in Same Segment of Circle are Equal
      - Proposition: 3.22: Opposite Angles of Cyclic Quadrilateral
      - Proposition: 3.23: Segment on Given Base Unique
      - Proposition: 3.24: Similar Segments on Equal Bases are Equal
      - Proposition: 3.25: Construction of Circle from Segment
      - Proposition: 3.26: Equal Angles and Arcs in Equal Circles
      - Proposition: 3.27: Angles on Equal Arcs are Equal
      - Proposition: 3.28: Straight Lines Cut Off Equal Arcs in Equal Circles
      - Proposition: 3.29: Equal Arcs of Circles Subtended by Equal Straight Lines
      - Proposition: 3.30: Bisection of Arc
      - Proposition: 3.31: Relative Sizes of Angles in Segments
      - Proposition: 3.32: Angles made by Chord with Tangent
      - Proposition: 3.33: Construction of Segment on Given Line Admitting Given Angle
      - Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle
      - Proposition: 3.35: Intersecting Chord Theorem
      - Proposition: 3.36: Tangent Secant Theorem
      - Proposition: 3.37: Converse of Tangent Secant Theorem
    - Book 4 Inscription And Circumscription (16)
      - Proposition: 4.01: Fitting Chord Into Circle
      - Proposition: 4.02: Inscribing in Circle Triangle Equiangular with Given Angles
      - Proposition: 4.03: Circumscribing about Circle Triangle Equiangular with Given Angles
      - Proposition: 4.04: Inscribing Circle in Triangle
      - Proposition: 4.05: Circumscribing Circle about Triangle
      - Proposition: 4.06: Inscribing Square in Circle
      - Proposition: 4.07: Circumscribing Square about Circle
      - Proposition: 4.08: Inscribing Circle in Square
      - Proposition: 4.09: Circumscribing Circle about Square
      - Proposition: 4.10: Construction of Isosceles Triangle whose Base Angle is Twice Apex
      - Proposition: 4.11: Inscribing Regular Pentagon in Circle
      - Proposition: 4.12: Circumscribing Regular Pentagon about Circle
      - Proposition: 4.13: Inscribing Circle in Regular Pentagon
      - Proposition: 4.14: Circumscribing Circle about Regular Pentagon
      - Proposition: 4.15: Side of Hexagon Inscribed in a Circle Equals the Radius of that Circle
      - Proposition: 4.16: Inscribing Regular Pentakaidecagon in Circle
    - Book 5 Proportion (25)
      - Proposition: 5.01: Multiplication of Numbers is Left Distributive over Addition
      - Proposition: 5.02: Multiplication of Numbers is Right Distributive over Addition
      - Proposition: 5.03: Multiplication of Numbers is Associative
      - Proposition: 5.04: Multiples of Terms in Equal Ratios
      - Proposition: 5.05: Multiplication of Real Numbers is Left Distributive over Subtraction
      - Proposition: 5.06: Multiplication of Real Numbers is Right Distributive over Subtraction
      - Proposition: 5.07: Ratios of Equal Magnitudes
      - Proposition: 5.08: Relative Sizes of Ratios on Unequal Magnitudes
      - Proposition: 5.09: Magnitudes with Same Ratios are Equal
      - Proposition: 5.10: Relative Sizes of Magnitudes on Unequal Ratios
      - Proposition: 5.11: Equality of Ratios is Transitive
      - Proposition: 5.12: Sum of Components of Equal Ratios
      - Proposition: 5.13: Relative Sizes of Proportional Magnitudes
      - Proposition: 5.14: Relative Sizes of Components of Ratios
      - Proposition: 5.15: Ratio Equals its Multiples
      - Proposition: 5.16: Proportional Magnitudes are Proportional Alternately
      - Proposition: 5.17: Magnitudes Proportional Compounded are Proportional Separated
      - Proposition: 5.18: Magnitudes Proportional Separated are Proportional Compounded
      - Proposition: 5.19: Proportional Magnitudes have Proportional Remainders
      - Proposition: 5.20: Relative Sizes of Successive Ratios
      - Proposition: 5.21: Relative Sizes of Elements in Perturbed Proportion
      - Proposition: 5.22: Equality of Ratios Ex Aequali
      - Proposition: 5.23: Equality of Ratios in Perturbed Proportion
      - Proposition: 5.24: Sum of Antecedents of Proportion
      - Proposition: 5.25: Sum of Antecedent and Consequent of Proportion
    - Book 6 Similar Figures (33)
      - Proposition: 6.01: Areas of Triangles and Parallelograms Proportional to Base
      - Proposition: 6.02: Parallel Line in Triangle Cuts Sides Proportionally
      - Proposition: 6.03: Angle Bisector Theorem
      - Proposition: 6.04: Equiangular Triangles are Similar
      - Proposition: 6.05: Triangles with Proportional Sides are Similar
      - Proposition: 6.06: Triangles with One Equal Angle and Two Sides Proportional are Similar
      - Proposition: 6.07: Triangles with One Equal Angle and Two Other Sides Proportional are Similar
      - Proposition: 6.08: Perpendicular in Right-Angled Triangle makes two Similar Triangles
      - Proposition: 6.09: Construction of Part of Line
      - Proposition: 6.10: Construction of Similarly Cut Straight Line
      - Proposition: 6.11: Construction of Segment in Squared Ratio
      - Proposition: 6.12: Construction of Fourth Proportional Straight Line
      - Proposition: 6.13: Construction of Mean Proportional
      - Proposition: 6.14: Characterization of Congruent Parallelograms
      - Proposition: 6.15: Characterization of Congruent Triangles
      - Proposition: 6.16: Rectangles Contained by Proportional Straight Lines
      - Proposition: 6.17: Rectangles Contained by Three Proportional Straight Lines
      - Proposition: 6.18: Construction of Similar Polygon
      - Proposition: 6.19: Ratio of Areas of Similar Triangles
      - Proposition: 6.20: Similar Polygons are Composed of Similar Triangles
      - Proposition: 6.21: Similarity of Polygons is Transitive
      - Proposition: 6.22: Similar Figures on Proportional Straight Lines
      - Proposition: 6.23: Ratio of Areas of Equiangular Parallelograms
      - Proposition: 6.24: Parallelograms About Diameter are Similar
      - Proposition: 6.25: Construction of Figure Similar to One and Equal to Another
      - Proposition: 6.26: Parallelogram Similar and in Same Angle has Same Diameter
      - Proposition: 6.27: Similar Parallelogram on Half a Straight Line
      - Proposition: 6.28: Construction of Parallelogram Equal to Given Figure Less a Parallelogram
      - Proposition: 6.29: Construction of Parallelogram Equal to Given Figure Exceeding a Parallelogram
      - Proposition: 6.30: Construction of the Inverse Golden Section
      - Proposition: 6.31: Similar Figures on Sides of Right-Angled Triangle
      - Proposition: 6.32: Triangles with Two Sides Parallel and Equal
      - Proposition: 6.33: Angles in Circles have Same Ratio as Arcs
    - Book 7 Elementary Number Theory (39)
      - Proposition: 7.01: Sufficient Condition for Coprimality
      - Proposition: 7.02: Greatest Common Divisor of Two Numbers - Euclidean Algorithm
      - Proposition: 7.03: Greatest Common Divisor of Three Numbers
      - Proposition: 7.04: Smaller Numbers are Dividing or not Dividing Larger Numbers
      - Proposition: 7.05: Divisors Obey Distributive Law (Sum)
      - Proposition: 7.06: Division with Quotient and Remainder Obeys Distributive Law (Sum)
      - Proposition: 7.07: Divisors Obey Distributive Law (Difference)
      - Proposition: 7.08: Division with Quotient and Remainder Obeys Distributivity Law (Difference)
      - Proposition: 7.09: Alternate Ratios of Equal Fractions
      - Proposition: 7.10: Multiples of Alternate Ratios of Equal Fractions
      - Proposition: 7.11: Proportional Numbers have Proportional Differences
      - Proposition: 7.12: Ratios of Numbers is Distributive over Addition
      - Proposition: 7.13: Proportional Numbers are Proportional Alternately
      - Proposition: 7.14: Proportion of Numbers is Transitive
      - Proposition: 7.15: Alternate Ratios of Multiples
      - Proposition: 7.16: Natural Number Multiplication is Commutative
      - Proposition: 7.17: Multiples of Ratios of Numbers
      - Proposition: 7.18: Ratios of Multiples of Numbers
      - Proposition: 7.19: Relation of Ratios to Products
      - Proposition: 7.20: Ratios of Fractions in Lowest Terms
      - Proposition: 7.21: Co-prime Numbers form Fraction in Lowest Terms
      - Proposition: 7.22: Numbers forming Fraction in Lowest Terms are Co-prime
      - Proposition: 7.23: Divisor of One of Co-prime Numbers is Co-prime to Other
      - Proposition: 7.24: Integer Co-prime to all Factors is Co-prime to Whole
      - Proposition: 7.25: Square of Co-prime Number is Co-prime
      - Proposition: 7.26: Product of Co-prime Pairs is Co-prime
      - Proposition: 7.27: Powers of Co-prime Numbers are Co-prime
      - Proposition: 7.28: Numbers are Co-prime iff Sum is Co-prime to Both
      - Proposition: 7.29: Prime not Divisor implies Co-prime
      - Proposition: 7.30: Euclidean Lemma
      - Proposition: 7.31: Existence of Prime Divisors
      - Proposition: 7.32: Natural Number is Prime or has Prime Factor
      - Proposition: 7.33: Least Ratio of Numbers
      - Proposition: 7.34: Existence of Least Common Multiple
      - Proposition: 7.35: Least Common Multiple Divides Common Multiple
      - Proposition: 7.36: Least Common Multiple of Three Numbers
      - Proposition: 7.37: Integer Divided by Divisor is Integer
      - Proposition: 7.38: Divisor is Reciprocal of Divisor of Integer
      - Proposition: 7.39: Least Number with Three Given Fractions
    - Book 8 Continued Proportion (27)
      - Proposition: 8.01: Geometric Progression with Co-prime Extremes is in Lowest Terms
      - Proposition: 8.02: Construction of Geometric Progression in Lowest Terms
      - Proposition: 8.03: Geometric Progression in Lowest Terms has Co-prime Extremes
      - Proposition: 8.04: Construction of Sequence of Numbers with Given Ratios
      - Proposition: 8.05: Ratio of Products of Sides of Plane Numbers
      - Proposition: 8.06: First Element of Geometric Progression not dividing Second
      - Proposition: 8.07: First Element of Geometric Progression that divides Last also divides Second
      - Proposition: 8.08: Geometric Progressions in Proportion have Same Number of Elements
      - Proposition: Prop. 8.09: Elements of Geometric Progression between Co-prime Numbers
      - Proposition: Prop. 8.10: Product of Geometric Progressions from One
      - Proposition: Prop. 8.11: Between two Squares exists one Mean Proportional
      - Proposition: Prop. 8.12: Between two Cubes exist two Mean Proportionals
      - Proposition: Prop. 8.13: Powers of Elements of Geometric Progression are in Geometric Progression
      - Proposition: Prop. 8.14: Number divides Number iff Square divides Square
      - Proposition: Prop. 8.15: Number divides Number iff Cube divides Cube
      - Proposition: Prop. 8.16: Number does not divide Number iff Square does not divide Square
      - Proposition: Prop. 8.17: Number does not divide Number iff Cube does not divide Cube
      - Proposition: Prop. 8.18: Between two Similar Plane Numbers exists one Mean Proportional
      - Proposition: Prop. 8.19: Between two Similar Solid Numbers exist two Mean Proportionals
      - Proposition: Prop. 8.20: Numbers between which exists one Mean Proportional are Similar Plane
      - Proposition: Prop. 8.21: Numbers between which exist two Mean Proportionals are Similar Solid
      - Proposition: Prop. 8.22: If First of Three Numbers in Geometric Progression is Square then Third is Square
      - Proposition: Prop. 8.23: If First of Four Numbers in Geometric Progression is Cube then Fourth is Cube
      - Proposition: Prop. 8.24: If Ratio of Square to Number is as between Two Squares then Number is Square
      - Proposition: Prop. 8.25: If Ratio of Cube to Number is as between Two Cubes then Number is Cube
      - Proposition: Prop. 8.26: Similar Plane Numbers have Same Ratio as between Two Squares
      - Proposition: Prop. 8.27: Similar Solid Numbers have Same Ratio as between Two Cubes
    - Book 9 Number Theory Applications (35)
      - Proposition: 9.35: Sum of Geometric Progression
      - Proposition: 9.36: Theorem of Even Perfect Numbers (First Part)
      - Proposition: Prop. 9.01: Product of Similar Plane Numbers is Square
      - Proposition: Prop. 9.02: Numbers whose Product is Square are Similar Plane Numbers
      - Proposition: Prop. 9.03: Square of Cube Number is Cube
      - Proposition: Prop. 9.04: Cube Number multiplied by Cube Number is Cube
      - Proposition: Prop. 9.05: Number multiplied by Cube Number making Cube is itself Cube
      - Proposition: Prop. 9.06: Number Squared making Cube is itself Cube
      - Proposition: Prop. 9.07: Product of Composite Number with Number is Solid Number
      - Proposition: Prop. 9.08: Elements of Geometric Progression from One which are Powers of Number
      - Proposition: Prop. 9.09: Elements of Geometric Progression from One where First Element is Power of Number
      - Proposition: Prop. 9.10: Elements of Geometric Progression from One where First Element is not Power of Number
      - Proposition: Prop. 9.11: Elements of Geometric Progression from One which Divide Later Elements
      - Proposition: Prop. 9.12: Elements of Geometric Progression from One Divisible by Prime
      - Proposition: Prop. 9.13: Divisibility of Elements of Geometric Progression from One where First Element is Prime
      - Proposition: Prop. 9.15: Sum of Pair of Elements of Geometric Progression with Three Elements in Lowest Terms is Co-prime to other Element
      - Proposition: Prop. 9.16: Two Co-prime Integers have no Third Integer Proportional
      - Proposition: Prop. 9.17: Last Element of Geometric Progression with Co-prime Extremes has no Integer Proportional as First to Second
      - Proposition: Prop. 9.18: Condition for Existence of Third Number Proportional to Two Numbers
      - Proposition: Prop. 9.19: Condition for Existence of Fourth Number Proportional to Three Numbers
      - Proposition: Prop. 9.20: Infinite Number of Primes
      - Proposition: Prop. 9.21: Sum of Even Numbers is Even
      - Proposition: Prop. 9.22: Sum of Even Number of Odd Numbers is Even
      - Proposition: Prop. 9.23: Sum of Odd Number of Odd Numbers is Odd
      - Proposition: Prop. 9.24: Even Number minus Even Number is Even
      - Proposition: Prop. 9.25: Even Number minus Odd Number is Odd
      - Proposition: Prop. 9.26: Odd Number minus Odd Number is Even
      - Proposition: Prop. 9.27: Odd Number minus Even Number is Odd
      - Proposition: Prop. 9.28: Odd Number multiplied by Even Number is Even
      - Proposition: Prop. 9.29: Odd Number multiplied by Odd Number is Odd
      - Proposition: Prop. 9.30: Odd Divisor of Even Number Also Divides Its Half
      - Proposition: Prop. 9.31: Odd Number Co-prime to Number is also Co-prime to its Double
      - Proposition: Prop. 9.32: Power of Two is Even-Times Even Only
      - Proposition: Prop. 9.33: Number whose Half is Odd is Even-Times Odd
      - Proposition: Prop. 9.34: Number neither whose Half is Odd nor Power of Two is both Even-Times Even and Even-Times Odd
    - Book 10 Incommensurable Magnitudes (115)
      - Proposition: Prop. 10.001: Existence of Fraction of Number Smaller than Given Number
      - Proposition: Prop. 10.002: Incommensurable Magnitudes do not Terminate in Euclidean Algorithm
      - Proposition: Prop. 10.003: Greatest Common Measure of Commensurable Magnitudes
      - Proposition: Prop. 10.004: Greatest Common Measure of Three Commensurable Magnitudes
      - Proposition: Prop. 10.005: Ratio of Commensurable Magnitudes
      - Proposition: Prop. 10.006: Magnitudes with Rational Ratio are Commensurable
      - Proposition: Prop. 10.007: Incommensurable Magnitudes Have Irrational Ratio
      - Proposition: Prop. 10.008: Magnitudes with Irrational Ratio are Incommensurable
      - Proposition: Prop. 10.009: Commensurability of Squares
      - Proposition: Prop. 10.010: Construction of Incommensurable Lines
      - Proposition: Prop. 10.011: Commensurability of Elements of Proportional Magnitudes
      - Proposition: Prop. 10.012: Commensurability is Transitive Relation
      - Proposition: Prop. 10.013: Commensurable Magnitudes are Incommensurable with Same Magnitude
      - Proposition: Prop. 10.014: Commensurability of Squares on Proportional Straight Lines
      - Proposition: Prop. 10.015: Commensurability of Sum of Commensurable Magnitudes
      - Proposition: Prop. 10.016: Incommensurability of Sum of Incommensurable Magnitudes
      - Proposition: Prop. 10.017: Condition for Commensurability of Roots of Quadratic Equation
      - Proposition: Prop. 10.018: Condition for Incommensurability of Roots of Quadratic Equation
      - Proposition: Prop. 10.019: Product of Rational Numbers is Rational
      - Proposition: Prop. 10.020: Quotient of Rational Numbers is Rational
      - Proposition: Prop. 10.021: Medial is Irrational
      - Proposition: Prop. 10.022: Square on Medial Straight Line
      - Proposition: Prop. 10.023: Segment Commensurable with Medial Segment is Medial
      - Proposition: Prop. 10.024: Rectangle Contained by Medial Straight Lines Commensurable in Length is Medial
      - Proposition: Prop. 10.025: Rationality of Rectangle Contained by Medial Straight Lines Commensurable in Square
      - Proposition: Prop. 10.026: Medial Area not greater than Medial Area by Rational Area
      - Proposition: Prop. 10.027: Construction of Components of First Bimedial
      - Proposition: Prop. 10.028: Construction of Components of Second Bimedial
      - Proposition: Prop. 10.029: Construction of Rational Straight Lines Commensurable in Square When Square Differences Commensurable
      - Proposition: Prop. 10.030: Construction of Rational Straight Lines Commensurable in Square Only When Square Differences Incommensurable
      - Proposition: Prop. 10.031: Constructing Medial Commensurable in Square I
      - Proposition: Prop. 10.032: Constructing Medial Commensurable in Square II
      - Proposition: Prop. 10.033: Construction of Components of Major
      - Proposition: Prop. 10.034: Construction of Components of Side of Rational plus Medial Area
      - Proposition: Prop. 10.035: Construction of Components of Side of Sum of Medial Areas
      - Proposition: Prop. 10.036: Binomial is Irrational
      - Proposition: Prop. 10.037: First Bimedial is Irrational
      - Proposition: Prop. 10.038: Second Bimedial is Irrational
      - Proposition: Prop. 10.039: Major is Irrational
      - Proposition: Prop. 10.040: Side of Rational plus Medial Area is Irrational
      - Proposition: Prop. 10.041: Side of Sum of Medial Areas is Irrational
      - Proposition: Prop. 10.042: Binomial Straight Line is Divisible into Terms Uniquely
      - Proposition: Prop. 10.043: First Bimedial Straight Line is Divisible Uniquely
      - Proposition: Prop. 10.044: Second Bimedial Straight Line is Divisible Uniquely
      - Proposition: Prop. 10.045: Major Straight Line is Divisible Uniquely
      - Proposition: Prop. 10.046: Side of Rational Plus Medial Area is Divisible Uniquely
      - Proposition: Prop. 10.047: Side of Sum of Two Medial Areas is Divisible Uniquely
      - Proposition: Prop. 10.048: Construction of First Binomial Straight Line
      - Proposition: Prop. 10.049: Construction of Second Binomial Straight Line
      - Proposition: Prop. 10.050: Construction of Third Binomial Straight Line
      - Proposition: Prop. 10.051: Construction of Fourth Binomial Straight Line
      - Proposition: Prop. 10.052: Construction of Fifth Binomial Straight Line
      - Proposition: Prop. 10.053: Construction of Sixth Binomial Straight Line
      - Proposition: Prop. 10.054: Root of Area contained by Rational Straight Line and First Binomial
      - Proposition: Prop. 10.055: Root of Area contained by Rational Straight Line and Second Binomial
      - Proposition: Prop. 10.056: Root of Area contained by Rational Straight Line and Third Binomial
      - Proposition: Prop. 10.057: Root of Area contained by Rational Straight Line and Fourth Binomial
      - Proposition: Prop. 10.058: Root of Area contained by Rational Straight Line and Fifth Binomial
      - Proposition: Prop. 10.059: Root of Area contained by Rational Straight Line and Sixth Binomial
      - Proposition: Prop. 10.060: Square on Binomial Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.061: Square on First Bimedial Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.062: Square on Second Bimedial Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.063: Square on Major Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.064: Square on Side of Rational plus Medial Area applied to Rational Straight Line
      - Proposition: Prop. 10.065: Square on Side of Sum of two Medial Area applied to Rational Straight Line
      - Proposition: Prop. 10.066: Straight Line Commensurable with Binomial Straight Line is Binomial and of Same Order
      - Proposition: Prop. 10.067: Straight Line Commensurable with Bimedial Straight Line is Bimedial and of Same Order
      - Proposition: Prop. 10.068: Straight Line Commensurable with Major Straight Line is Major
      - Proposition: Prop. 10.069: Straight Line Commensurable with Side of Rational plus Medial Area
      - Proposition: Prop. 10.070: Straight Line Commensurable with Side of Sum of two Medial Areas
      - Proposition: Prop. 10.071: Sum of Rational Area and Medial Area gives rise to four Irrational Straight Lines
      - Proposition: Prop. 10.072: Sum of two Incommensurable Medial Areas give rise to two Irrational Straight Lines
      - Proposition: Prop. 10.073: Apotome is Irrational
      - Proposition: Prop. 10.074: First Apotome of Medial is Irrational
      - Proposition: Prop. 10.075: Second Apotome of Medial is Irrational
      - Proposition: Prop. 10.076: Minor is Irrational
      - Proposition: Prop. 10.077: That which produces Medial Whole with Rational Area is Irrational
      - Proposition: Prop. 10.078: That which produces Medial Whole with Medial Area is Irrational
      - Proposition: Prop. 10.079: Construction of Apotome is Unique
      - Proposition: Prop. 10.080: Construction of First Apotome of Medial is Unique
      - Proposition: Prop. 10.081: Construction of Second Apotome of Medial is Unique
      - Proposition: Prop. 10.082: Construction of Minor is Unique
      - Proposition: Prop. 10.083: Construction of that which produces Medial Whole with Rational Area is Unique
      - Proposition: Prop. 10.084: Construction of that which produces Medial Whole with Medial Area is Unique
      - Proposition: Prop. 10.085: Construction of First Apotome
      - Proposition: Prop. 10.086: Construction of Second Apotome
      - Proposition: Prop. 10.087: Construction of Third Apotome
      - Proposition: Prop. 10.088: Construction of Fourth Apotome
      - Proposition: Prop. 10.089: Construction of Fifth Apotome
      - Proposition: Prop. 10.090: Construction of Sixth Apotome
      - Proposition: Prop. 10.091: Side of Area Contained by Rational Straight Line and First Apotome
      - Proposition: Prop. 10.092: Side of Area Contained by Rational Straight Line and Second Apotome
      - Proposition: Prop. 10.093: Side of Area Contained by Rational Straight Line and Third Apotome
      - Proposition: Prop. 10.094: Side of Area Contained by Rational Straight Line and Fourth Apotome
      - Proposition: Prop. 10.095: Side of Area Contained by Rational Straight Line and Fifth Apotome
      - Proposition: Prop. 10.096: Side of Area Contained by Rational Straight Line and Sixth Apotome
      - Proposition: Prop. 10.097: Square on Apotome applied to Rational Straight Line
      - Proposition: Prop. 10.098: Square on First Apotome of Medial Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.099: Square on Second Apotome of Medial Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.100: Square on Minor Straight Line applied to Rational Straight Line
      - Proposition: Prop. 10.101: Square on Straight Line which produces Medial Whole with Rational Area applied to Rational Straight Line
      - Proposition: Prop. 10.102: Square on Straight Line which produces Medial Whole with Medial Area applied to Rational Straight Line
      - Proposition: Prop. 10.103: Straight Line Commensurable with Apotome
      - Proposition: Prop. 10.104: Straight Line Commensurable with Apotome of Medial Straight Line
      - Proposition: Prop. 10.105: Straight Line Commensurable with Minor Straight Line
      - Proposition: Prop. 10.106: Straight Line Commensurable with that which produces Medial Whole with Rational Area
      - Proposition: Prop. 10.107: Straight Line Commensurable With That Which Produces Medial Whole With Medial Area
      - Proposition: Prop. 10.108: Side of Remaining Area from Rational Area from which Medial Area Subtracted
      - Proposition: Prop. 10.109: Two Irrational Straight Lines arising from Medial Area from which Rational Area Subtracted
      - Proposition: Prop. 10.110: Two Irrational Straight Lines arising from Medial Area from which Medial Area Subtracted
      - Proposition: Prop. 10.111: Apotome not same with Binomial Straight Line
      - Proposition: Prop. 10.112: Square on Rational Straight Line applied to Binomial Straight Line
      - Proposition: Prop. 10.113: Square on Rational Straight Line applied to Apotome
      - Proposition: Prop. 10.114: Area contained by Apotome and Binomial Straight Line Commensurable with Terms of Apotome and in same Ratio
      - Proposition: Prop. 10.115: From Medial Straight Line arises Infinite Number of Irrational Straight Lines
    - Book 11 Elementary Stereometry (39)
    - Book 12 Proportional Stereometry (18)
      - Proposition: Prop. 12.01: Areas of Similar Polygons Inscribed in Circles are as Squares on Diameters
      - Proposition: Prop. 12.02: Areas of Circles are as Squares on Diameters
      - Proposition: Prop. 12.03: Tetrahedron divided into Two Similar Tetrahedra and Two Equal Prisms
      - Proposition: Prop. 12.04: Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms
      - Proposition: Prop. 12.05: Sizes of Tetrahedra of Same Height are as Bases
      - Proposition: Prop. 12.06: Sizes of Pyramids of Same Height with Polygonal Bases are as Bases
      - Proposition: Prop. 12.07: Prism on Triangular Base divided into Three Equal Tetrahedra
      - Proposition: Prop. 12.08: Volumes of Similar Tetrahedra are in Cubed Ratio of Corresponding Sides
      - Proposition: Prop. 12.09: Tetrahedra are Equal iff Bases are Reciprocally Proportional to Heights
      - Proposition: Prop. 12.10: Volume of Cone is Third of Cylinder on Same Base and of Same Height
      - Proposition: Prop. 12.11: Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases
      - Proposition: Prop. 12.12: Volumes of Similar Cones and Cylinders are in Triplicate Ratio of Diameters of Bases
      - Proposition: Prop. 12.13: Volumes of Parts of Cylinder cut by Plane Parallel to Opposite Planes are as Parts of Axis
      - Proposition: Prop. 12.14: Volumes of Cones or Cylinders on Equal Bases are in Same Ratio as Heights
      - Proposition: Prop. 12.15: Cones or Cylinders are Equal iff Bases are Reciprocally Proportional to Heights
      - Proposition: Prop. 12.16: Construction of Equilateral Polygon with Even Number of Sides in Outer of Concentric Circles
      - Proposition: Prop. 12.17: Construction of Polyhedron in Outer of Concentric Spheres
      - Proposition: Prop. 12.18: Volumes of Spheres are in Triplicate Ratio of Diameters
    - Book 13 Platonic Solids (18)
  - Euclidean Geometry (4)
    - Proposition: Common Points of Two Distinct Straight Lines in a Plane
    - Proposition: Common Points of a Plane and a Straight Line Not in the Plane
    - Proposition: Plane Determined by a Straight Line and a Point not on the Straight Line
    - Proposition: Plane Determined by two Crossing Straight Lines
- Graph Theory (9)
  - Proposition: A Necessary Condition for a Graph to be Planar
  - Proposition: A Necessary Condition for a Graph with Shortest Cycles to Be Planar
  - Proposition: A Necessary Condition for a Graph with Shortest Cycles to Be Planar (II)
  - Proposition: Characterization of Cutvertices
  - Proposition: Chromatic Number and Maximum Vertex Degree
  - Proposition: Connectivity Is an Equivalence Relation - Components Are a Partition of a Graph
  - Proposition: Equivalent Definitions of Trees
  - Proposition: Relationship Between Planarity and Biconnectivity of Graphs
  - Proposition: Relationship Between Planarity and Connectivity of Graphs
- Knot Theory (1)
  - Proposition: Equivalent Knot Diagrams
- Logic (2)
  - Proposition: Associativity of Conjunction
  - Proposition: Associativity of Disjunction
- Number Systems Arithmetics (160)
  - Proposition: Abelian Partial Summation Method
  - Proposition: Absolute Value of Complex Conjugate
  - Proposition: Absolute Value of the Product of Complex Numbers
  - Proposition: Addition Of Natural Numbers
  - Proposition: Addition Of Natural Numbers Is Associative
  - Proposition: Addition Of Rational Numbers
  - Proposition: Addition Of Real Numbers Is Associative
  - Proposition: Addition Of Real Numbers Is Commutative
  - Proposition: Addition of Complex Numbers Is Associative
  - Proposition: Addition of Complex Numbers Is Commutative
  - Proposition: Addition of Integers
  - Proposition: Addition of Integers Is Associative
  - Proposition: Addition of Integers Is Cancellative
  - Proposition: Addition of Integers Is Commutative
  - Proposition: Addition of Natural Numbers Is Cancellative
  - Proposition: Addition of Natural Numbers Is Cancellative With Respect To Inequalities
  - Proposition: Addition of Natural Numbers Is Commutative
  - Proposition: Addition of Rational Cauchy Sequences
  - Proposition: Addition of Rational Cauchy Sequences Is Associative
  - Proposition: Addition of Rational Cauchy Sequences Is Cancellative
  - Proposition: Addition of Rational Cauchy Sequences Is Commutative
  - Proposition: Addition of Rational Numbers Is Associative
  - Proposition: Addition of Rational Numbers Is Cancellative
  - Proposition: Addition of Rational Numbers Is Commutative
  - Proposition: Addition of Real Numbers
  - Proposition: Addition of Real Numbers Is Cancellative
  - Proposition: Algebraic Structure Of Natural Numbers Together With Addition
  - Proposition: Algebraic Structure Of Natural Numbers Together With Multiplication
  - Proposition: Algebraic Structure of Complex Numbers Together with Addition
  - Proposition: Algebraic Structure of Complex Numbers Together with Addition and Multiplication
  - Proposition: Algebraic Structure of Integers Together with Addition
  - Proposition: Algebraic Structure of Integers Together with Addition and Multiplication
  - Proposition: Algebraic Structure of Non-Zero Complex Numbers Together with Multiplication
  - Proposition: Algebraic Structure of Non-Zero Rational Numbers Together with Multiplication
  - Proposition: Algebraic Structure of Non-Zero Real Numbers Together with Multiplication
  - Proposition: Algebraic Structure of Rational Numbers Together with Addition
  - Proposition: Algebraic Structure of Rational Numbers Together with Addition and Multiplication
  - Proposition: Algebraic Structure of Real Numbers Together with Addition
  - Proposition: Algebraic Structure of Real Numbers Together with Addition and Multiplication
  - Proposition: Alternating Sum of Binomial Coefficients
  - Proposition: Basic Rules of Manipulating Finite Sums
  - Proposition: Calculating with Complex Conjugates
  - Proposition: Comparing Natural Numbers Using the Concept of Addition
  - Proposition: Complex Numbers Cannot Be Ordered
  - Proposition: Complex Numbers are a Field Extension of Real Numbers
  - Proposition: Complex Numbers as a Vector Space Over the Field of Real Numbers
  - Proposition: Contraposition of Cancellative Law for Adding Integers
  - Proposition: Contraposition of Cancellative Law for Adding Rational Numbers
  - Proposition: Contraposition of Cancellative Law for Adding Real Numbers
  - Proposition: Contraposition of Cancellative Law for Multiplying Integers
  - Proposition: Contraposition of Cancellative Law for Multiplying Natural Numbers
  - Proposition: Contraposition of Cancellative Law for Multiplying Rational Numbers
  - Proposition: Contraposition of Cancellative Law of for Multiplying Real Numbers
  - Proposition: Definition of Integers
  - Proposition: Definition of Rational Numbers
  - Proposition: Definition of Real Numbers
  - Proposition: Discovery of Irrational Numbers
  - Proposition: Distributivity Law For Integers
  - Proposition: Distributivity Law For Natural Numbers
  - Proposition: Distributivity Law For Rational Cauchy Sequences
  - Proposition: Distributivity Law For Rational Numbers
  - Proposition: Distributivity Law For Real Numbers
  - Proposition: Distributivity Law for Complex Numbers
  - Proposition: Double Summation
  - Proposition: Equality of Two Ratios
  - Proposition: Every Natural Number Is Greater or Equal Zero
  - Proposition: Existence and Uniqueness of Greatest Elements in Subsets of Natural Numbers
  - Proposition: Existence of Complex One (Neutral Element of Multiplication of Complex Numbers)
  - Proposition: Existence of Complex Zero (Neutral Element of Addition of Complex Numbers)
  - Proposition: Existence of Integer One (Neutral Element of Multiplication of Integers)
  - Proposition: Existence of Integer Zero (Neutral Element of Addition of Integers)
  - Proposition: Existence of Inverse Complex Numbers With Respect to Addition
  - Proposition: Existence of Inverse Complex Numbers With Respect to Multiplication
  - Proposition: Existence of Inverse Integers With Respect to Addition
  - Proposition: Existence of Inverse Rational Cauchy Sequences With Respect to Addition
  - Proposition: Existence of Inverse Rational Numbers With Respect to Addition
  - Proposition: Existence of Inverse Rational Numbers With Respect to Multiplication
  - Proposition: Existence of Inverse Real Numbers With Respect to Addition
  - Proposition: Existence of Inverse Real Numbers With Respect to Multiplication
  - Proposition: Existence of Rational Cauchy Sequence of Ones (Neutral Element of Multiplication of Rational Cauchy Sequences)
  - Proposition: Existence of Rational Cauchy Sequence of Zeros (Neutral Element of Addition of Rational Cauchy Sequences)
  - Proposition: Existence of Rational One (Neutral Element of Multiplication of Rational Numbers)
  - Proposition: Existence of Rational Zero (Neutral Element of Addition of Rational Numbers)
  - Proposition: Existence of Real One (Neutral Element of Multiplication of Real Numbers)
  - Proposition: Existence of Real Zero (Neutral Element of Addition of Real Numbers)
  - Proposition: Extracting the Real and the Imaginary Part of a Complex Number
  - Proposition: Geometric Sum
  - Proposition: Imaginary Unit
  - Proposition: Inequality of Natural Numbers and Their Successors
  - Proposition: Multiplication Of Rational Cauchy Sequences
  - Proposition: Multiplication Of Rational Numbers
  - Proposition: Multiplication Of Rational Numbers Is Cancellative
  - Proposition: Multiplication Of Rational Numbers Is Commutative
  - Proposition: Multiplication of Complex Numbers Is Associative
  - Proposition: Multiplication of Complex Numbers Is Commutative
  - Proposition: Multiplication of Complex Numbers Using Polar Coordinates
  - Proposition: Multiplication of Integers
  - Proposition: Multiplication of Integers Is Associative
  - Proposition: Multiplication of Integers Is Cancellative
  - Proposition: Multiplication of Integers Is Commutative
  - Proposition: Multiplication of Natural Numbers Is Associative
  - Proposition: Multiplication of Natural Numbers Is Cancellative
  - Proposition: Multiplication of Natural Numbers Is Cancellative With Respect to the Order Relation
  - Proposition: Multiplication of Natural Numbers is Commutative
  - Proposition: Multiplication of Rational Cauchy Sequences Is Associative
  - Proposition: Multiplication of Rational Cauchy Sequences Is Cancellative
  - Proposition: Multiplication of Rational Cauchy Sequences Is Commutative
  - Proposition: Multiplication of Rational Numbers Is Associative
  - Proposition: Multiplication of Real Numbers
  - Proposition: Multiplication of Real Numbers Is Associative
  - Proposition: Multiplication of Real Numbers Is Cancellative
  - Proposition: Multiplication of Real Numbers Is Commutative
  - Proposition: Multiplying Negative and Positive Integers
  - Proposition: Multiplying Negative and Positive Rational Numbers
  - Proposition: Multiplying Negative and Positive Real Numbers
  - Proposition: Order Relation for Integers is Strict Total
  - Proposition: Order Relation for Natural Numbers, Revised
  - Proposition: Order Relation for Rational Numbers is Strict Total
  - Proposition: Order Relation for Real Numbers is Strict and Total
  - Proposition: Polar Coordinates of a Complex Number
  - Proposition: Position of Minus Sign in Rational Numbers Representations
  - Proposition: Product of Two Ratios
  - Proposition: Product of Two Sums (Generalized Distributivity Rule)
  - Proposition: Ratio of Two Ratios
  - Proposition: Rational Cauchy Sequence Members Are Bounded
  - Proposition: Rule of Combining Different Sets of Indices
  - Proposition: Sum and Difference of Two Ratios
  - Proposition: Sum of Arithmetic Progression
  - Proposition: Sum of Binomial Coefficients
  - Proposition: Sum of Binomial Coefficients I
  - Proposition: Sum of Binomial Coefficients II
  - Proposition: Sum of Binomial Coefficients III
  - Proposition: Sum of Binomial Coefficients IV
  - Proposition: Sum of Consecutive Natural Numbers
  - Proposition: Sum of Consecutive Odd Numbers
  - Proposition: Sum of Cosines
  - Proposition: Sum of Cube Numbers
  - Proposition: Sum of Factorials (I)
  - Proposition: Sum of Geometric Progression
  - Proposition: Sum of Squares
  - Proposition: The General Perturbation Method
  - Proposition: Transitivity of the Order Relation of Natural Numbers
  - Proposition: Unique Solvability of `$ax=b$`
  - Proposition: Unique Solvability of `\(a+x=b\)`
  - Proposition: Uniqueness Of Natural One
  - Proposition: Uniqueness Of Predecessors Of Natural Numbers
  - Proposition: Uniqueness Of Rational One
  - Proposition: Uniqueness of Complex Zero
  - Proposition: Uniqueness of Integer One
  - Proposition: Uniqueness of Integer Zero
  - Proposition: Uniqueness of Inverse Rational Numbers With Respect to Multiplication
  - Proposition: Uniqueness of Inverse Real Numbers With Respect to Multiplication
  - Proposition: Uniqueness of Natural Zero
  - Proposition: Uniqueness of Negative Numbers
  - Proposition: Uniqueness of Rational Zero
  - Proposition: Uniqueness of Real One
  - Proposition: Uniqueness of Real Zero
  - Proposition: Well-Ordering Principle of Natural Numbers
  - Proposition: `\((xy)^{-1}=x^{-1}y^{-1}\)`
  - Proposition: `\(-(x+y)=-x-y\)`
- Number Theory (58)
  - Proposition: A Linear Term for 1 Using Two Co-prime Coefficients
  - Proposition: A Necessary Condition for an Integer to be Prime
  - Proposition: Addition, Subtraction and Multiplication of Congruences, the Commutative Ring `$\mathbb Z_m$`
  - Proposition: All Solutions Given a Solution of an LDE With Two Variables
  - Proposition: Calculating the Number of Positive Divisors
  - Proposition: Calculating the Sum of Divisors
  - Proposition: Cancellation of Congruences With Factor Co-Prime To Module, Field `$\mathbb Z_p$`
  - Proposition: Cancellation of Congruences with General Factor
  - Proposition: Co-prime Primes
  - Proposition: Complete and Reduced Residue Systems (Revised)
  - Proposition: Congruence Classes
  - Proposition: Congruence Modulo a Divisor
  - Proposition: Congruences and Division with Quotient and Remainder
  - Proposition: Connection between Quotient, Remainder, Modulo and Floor Function
  - Proposition: Convergence of Alternating Harmonic Series
  - Proposition: Counting the Roots of a Diophantine Polynomial Modulo a Prime Number
  - Proposition: Counting the Solutions of Diophantine Equations of Congruences
  - Proposition: Creation of Complete Residue Systems From Others
  - Proposition: Creation of Reduced Residue Systems From Others
  - Proposition: Diophantine Equations of Congruences
  - Proposition: Divergence of Harmonic Series
  - Proposition: Divisibility Laws
  - Proposition: Divisors of a Product Of Two Factors, Co-Prime to One Factor Divide the Other Factor
  - Proposition: Euler's Criterion For Quadratic Residues
  - Proposition: Even Perfect Numbers
  - Proposition: Every Integer Is Either Even or Odd
  - Proposition: Existence and Number of Solutions of Congruence With One Variable
  - Proposition: Existence of Prime Divisors
  - Proposition: Existence of Solutions of an LDE With More Variables
  - Proposition: Explicit Formula for the Euler Function
  - Proposition: Factorization of Greatest Common Divisor and Least Common Multiple
  - Proposition: Finite Number of Divisors
  - Proposition: Floor Function and Division with Quotient and Remainder
  - Proposition: Generating Co-Prime Numbers Knowing the Greatest Common Divisor
  - Proposition: Generating the Greatest Common Divisor Knowing Co-Prime Numbers
  - Proposition: Greatest Common Divisor
  - Proposition: Greatest Common Divisor of More Than Two Numbers
  - Proposition: Greatest Common Divisors Of Integers and Prime Numbers
  - Proposition: Least Common Multiple
  - Proposition: Least Common Multiple of More Than Two Numbers
  - Proposition: Legendre Symbols of Equal Residues
  - Proposition: Multiplication of Congruences with a Positive Factor
  - Proposition: Multiplicative Group Modulo an Integer `$(\mathbb Z_m^*,\cdot)$`
  - Proposition: Multiplicativity of the Legendre Symbol
  - Proposition: Natural Logarithm Sum of von Mangoldt Function Over Divisors
  - Proposition: Natural Numbers and Products of Prime Numbers
  - Proposition: Number of Multiples of a Given Number Less Than Another Number
  - Proposition: Number of Quadratic Residues in Reduced Residue Systems Modulo a Prime
  - Proposition: Numbers Being the Product of Their Divisors
  - Proposition: Product of Two Even Numbers
  - Proposition: Product of Two Odd Numbers
  - Proposition: Product of an Even and an Odd Number
  - Proposition: Properties of Floors and Ceilings
  - Proposition: Relationship Between the Greatest Common Divisor and the Least Common Multiple
  - Proposition: Sign of Divisors of Integers
  - Proposition: Sum of Euler Function
  - Proposition: Sum of Möbius Function Over Divisors
  - Proposition: Wilson's Condition for an Integer to be Prime
- Probability Theory And Statistics (14)
  - Proposition: Binomial Distribution
  - Proposition: Characterization of Independent Events
  - Proposition: Characterization of Independent Events II
  - Proposition: Geometric Distribution
  - Proposition: Monotonically Increasing Property of Probability Distributions
  - Proposition: Multinomial Distribution
  - Proposition: Probability of Event Difference
  - Proposition: Probability of Event Union
  - Proposition: Probability of Included Event
  - Proposition: Probability of Joint Events
  - Proposition: Probability of the Complement Event
  - Proposition: Replacing Mutually Independent Events by Their Complements
  - Proposition: Urn Model With Replacement
  - Proposition: Urn Model Without Replacement
- Set Theory (39)
  - Proposition: Cardinal Number
  - Proposition: Cardinals of a Set and Its Power Set
  - Proposition: Characterization of Bijective Functions
  - Proposition: Composition of Bijective Functions is Bijective
  - Proposition: Composition of Functions is Associative
  - Proposition: Composition of Injective Functions is Injective
  - Proposition: Composition of Surjective Functions is Surjective
  - Proposition: Contained Relation is a Strict Order
  - Proposition: Counting the Set's Elements Using Its Partition
  - Proposition: De Morgan's Laws (Sets)
  - Proposition: Distributivity Laws For Sets
  - Proposition: Equivalent Notions of Ordinals
  - Proposition: Finite Chains are Well-ordered
  - Proposition: Functions Constitute Equivalence Relations
  - Proposition: Injective, Surjective and Bijective Compositions
  - Proposition: Intersection of a Set With Another Set is Subset of This Set
  - Proposition: More Characterizations of Finite Sets
  - Proposition: Ordinals Are Downward Closed
  - Proposition: Partial Orders are Extensional
  - Proposition: Rational Numbers are Countable
  - Proposition: Real Numbers are Uncountable
  - Proposition: Set Intersection is Associative
  - Proposition: Set Intersection is Commutative
  - Proposition: Set Union is Associative
  - Proposition: Set Union is Commutative
  - Proposition: Set-Theoretical Meaning of Ordered Tuples
  - Proposition: Sets and Their Complements
  - Proposition: Sets are Subsets of Their Union
  - Proposition: Strict Orders are Extensional
  - Proposition: Subset of a Countable Set is Countable
  - Proposition: Subsets of Finite Sets
  - Proposition: The Contained Relation is Extensional
  - Proposition: The Equality of Sets Is an Equivalence Relation
  - Proposition: The Inverse Of a Composition
  - Proposition: Transitive Recursion
  - Proposition: Uncountable and Countable Subsets of Natural Numbers
  - Proposition: Union of Countably Many Countable Sets
  - Proposition: Well-ordered Sets are Chains
  - Proposition: Zorn's Lemma is Equivalent To the Axiom of Choice
- Theoretical Computer Science (1)
  - Complexity Theory (1)
    - Proposition: Calculation Rules for the Big O Notation
- Theoretical Physics (2)
  - Special Relativity (2)
    - Proposition: Construction of a Light Clock
    - Proposition: Time Dilation, Lorentz Factor
- Topology (28)
  - Proposition: A Necessary Condition of a Neighborhood to be Open
  - Proposition: Alternative Characterization of Topological Spaces
  - Proposition: Bijective Open Functions
  - Proposition: Characterization of `$T_1$` Spaces
  - Proposition: Characterization of `$T_2$` Spaces
  - Proposition: Clopen Sets and Boundaries
  - Proposition: Construction of Topological Spaces Using a Subbasis
  - Proposition: Continuity of Compositions of Functions
  - Proposition: Distance in Normed Vector Spaces
  - Proposition: Equivalent Notions of Continuous Functions
  - Proposition: Equivalent Notions of Homeomorphisms
  - Proposition: Filter Base
  - Proposition: How the Boundary Changes the Property of a Set of Being Open
  - Proposition: Inheritance of the `$T_1$` Property
  - Proposition: Inheritance of the `$T_2$` Property
  - Proposition: Integral p-Norm
  - Proposition: Isometry is Injective
  - Proposition: Maximum Norm as a Limit of p-Norms
  - Proposition: Metric Spaces and Empty Sets are Clopen
  - Proposition: Metric Spaces are Hausdorff Spaces
  - Proposition: Modulus of Continuity is Continuous
  - Proposition: Modulus of Continuity is Monotonically Increasing
  - Proposition: Modulus of Continuity is Subadditive
  - Proposition: Perfect Sets vs. Derived Sets
  - Proposition: Properties of the Set of All Neighborhoods of a Point
  - Proposition: Uniqueness of the Limit of a Sequence
  - Proposition: \(\epsilon\)-\(\delta\) Definition of Continuity
  - Proposition: p-Norm, Taxicab Norm, Euclidean Norm, Maximum Norm
Corollaries (147)
Proofs (1446)

Other Building Blocks

Algorithms (23)
- Graph Theory (3)
  - Algorithm: Get All Components of a Graph
  - Algorithm: Get the Component Induced by Vertices Connected to a Given Vertex
  - Algorithm: Get the Cut Vertices and Biconnected Components of a Connected Graph
- Theoretical Computer Science (20)
  - Basic Algorithms (1)
    - Algorithm: Sequential Search
  - Computability (8)
    - Algorithm: Addition (or Subtraction) of Two Registers
    - Algorithm: Assignment of a Constant `\(c\)` to the Register `\(r_i\)` with a `\(L O O P\)`-Program
    - Algorithm: Conditional execution of `\(L O O P\)` programs - IF-THEN construct
    - Algorithm: Conditional execution of `\(L O O P\)` programs - IF-THEN-ELSE construct
    - Algorithm: Division with Quotient and Remainder (Unit-cost Random Access Machine)
    - Algorithm: Multiplication of Two Registers
    - Algorithm: No-Operation Command (NOP)
    - Algorithm: Setting the value of a register to the value of another register plus or minus a constant
  - Data Structures (2)
    - Algorithm: Graph (Python)
    - Algorithm: getSubgraph
  - Semi Numerical Algorithms (9)
    - Algorithm: Calculation of Inverses Modulo a Number (Python)
    - Algorithm: Complex Numbers
    - Algorithm: Continued Fraction (Python)
    - Algorithm: Converting Decimal Numbers to Roman Numbers
    - Algorithm: Converting Roman Numbers to Decimal Numbers
    - Algorithm: Extended Greatest Common Divisor (Python)
    - Algorithm: Greatest Common Divisor (Python)
    - Algorithm: Horner Scheme
    - Algorithm: Jacobi Symbol (Python)
Motivations (16)
- Algebra (3)
- Combinatorics (1)
  - Motivation: Formulae of Negative Factorial Powers Explained (related to Definition: Falling And Rising Factorial Powers)
- Logic (1)
  - Motivation: What does not have to be proved in mathematics? (related to Part: Methods of Mathematical Proving)
- Number Systems Arithmetics (1)
  - Motivation: Motivation for the Proof of Uniqueness of Zero (related to Proposition: Uniqueness of Negative Numbers)
- Set Theory (8)
- Theoretical Physics (2)
  - Special Relativity (2)
    - Motivation: Measurement of the Speed of Light - First Experimental Proof that the Speed of Light is Finite (related to Part: Special Relativity)
    - Motivation: Michelson-Morley Experiment (related to Part: Special Relativity)
Applications (5)
- Algebra (1)
  - Application: SLEs Revised in the Light of Vector Spaces (related to Chapter: Vectors Revised - Vector Spaces)
- Analysis (1)
  - Application: Application of Monotonic Convergence (related to Theorem: Every Bounded Monotonic Sequence Is Convergent)
- Fun (1)
  - Oddities (1)
    - Application: Lightning and Thunder or the Relativity of Acoustic Signals (related to Part: Oddities and Curiosities)
- Theoretical Computer Science (2)
  - Formal Languages (2)
    - Application: Application of the Rabin-Scott Theorem - the Rabin-Scott Algorithm (related to Chapter: Finite Automata (Finite Sequential Machines))
    - Application: Application of the Theorem to Reduce `$\epsilon$`-NFA to NFA (related to Chapter: Finite Automata (Finite Sequential Machines))
Explanations (57)
- Algebra (7)
  - Explanation: All Types of Morphisms and Their Properties (related to Motivation: Common Concepts Of Algebra: Substructures and Morphisms)
  - Explanation: Calculation Rules in a Group with Additive Notation (related to Motivation: Calculations in a Group)
  - Explanation: Characteristic Zero Instead of Characteristic Infinite (related to Definition: Characteristic of a Ring)
  - Explanation: Kernel and Image (related to Definition: Linear Map)
  - Explanation: Matrices of Linear Maps (related to Definition: Linear Map)
  - Explanation: Operation Table (related to Part: Algebraic Structures - Overview)
  - Explanation: Unions of Subgroups Are Not Subgroups (related to Chapter: Groups (Overview))
- Analysis (2)
  - Explanation: Explanation of the Heine-Borel Property (related to Definition: Heine-Borel Property Defines Compact Subsets)
  - Explanation: Local Extrema on a Closed Interval (related to Proposition: Zero-Derivative as a Necessary Condition for a Local Extremum)
- Combinatorics (7)
- Geometry (9)
  - Analytic Geometry (1)
    - Explanation: Geometrical Interpretation of Hyperplanes (related to Definition: Hyperplane of a Number Space)
  - Elements Euclid (8)
    - Book 1 Plane Geometry (8)
- Graph Theory (1)
  - Explanation: Examples of Dual Statements for Planar Graphs (related to Chapter: Conditions for Planarity and Planarity Testing)
- Logic (6)
- Number Systems Arithmetics (3)
- Number Theory (3)
- Probability Theory And Statistics (3)
- Set Theory (13)
- Theoretical Computer Science (1)
  - Formal Languages (1)
    - Explanation: Chomsky's Hierarchy of Languages (related to Chapter: Classification of Formal Languages)
- Theoretical Physics (1)
  - Special Relativity (1)
    - Explanation: Einstein's Interpretation of the Time Dilation (related to Proposition: Time Dilation, Lorentz Factor)
- Topology (1)
  - Explanation: Fourteen Sets Formed By Closure, Interior and Complement Operations (related to Chapter: Basic Topological Concepts)
Examples (71)
- Algebra (15)
- Analysis (8)
- Combinatorics (2)
  - Example: Difference Operators of Some Functions (related to Part: Discrete Calculus and Difference Equations)
  - Example: Examples of Multinomial Coefficients (related to Proposition: Multinomial Coefficient)
- Fun (11)
  - Dudeney (1)
    - Geometrical Problems (1)
      - Various Dissection Puzzles (1)
        
        Example: The Paper Box (related to Section: Various Dissection Puzzles)
  - Jokes (5)
    - Example: Analytical Thinking Joke (related to Part: Jokes)
    - Example: Is Reality Real? (related to Part: Jokes)
    - Example: Pizza Lovers (related to Part: Jokes)
    - Example: Sexy Parabola (Joke) (related to Part: Jokes)
    - Example: What is time? (related to Part: Jokes)
  - Oddities (2)
    - Example: Bad Luck For People Suffering From Triskaidekaphobia (related to Part: Oddities and Curiosities)
    - Example: Interesting Nine (related to Part: Oddities and Curiosities)
  - Tricks (3)
- Graph Theory (2)
  - Example: A digraph with a loop, and parallel and inverse edges (related to Definition: Digraph, Initial and Terminal Vertices, Loops, Parallel and Inverse Edges, Simple Digraph)
  - Example: Examples of Adjacency Matrices (related to Definition: Adjacency Matrix)
- Logic (14)
- Number Theory (3)
- Probability Theory And Statistics (1)
  - Example: Fair Dice (related to Definition: Laplace Experiments and Elementary Events)
- Set Theory (6)
- Theoretical Computer Science (6)
  - Computability (2)
    - Example: Examples of Computational Problems (related to Part: Computability)
    - Example: Simulating More Complex Commands Using Basic `\(L O O P\)` Commands (related to Definition: LOOP Command, LOOP Program)
  - Formal Languages (4)
- Topology (3)
Problems (449)
- Algebra (2)
  - Problem: Verifying Group Properties
  - Problem: Verifying Subgroup Properties
- Combinatorics (6)
  - Problem: Calculating an Infinite Sum
  - Problem: Interpolating Numbers With a Polynomial
  - Problem: Sum of Consecutive Positive Integers
  - Problem: Sum of Consecutive Squares
  - Problem: Sums of Falling Factorial Powers
  - Problem: Sums of Powers of Two
- Fun (429)
  - Dudeney (429)
    - Arithmetical And Algebraic Problems (141)
      - Age And Kinship Puzzles (17)
        
        Problem: A Census Puzzle
        
        Problem: A Family Party
        
        Problem: A Mixed Pedigree
        
        Problem: Concerning Tommy's Age
        
        Problem: Heard on the Tube Railway
        
        Problem: How Old Was Mary?
        
        Problem: Mamma's Age
        
        Problem: Mary and Marmaduke
        
        Problem: Mother and Daughter
        
        Problem: Mrs. Timpkin's Age
        
        Problem: Next-door Neighbors
        
        Problem: Queer Relationships
        
        Problem: Rover's Age
        
        Problem: The Bag of Nuts
        
        Problem: The Family Ages
        
        Problem: Their Ages
        
        Problem: Wilson's Poser
      - Clock Puzzles (10)
        
        Problem: A Puzzling Watch
        
        Problem: A Time Puzzle
        
        Problem: Changing Places
        
        Problem: The Club Clock
        
        Problem: The Railway Station Clock
        
        Problem: The Stop-Watch
        
        Problem: The Three Clocks
        
        Problem: The Village Simpleton
        
        Problem: The Wapshaw's Wharf Mystery
        
        Problem: What Was the Time?
      - Digital Puzzles (21)
        
        Problem: Adding The Digits
        
        Problem: Digital Division
        
        Problem: Digital Multiplication
        
        Problem: Digital Square Numbers
        
        Problem: Digits and Squares
        
        Problem: More Mixed Fractions
        
        Problem: Odd And Even Digits
        
        Problem: Queer Multiplication
        
        Problem: The Barrel of Beer
        
        Problem: The Cab Numbers
        
        Problem: The Century Puzzle
        
        Problem: The Dice Numbers
        
        Problem: The Digital Century
        
        Problem: The Four Sevens
        
        Problem: The Lockers Puzzle
        
        Problem: The Mystic Eleven
        
        Problem: The Nine Counters
        
        Problem: The Number Checks Puzzle
        
        Problem: The Pierrot's Puzzle
        
        Problem: The Ten Counters
        
        Problem: The Three Groups
      - Locomotion And Speed Puzzles (9)
        
        Problem: Average Speed
        
        Problem: Donkey Riding
        
        Problem: Drawing Her Pension
        
        Problem: Sir Edwyn De Tudor
        
        Problem: The Basket Of Potatoes
        
        Problem: The Hydroplane Question
        
        Problem: The Passenger's Fare
        
        Problem: The Three Villages
        
        Problem: The Two Trains
      - Money Puzzles (39)
        
        Problem: A Charitable Bequest
        
        Problem: A Deal in Apples
        
        Problem: A Deal in Eggs
        
        Problem: A New Money Puzzle
        
        Problem: A Postoffice Perplexity
        
        Problem: A Puzzle in Reversals
        
        Problem: A Queer Coincidence
        
        Problem: A Queer Thing in Money
        
        Problem: A Shopping Perplexity
        
        Problem: At a Cattle Market
        
        Problem: Awkward Money
        
        Problem: Beef and Sausages
        
        Problem: Buying Apples
        
        Problem: Buying Chestnuts
        
        Problem: Buying Presents
        
        Problem: Defective Observation
        
        Problem: Domestic Economy
        
        Problem: Giving Change
        
        Problem: Indiscriminate Charity
        
        Problem: Judkins's Cattle
        
        Problem: Pocket Money
        
        Problem: Square Money
        
        Problem: The Beanfeast Puzzle
        
        Problem: The Bicylce Thief
        
        Problem: The Broken Coins
        
        Problem: The Christmas-Boxes
        
        Problem: The Costermonger's Puzzle
        
        Problem: The Cyclists' Feast
        
        Problem: The Excursion Ticket Puzzle
        
        Problem: The Grocer and Draper
        
        Problem: The Junior Clerk's Puzzle
        
        Problem: The Market Women
        
        Problem: The Millionaire's Perplexity
        
        Problem: The Puzzling Money-Boxes
        
        Problem: The Two Aeroplanes
        
        Problem: The Widow's Legacy
        
        Problem: The new Year's Eve Suppers
        
        Problem: Two Questions in Probabilities
        
        Problem: Youthful Precocity
      - Various Other Aa Problems (45)
        
        Problem: A Fence Problem
        
        Problem: A Legal Difficulty
        
        Problem: A Printer's Error
        
        Problem: A Problem in Squares
        
        Problem: A Puzzling Legacy
        
        Problem: A Question of Definition
        
        Problem: A Study in Thrift
        
        Problem: Academic Courtesies
        
        Problem: Catching the Thief
        
        Problem: Circling the Squares
        
        Problem: Curious Numbers
        
        Problem: Find Ada's Surname
        
        Problem: Heads or Tails
        
        Problem: Mr. Gubbins in a Fog
        
        Problem: Painting the Lamp-Posts
        
        Problem: Rackbrane's Little Loss
        
        Problem: Reeping the Corn
        
        Problem: Saturday Marketing
        
        Problem: Simple Division
        
        Problem: Simple Multiplication
        
        Problem: The Abbot's Puzzle
        
        Problem: The Artilleryman's Dilemma
        
        Problem: The Banker's Puzzle
        
        Problem: The Battle of Hastings
        
        Problem: The Converted Miser
        
        Problem: The Dutchmen's Wives
        
        Problem: The Farmer and His Sheep
        
        Problem: The Five Brigands
        
        Problem: The Great Scramble
        
        Problem: The Laborer's Puzzle
        
        Problem: The Leap-Year Ladies
        
        Problem: The Miners' Holiday
        
        Problem: The Muddletown Election
        
        Problem: The Nine Treasure Boxes
        
        Problem: The Parish Council Election
        
        Problem: The Sculptor's Problem
        
        Problem: The See-saw Puzzle
        
        Problem: The Spanish Miser
        
        Problem: The Spot on the Table
        
        Problem: The Stonemason's Problem
        
        Problem: The Suffragists' Meeting
        
        Problem: The Sultan's Army
        
        Problem: The Thirty-Three Pearls
        
        Problem: The Torn Number
        
        Problem: The Trusses of Hay
    - Chessboard Problems (74)
      - Dynamical Chess Puzzles (26)
        
        Problem: A Dungeon Puzzle
        
        Problem: A New Bishop's Puzzle
        
        Problem: A New Counter Puzzle
        
        Problem: An Episcopal Visitation
        
        Problem: Exercise For Prisoners
        
        Problem: Farmer Lawrence's Cornfields
        
        Problem: St. George And The Dragon
        
        Problem: The Board In Compartments
        
        Problem: The Cubic Knight's Tour
        
        Problem: The Forty-nine Stars
        
        Problem: The Four Frogs
        
        Problem: The Four Kangaroos
        
        Problem: The Four Knights' Tours
        
        Problem: The Greyhound Puzzle
        
        Problem: The Kennel Puzzle
        
        Problem: The Languishing Maiden
        
        Problem: The Lion And The Man
        
        Problem: The Mandarin's Puzzle
        
        Problem: The Queen's Journey
        
        Problem: The Queen's Tour
        
        Problem: The Rook's Journey
        
        Problem: The Rook's Tour
        
        Problem: The Scientific Skater
        
        Problem: The Star Puzzle
        
        Problem: The Two Pawns
        
        Problem: The Yacht Race
      - Statical Chess Puzzles (25)
        
        Problem: A Problem in Mosaics
        
        Problem: A Puzzle With Pawns
        
        Problem: Bachet's Square
        
        Problem: Bishops in Convocation
        
        Problem: Bishops — guarded
        
        Problem: Bishops — unguarded
        
        Problem: Lion-hunting
        
        Problem: Queens And Bishop Puzzle
        
        Problem: The Amazons
        
        Problem: The Coloured Counters
        
        Problem: The Crowded Chessboard
        
        Problem: The Eight Queens
        
        Problem: The Eight Rooks
        
        Problem: The Eight Stars
        
        Problem: The Five Crescents of Byzantium
        
        Problem: The Five Dogs Puzzle
        
        Problem: The Forty-nine Counters
        
        Problem: The Four Lions
        
        Problem: The Gentle Art Of Stamp-licking
        
        Problem: The Hat-peg Puzzle
        
        Problem: The Knight-guards
        
        Problem: The Southern Cross
        
        Problem: The Thirty-six Letter Blocks
        
        Problem: The Three Sheep
        
        Problem: Under the Veil
      - The Chessboard (7)
        
        Problem: Boards With An Odd Number Of Squares
        
        Problem: Chequered Board Divisions
        
        Problem: Lions And Crowns
        
        Problem: The Abbot's Window
        
        Problem: The Chessboard Sentence
        
        Problem: The Chinese Chessboard
        
        Problem: The Grand Lama's Problem
      - Various Chess Puzzles (16)
        
        Problem: An Amazing Dilemma
        
        Problem: Ancient Chinese Puzzle
        
        Problem: Checkmate!
        
        Problem: Chessboard Solitaire
        
        Problem: Counter Solitaire
        
        Problem: Counting The Rectangles
        
        Problem: Immovable Pawns
        
        Problem: Queer Chess
        
        Problem: Setting The Board
        
        Problem: Stalemate
        
        Problem: The Crusader
        
        Problem: The Forsaken King
        
        Problem: The Monstrosity
        
        Problem: The Rookery
        
        Problem: The Six Pawns
        
        Problem: Thirty-six Mates
    - Combination And Group Problems (26)
      - Problem: A Dormitory Puzzle
      - Problem: A Puzzle for Card-players
      - Problem: A Tennis Tournament
      - Problem: An Acrostic Puzzle
      - Problem: Building The Tetrahedron
      - Problem: Counter Crosses
      - Problem: Fifteen Letter Puzzle
      - Problem: King Arthur's Knights
      - Problem: Painting A Pyramid
      - Problem: Painting The Die
      - Problem: The Antiquary's Chain
      - Problem: The Barrels Of Balsam
      - Problem: The City Luncheons
      - Problem: The Cross Target
      - Problem: The Eight Villas
      - Problem: The Fifteen Dominoes
      - Problem: The Four Postage Stamps
      - Problem: The Glass Balls
      - Problem: The Mouse-trap Puzzle
      - Problem: The Nine Schoolboys
      - Problem: The Peal Of Bells
      - Problem: The Round Table
      - Problem: The Sixteen Sheep
      - Problem: The Wrong Hats
      - Problem: Those Fifteen Sheep
      - Problem: Three Men In A Boat
    - Crossing River Problems (5)
      - Problem: Crossing The River Axe
      - Problem: Crossing The Stream
      - Problem: Five Jealous Husbands
      - Problem: Stealing The Castle Treasure
      - Problem: The Four Elopements
    - Geometrical Problems (63)
      - Greek Cross Puzzles (4)
        
        Problem: The Cross and the Triangle
        
        Problem: The Folded Cross
        
        Problem: The Silk Patchwork
        
        Problem: Two Crosses From One
      - Patchwork Puzzles (8)
        
        Problem: Another Linoleum Puzzle
        
        Problem: Another Patchwork Puzzle
        
        Problem: He Banner Puzzle
        
        Problem: Linoleum Cutting
        
        Problem: Mrs. Perkins's Quilt
        
        Problem: Mrs. Smiley's Christmas Present
        
        Problem: The Cushion Covers
        
        Problem: The Squares Of Brocade
      - Various Dissection Puzzles (23)
        
        Problem: A Cutting-out Puzzle
        
        Problem: A Tangram Paradox
        
        Problem: An Easy Dissection Puzzle
        
        Problem: An Easy Square Puzzle
        
        Problem: Another Joiner's Problem
        
        Problem: Dissecting a Mittre
        
        Problem: Mrs. Hobson's Hearthrug
        
        Problem: The Betsy Ross Puzzle
        
        Problem: The Bun Puzzle
        
        Problem: The Cardboard Chain
        
        Problem: The Chocolate Squares
        
        Problem: The Christmas Pudding
        
        Problem: The Dissected Triangle
        
        Problem: The Great Monad
        
        Problem: The Joiner's Problem
        
        Problem: The Landowner's Fences
        
        Problem: The Pentagon and Square
        
        Problem: The Potato Puzzle
        
        Problem: The Seven Pigs
        
        Problem: The Square of Veneer
        
        Problem: The Table-top and Stools
        
        Problem: The Two Horseshoes
        
        Problem: The Wizard's Cats
      - Various Other Geometrical Puzzles (28)
        
        Problem: A Kite-flying Puzzle
        
        Problem: A New Match Puzzle
        
        Problem: Concerning Wheels
        
        Problem: Drawing A Spiral
        
        Problem: Farmer Wurzel's Estate
        
        Problem: How To Draw An Oval
        
        Problem: How To Make Cisterns
        
        Problem: Lady Belinda's Garden
        
        Problem: Papa's Puzzle
        
        Problem: St. George's Banner
        
        Problem: Stealing The Bell-ropes
        
        Problem: The Ball Problem
        
        Problem: The Cardboard Box
        
        Problem: The Clothes Line Puzzle
        
        Problem: The Compasses Puzzle
        
        Problem: The Cone Puzzle
        
        Problem: The Crescent Puzzle
        
        Problem: The Eight Sticks
        
        Problem: The Four Sons
        
        Problem: The Garden Puzzle
        
        Problem: The Garden Walls
        
        Problem: The Milkmaid Puzzle
        
        Problem: The Puzzle Wall
        
        Problem: The Sheep-fold
        
        Problem: The Six Sheep-pens
        
        Problem: The Tethered Goat
        
        Problem: The Three Railway Stations
        
        Problem: The Yorkshire Estates
    - Magic Square Problems (14)
      - Problem: Card Magic Squares
      - Problem: Eight Jolly Gaol Birds
      - Problem: Nine Jolly Gaol Birds
      - Problem: The Eighteen Dominoes
      - Problem: The Magic Strips
      - Problem: The Siberian Dungeons
      - Problem: The Spanish Dungeon
      - Problem: The Troublesome Eight
      - Magic Squares Calculations (2)
        
        Problem: Magic Squares Of Two Degrees
        
        Problem: Two New Magic Squares
      - Magic Squares Of Primes (4)
        
        Problem: A Magic Square Of Composites
        
        Problem: The Baskets Of Plums
        
        Problem: The Magic Knight's Tour
        
        Problem: The Mandarin's "T" Puzzle
    - Measuring Weighing And Packing Problems (11)
      - Problem: A Packing Puzzle
      - Problem: Gold Packing In Russia
      - Problem: Mixing The Tea
      - Problem: New Measuring Puzzle
      - Problem: The Barrel Puzzle
      - Problem: The Barrels Of Honey
      - Problem: The Doctor's Query
      - Problem: The Honest Dairyman
      - Problem: The Keg Of Wine
      - Problem: The Wassail Bowl
      - Problem: Wine And Water
    - Moving Counter Problems (25)
      - Problem: A Lodging-house Difficulty
      - Problem: A Railway Muddle
      - Problem: A Railway Puzzle
      - Problem: Arranging The Jampots
      - Problem: Boys And Girls
      - Problem: Catching The Mice
      - Problem: Central Solitaire
      - Problem: Plates And Coins
      - Problem: Round The Coast
      - Problem: The Eccentric Cheesemonger
      - Problem: The Educated Frogs
      - Problem: The Eight Engines
      - Problem: The Exchange Puzzle
      - Problem: The Grasshopper Puzzle
      - Problem: The Hat Puzzle
      - Problem: The Letter Block Puzzle
      - Problem: The Motor-garage Puzzle
      - Problem: The Nine Almonds
      - Problem: The Six Frogs
      - Problem: The Ten Apples
      - Problem: The Ten Prisoners
      - Problem: The Twelve Pennies
      - Problem: The Twickenham Puzzle
      - Problem: The Victoria Cross Puzzle
      - Problem: Torpedo Practice
    - Points And Lines Problems (8)
      - Problem: A Plantation Puzzle
      - Problem: Cherries And Plums
      - Problem: The Burmese Plantation
      - Problem: The King And The Castles
      - Problem: The Ten Coins
      - Problem: The Twelve Mince-pies
      - Problem: The Twenty-one Trees
      - Problem: Turks And Russians
    - Problems Concerning Games (14)
      - Problem: "Strand" Patience
      - Problem: A Trick With Dice
      - Problem: Card Triangles
      - Problem: Dominoes In Progression
      - Problem: Slow Cricket
      - Problem: The "T" Card Puzzle
      - Problem: The Card Frame Puzzle
      - Problem: The Cross Of Cards
      - Problem: The Domino Frame Puzzle
      - Problem: The Five Dominoes
      - Problem: The Football Players
      - Problem: The Horse-race Puzzle
      - Problem: The Motor-car Race
      - Problem: The Village Cricket Match
    - Puzzle Games (7)
      - Problem: A Match Mystery
      - Problem: A War Puzzle Game
      - Problem: Puss In The Corner
      - Problem: The Cigar Puzzle
      - Problem: The Montenegrin Dice Game
      - Problem: The Pebble Game
      - Problem: The Two Rooks
    - The Paradox Party (1)
      - Problem: A Chessboard Fallacy
    - Unclassified Problems (17)
      - Problem: A Calendar Puzzle
      - Problem: A Chain Puzzle
      - Problem: A Wonderful Village
      - Problem: Find The Man's Wife
      - Problem: Jack And The Beanstalk
      - Problem: Pheasant-shooting
      - Problem: Placing Halfpennies
      - Problem: Such A Getting Upstairs
      - Problem: The Dovetailed Block
      - Problem: The Five Pennies
      - Problem: The Gardener And The Cook
      - Problem: The Hymn-board Poser
      - Problem: The Industrious Bookworm
      - Problem: The Ruby Brooch
      - Problem: The Sabbath Puzzle
      - Problem: The Tiring Irons
      - Problem: Who Was First?
    - Unicursal And Route Problems (23)
      - Problem: A Bank Holiday Puzzle
      - Problem: A Juvenile Puzzle
      - Problem: A Puzzle For Motorists
      - Problem: Hannah's Puzzle
      - Problem: Inspecting A Mine
      - Problem: The Cyclists' Tour
      - Problem: The Deified Puzzle
      - Problem: The Diamond Puzzle
      - Problem: The Dissected Circle
      - Problem: The Fifteen Turnings
      - Problem: The Fly On The Octahedron
      - Problem: The Grand Tour
      - Problem: The Honeycomb Puzzle
      - Problem: The Icosahedron Puzzle
      - Problem: The Level Puzzle
      - Problem: The Monk And The Bridges
      - Problem: The Motor-car Tour
      - Problem: The Sailor's Puzzle
      - Problem: The Tube Inspector's Puzzle
      - Problem: The Union Jack
      - Problem: The Voters' Puzzle
      - Problem: Visiting The Towns
      - Problem: Water, Gas, And Electricity
- Graph Theory (2)
  - Problem: Checking if `$K_5$` is Planar
  - Problem: Checking if `$K_{3,3}$` is Planar
- Number Theory (6)
  - Problem: Applications of the Jacobi Symbol
  - Problem: Are there infinitely many primorial primes?
  - Problem: Calculating Quadratic Residues
  - Problem: Even Perfect Numbers Problem
  - Problem: Odd Perfect Numbers Problem
  - Problem: Twin Prime Problem
- Probability Theory And Statistics (2)
  - Problem: Broken Items in the Box
  - Problem: Broken Items in the Box II
- Set Theory (1)
  - Problem: To Construct a Partition of a Given Set
- Theoretical Computer Science (1)
  - Complexity Theory (1)
    - Problem: TSP - The Traveling Salesman Problem
Solutions (445)
- Algebra (2)
  - Solution: (related to Problem: Verifying Group Properties)
  - Solution: (related to Problem: Verifying Subgroup Properties)
- Combinatorics (6)
  - Solution: (related to Problem: Calculating an Infinite Sum)
  - Solution: (related to Problem: Interpolating Numbers With a Polynomial)
  - Solution: (related to Problem: Sum of Consecutive Positive Integers)
  - Solution: (related to Problem: Sum of Consecutive Squares)
  - Solution: (related to Problem: Sums of Falling Factorial Powers)
  - Solution: (related to Problem: Sums of Powers of Two)
- Fun (430)
  - Dudeney (430)
    - Arithmetical And Algebraic Problems (141)
      - Age And Kinship Puzzles (17)
        
        Solution: (related to Problem: A Census Puzzle)
        
        Solution: (related to Problem: A Family Party)
        
        Solution: (related to Problem: A Mixed Pedigree)
        
        Solution: (related to Problem: Concerning Tommy's Age)
        
        Solution: (related to Problem: Heard on the Tube Railway)
        
        Solution: (related to Problem: How Old Was Mary?)
        
        Solution: (related to Problem: Mamma's Age)
        
        Solution: (related to Problem: Mary and Marmaduke)
        
        Solution: (related to Problem: Mother and Daughter)
        
        Solution: (related to Problem: Mrs. Timpkin's Age)
        
        Solution: (related to Problem: Next-door Neighbors)
        
        Solution: (related to Problem: Queer Relationships)
        
        Solution: (related to Problem: Rover's Age)
        
        Solution: (related to Problem: The Bag of Nuts)
        
        Solution: (related to Problem: The Family Ages)
        
        Solution: (related to Problem: Their Ages)
        
        Solution: (related to Problem: Wilson's Poser)
      - Clock Puzzles (10)
        
        Solution: (related to Problem: A Puzzling Watch)
        
        Solution: (related to Problem: A Time Puzzle)
        
        Solution: (related to Problem: Changing Places)
        
        Solution: (related to Problem: The Club Clock)
        
        Solution: (related to Problem: The Railway Station Clock)
        
        Solution: (related to Problem: The Stop-Watch)
        
        Solution: (related to Problem: The Three Clocks)
        
        Solution: (related to Problem: The Village Simpleton)
        
        Solution: (related to Problem: The Wapshaw's Wharf Mystery)
        
        Solution: (related to Problem: What Was the Time?)
      - Digital Puzzles (21)
        
        Solution: (related to Problem: Adding The Digits)
        
        Solution: (related to Problem: Digital Division)
        
        Solution: (related to Problem: Digital Multiplication)
        
        Solution: (related to Problem: Digital Square Numbers)
        
        Solution: (related to Problem: Digits and Squares)
        
        Solution: (related to Problem: More Mixed Fractions)
        
        Solution: (related to Problem: Odd And Even Digits)
        
        Solution: (related to Problem: Queer Multiplication)
        
        Solution: (related to Problem: The Barrel of Beer)
        
        Solution: (related to Problem: The Cab Numbers)
        
        Solution: (related to Problem: The Century Puzzle)
        
        Solution: (related to Problem: The Dice Numbers)
        
        Solution: (related to Problem: The Digital Century)
        
        Solution: (related to Problem: The Four Sevens)
        
        Solution: (related to Problem: The Lockers Puzzle)
        
        Solution: (related to Problem: The Mystic Eleven)
        
        Solution: (related to Problem: The Nine Counters)
        
        Solution: (related to Problem: The Number Checks Puzzle)
        
        Solution: (related to Problem: The Pierrot's Puzzle)
        
        Solution: (related to Problem: The Ten Counters)
        
        Solution: (related to Problem: The Three Groups)
      - Locomotion And Speed Puzzles (9)
        
        Solution: (related to Problem: Average Speed)
        
        Solution: (related to Problem: Donkey Riding)
        
        Solution: (related to Problem: Drawing Her Pension)
        
        Solution: (related to Problem: Sir Edwyn De Tudor)
        
        Solution: (related to Problem: The Basket Of Potatoes)
        
        Solution: (related to Problem: The Hydroplane Question)
        
        Solution: (related to Problem: The Passenger's Fare)
        
        Solution: (related to Problem: The Three Villages)
        
        Solution: (related to Problem: The Two Trains)
      - Money Puzzles (39)
        
        Solution: (related to Problem: A Charitable Bequest)
        
        Solution: (related to Problem: A Deal in Apples)
        
        Solution: (related to Problem: A Deal in Eggs)
        
        Solution: (related to Problem: A New Money Puzzle)
        
        Solution: (related to Problem: A Postoffice Perplexity)
        
        Solution: (related to Problem: A Puzzle in Reversals)
        
        Solution: (related to Problem: A Queer Coincidence)
        
        Solution: (related to Problem: A Queer Thing in Money)
        
        Solution: (related to Problem: A Shopping Perplexity)
        
        Solution: (related to Problem: At a Cattle Market)
        
        Solution: (related to Problem: Awkward Money)
        
        Solution: (related to Problem: Beef and Sausages)
        
        Solution: (related to Problem: Buying Apples)
        
        Solution: (related to Problem: Buying Chestnuts)
        
        Solution: (related to Problem: Buying Presents)
        
        Solution: (related to Problem: Defective Observation)
        
        Solution: (related to Problem: Domestic Economy)
        
        Solution: (related to Problem: Giving Change)
        
        Solution: (related to Problem: Indiscriminate Charity)
        
        Solution: (related to Problem: Judkins's Cattle)
        
        Solution: (related to Problem: Pocket Money)
        
        Solution: (related to Problem: Square Money)
        
        Solution: (related to Problem: The Beanfeast Puzzle)
        
        Solution: (related to Problem: The Bicylce Thief)
        
        Solution: (related to Problem: The Broken Coins)
        
        Solution: (related to Problem: The Christmas-Boxes)
        
        Solution: (related to Problem: The Costermonger's Puzzle)
        
        Solution: (related to Problem: The Cyclists' Feast)
        
        Solution: (related to Problem: The Excursion Ticket Puzzle)
        
        Solution: (related to Problem: The Grocer and Draper)
        
        Solution: (related to Problem: The Junior Clerk's Puzzle)
        
        Solution: (related to Problem: The Market Women)
        
        Solution: (related to Problem: The Millionaire's Perplexity)
        
        Solution: (related to Problem: The Puzzling Money-Boxes)
        
        Solution: (related to Problem: The Two Aeroplanes)
        
        Solution: (related to Problem: The Widow's Legacy)
        
        Solution: (related to Problem: The new Year's Eve Suppers)
        
        Solution: (related to Problem: Two Questions in Probabilities)
        
        Solution: (related to Problem: Youthful Precocity)
      - Various Other Aa Problems (45)
        
        Solution: (related to Problem: A Fence Problem)
        
        Solution: (related to Problem: A Legal Difficulty)
        
        Solution: (related to Problem: A Printer's Error)
        
        Solution: (related to Problem: A Problem in Squares)
        
        Solution: (related to Problem: A Puzzling Legacy)
        
        Solution: (related to Problem: A Question of Definition)
        
        Solution: (related to Problem: A Study in Thrift)
        
        Solution: (related to Problem: Academic Courtesies)
        
        Solution: (related to Problem: Catching the Thief)
        
        Solution: (related to Problem: Circling the Squares)
        
        Solution: (related to Problem: Curious Numbers)
        
        Solution: (related to Problem: Find Ada's Surname)
        
        Solution: (related to Problem: Heads or Tails)
        
        Solution: (related to Problem: Mr. Gubbins in a Fog)
        
        Solution: (related to Problem: Painting the Lamp-Posts)
        
        Solution: (related to Problem: Rackbrane's Little Loss)
        
        Solution: (related to Problem: Reeping the Corn)
        
        Solution: (related to Problem: Saturday Marketing)
        
        Solution: (related to Problem: Simple Division)
        
        Solution: (related to Problem: Simple Multiplication)
        
        Solution: (related to Problem: The Abbot's Puzzle)
        
        Solution: (related to Problem: The Artilleryman's Dilemma)
        
        Solution: (related to Problem: The Banker's Puzzle)
        
        Solution: (related to Problem: The Battle of Hastings)
        
        Solution: (related to Problem: The Converted Miser)
        
        Solution: (related to Problem: The Dutchmen's Wives)
        
        Solution: (related to Problem: The Farmer and His Sheep)
        
        Solution: (related to Problem: The Five Brigands)
        
        Solution: (related to Problem: The Great Scramble)
        
        Solution: (related to Problem: The Laborer's Puzzle)
        
        Solution: (related to Problem: The Leap-Year Ladies)
        
        Solution: (related to Problem: The Miners' Holiday)
        
        Solution: (related to Problem: The Muddletown Election)
        
        Solution: (related to Problem: The Nine Treasure Boxes)
        
        Solution: (related to Problem: The Parish Council Election)
        
        Solution: (related to Problem: The Sculptor's Problem)
        
        Solution: (related to Problem: The See-saw Puzzle)
        
        Solution: (related to Problem: The Spanish Miser)
        
        Solution: (related to Problem: The Spot on the Table)
        
        Solution: (related to Problem: The Stonemason's Problem)
        
        Solution: (related to Problem: The Suffragists' Meeting)
        
        Solution: (related to Problem: The Sultan's Army)
        
        Solution: (related to Problem: The Thirty-Three Pearls)
        
        Solution: (related to Problem: The Torn Number)
        
        Solution: (related to Problem: The Trusses of Hay)
    - Chessboard Problems (74)
      - Dynamical Chess Puzzles (26)
        
        Solution: (related to Problem: A Dungeon Puzzle)
        
        Solution: (related to Problem: A New Bishop's Puzzle)
        
        Solution: (related to Problem: A New Counter Puzzle)
        
        Solution: (related to Problem: An Episcopal Visitation)
        
        Solution: (related to Problem: Exercise For Prisoners)
        
        Solution: (related to Problem: Farmer Lawrence's Cornfields)
        
        Solution: (related to Problem: St. George And The Dragon)
        
        Solution: (related to Problem: The Board In Compartments)
        
        Solution: (related to Problem: The Cubic Knight's Tour)
        
        Solution: (related to Problem: The Forty-nine Stars)
        
        Solution: (related to Problem: The Four Frogs)
        
        Solution: (related to Problem: The Four Kangaroos)
        
        Solution: (related to Problem: The Four Knights' Tours)
        
        Solution: (related to Problem: The Greyhound Puzzle)
        
        Solution: (related to Problem: The Kennel Puzzle)
        
        Solution: (related to Problem: The Languishing Maiden)
        
        Solution: (related to Problem: The Lion And The Man)
        
        Solution: (related to Problem: The Mandarin's Puzzle)
        
        Solution: (related to Problem: The Queen's Journey)
        
        Solution: (related to Problem: The Queen's Tour)
        
        Solution: (related to Problem: The Rook's Journey)
        
        Solution: (related to Problem: The Rook's Tour)
        
        Solution: (related to Problem: The Scientific Skater)
        
        Solution: (related to Problem: The Star Puzzle)
        
        Solution: (related to Problem: The Two Pawns)
        
        Solution: (related to Problem: The Yacht Race)
      - Statical Chess Puzzles (25)
        
        Solution: (related to Problem: A Problem in Mosaics)
        
        Solution: (related to Problem: A Puzzle With Pawns)
        
        Solution: (related to Problem: Bachet's Square)
        
        Solution: (related to Problem: Bishops in Convocation)
        
        Solution: (related to Problem: Bishops — guarded)
        
        Solution: (related to Problem: Bishops — unguarded)
        
        Solution: (related to Problem: Lion-hunting)
        
        Solution: (related to Problem: Queens And Bishop Puzzle)
        
        Solution: (related to Problem: The Amazons)
        
        Solution: (related to Problem: The Coloured Counters)
        
        Solution: (related to Problem: The Crowded Chessboard)
        
        Solution: (related to Problem: The Eight Queens)
        
        Solution: (related to Problem: The Eight Rooks)
        
        Solution: (related to Problem: The Eight Stars)
        
        Solution: (related to Problem: The Five Crescents of Byzantium)
        
        Solution: (related to Problem: The Five Dogs Puzzle)
        
        Solution: (related to Problem: The Forty-nine Counters)
        
        Solution: (related to Problem: The Four Lions)
        
        Solution: (related to Problem: The Gentle Art Of Stamp-licking)
        
        Solution: (related to Problem: The Hat-peg Puzzle)
        
        Solution: (related to Problem: The Knight-guards)
        
        Solution: (related to Problem: The Southern Cross)
        
        Solution: (related to Problem: The Thirty-six Letter Blocks)
        
        Solution: (related to Problem: The Three Sheep)
        
        Solution: (related to Problem: Under the Veil)
      - The Chessboard (7)
        
        Solution: (related to Problem: Boards With An Odd Number Of Squares)
        
        Solution: (related to Problem: Chequered Board Divisions)
        
        Solution: (related to Problem: Lions And Crowns)
        
        Solution: (related to Problem: The Abbot's Window)
        
        Solution: (related to Problem: The Chessboard Sentence)
        
        Solution: (related to Problem: The Chinese Chessboard)
        
        Solution: (related to Problem: The Grand Lama's Problem)
      - Various Chess Puzzles (16)
        
        Solution: (related to Problem: An Amazing Dilemma)
        
        Solution: (related to Problem: Ancient Chinese Puzzle)
        
        Solution: (related to Problem: Checkmate!)
        
        Solution: (related to Problem: Chessboard Solitaire)
        
        Solution: (related to Problem: Counter Solitaire)
        
        Solution: (related to Problem: Counting The Rectangles)
        
        Solution: (related to Problem: Immovable Pawns)
        
        Solution: (related to Problem: Queer Chess)
        
        Solution: (related to Problem: Setting The Board)
        
        Solution: (related to Problem: Stalemate)
        
        Solution: (related to Problem: The Crusader)
        
        Solution: (related to Problem: The Forsaken King)
        
        Solution: (related to Problem: The Monstrosity)
        
        Solution: (related to Problem: The Rookery)
        
        Solution: (related to Problem: The Six Pawns)
        
        Solution: (related to Problem: Thirty-six Mates)
    - Combination And Group Problems (26)
      - Solution: (related to Problem: A Dormitory Puzzle)
      - Solution: (related to Problem: A Puzzle for Card-players)
      - Solution: (related to Problem: A Tennis Tournament)
      - Solution: (related to Problem: An Acrostic Puzzle)
      - Solution: (related to Problem: Building The Tetrahedron)
      - Solution: (related to Problem: Counter Crosses)
      - Solution: (related to Problem: Fifteen Letter Puzzle)
      - Solution: (related to Problem: King Arthur's Knights)
      - Solution: (related to Problem: Painting A Pyramid)
      - Solution: (related to Problem: Painting The Die)
      - Solution: (related to Problem: The Antiquary's Chain)
      - Solution: (related to Problem: The Barrels Of Balsam)
      - Solution: (related to Problem: The City Luncheons)
      - Solution: (related to Problem: The Cross Target)
      - Solution: (related to Problem: The Eight Villas)
      - Solution: (related to Problem: The Fifteen Dominoes)
      - Solution: (related to Problem: The Four Postage Stamps)
      - Solution: (related to Problem: The Glass Balls)
      - Solution: (related to Problem: The Mouse-trap Puzzle)
      - Solution: (related to Problem: The Nine Schoolboys)
      - Solution: (related to Problem: The Peal Of Bells)
      - Solution: (related to Problem: The Round Table)
      - Solution: (related to Problem: The Sixteen Sheep)
      - Solution: (related to Problem: The Wrong Hats)
      - Solution: (related to Problem: Those Fifteen Sheep)
      - Solution: (related to Problem: Three Men In A Boat)
    - Crossing River Problems (5)
      - Solution: (related to Problem: Crossing The River Axe)
      - Solution: (related to Problem: Crossing The Stream)
      - Solution: (related to Problem: Five Jealous Husbands)
      - Solution: (related to Problem: Stealing The Castle Treasure)
      - Solution: (related to Problem: The Four Elopements)
    - Geometrical Problems (63)
      - Greek Cross Puzzles (4)
        
        Solution: (related to Problem: The Cross and the Triangle)
        
        Solution: (related to Problem: The Folded Cross)
        
        Solution: (related to Problem: The Silk Patchwork)
        
        Solution: (related to Problem: Two Crosses From One)
      - Patchwork Puzzles (8)
        
        Solution: (related to Problem: Another Linoleum Puzzle)
        
        Solution: (related to Problem: Another Patchwork Puzzle)
        
        Solution: (related to Problem: He Banner Puzzle)
        
        Solution: (related to Problem: Linoleum Cutting)
        
        Solution: (related to Problem: Mrs. Perkins's Quilt)
        
        Solution: (related to Problem: Mrs. Smiley's Christmas Present)
        
        Solution: (related to Problem: The Cushion Covers)
        
        Solution: (related to Problem: The Squares Of Brocade)
      - Various Dissection Puzzles (23)
        
        Solution: (related to Problem: A Cutting-out Puzzle)
        
        Solution: (related to Problem: A Tangram Paradox)
        
        Solution: (related to Problem: An Easy Dissection Puzzle)
        
        Solution: (related to Problem: An Easy Square Puzzle)
        
        Solution: (related to Problem: Another Joiner's Problem)
        
        Solution: (related to Problem: Dissecting a Mittre)
        
        Solution: (related to Problem: Mrs. Hobson's Hearthrug)
        
        Solution: (related to Problem: The Betsy Ross Puzzle)
        
        Solution: (related to Problem: The Bun Puzzle)
        
        Solution: (related to Problem: The Cardboard Chain)
        
        Solution: (related to Problem: The Chocolate Squares)
        
        Solution: (related to Problem: The Christmas Pudding)
        
        Solution: (related to Problem: The Dissected Triangle)
        
        Solution: (related to Problem: The Great Monad)
        
        Solution: (related to Problem: The Joiner's Problem)
        
        Solution: (related to Problem: The Landowner's Fences)
        
        Solution: (related to Problem: The Pentagon and Square)
        
        Solution: (related to Problem: The Potato Puzzle)
        
        Solution: (related to Problem: The Seven Pigs)
        
        Solution: (related to Problem: The Square of Veneer)
        
        Solution: (related to Problem: The Table-top and Stools)
        
        Solution: (related to Problem: The Two Horseshoes)
        
        Solution: (related to Problem: The Wizard's Cats)
      - Various Other Geometrical Puzzles (28)
        
        Solution: (related to Problem: A Kite-flying Puzzle)
        
        Solution: (related to Problem: A New Match Puzzle)
        
        Solution: (related to Problem: Concerning Wheels)
        
        Solution: (related to Problem: Drawing A Spiral)
        
        Solution: (related to Problem: Farmer Wurzel's Estate)
        
        Solution: (related to Problem: How To Draw An Oval)
        
        Solution: (related to Problem: How To Make Cisterns)
        
        Solution: (related to Problem: Lady Belinda's Garden)
        
        Solution: (related to Problem: Papa's Puzzle)
        
        Solution: (related to Problem: St. George's Banner)
        
        Solution: (related to Problem: Stealing The Bell-ropes)
        
        Solution: (related to Problem: The Ball Problem)
        
        Solution: (related to Problem: The Cardboard Box)
        
        Solution: (related to Problem: The Clothes Line Puzzle)
        
        Solution: (related to Problem: The Compasses Puzzle)
        
        Solution: (related to Problem: The Cone Puzzle)
        
        Solution: (related to Problem: The Crescent Puzzle)
        
        Solution: (related to Problem: The Eight Sticks)
        
        Solution: (related to Problem: The Four Sons)
        
        Solution: (related to Problem: The Garden Puzzle)
        
        Solution: (related to Problem: The Garden Walls)
        
        Solution: (related to Problem: The Milkmaid Puzzle)
        
        Solution: (related to Problem: The Puzzle Wall)
        
        Solution: (related to Problem: The Sheep-fold)
        
        Solution: (related to Problem: The Six Sheep-pens)
        
        Solution: (related to Problem: The Tethered Goat)
        
        Solution: (related to Problem: The Three Railway Stations)
        
        Solution: (related to Problem: The Yorkshire Estates)
    - Magic Square Problems (14)
      - Solution: (related to Problem: Card Magic Squares)
      - Solution: (related to Problem: Eight Jolly Gaol Birds)
      - Solution: (related to Problem: Nine Jolly Gaol Birds)
      - Solution: (related to Problem: The Eighteen Dominoes)
      - Solution: (related to Problem: The Magic Strips)
      - Solution: (related to Problem: The Siberian Dungeons)
      - Solution: (related to Problem: The Spanish Dungeon)
      - Solution: (related to Problem: The Troublesome Eight)
      - Magic Squares Calculations (2)
        
        Solution: (related to Problem: Magic Squares Of Two Degrees)
        
        Solution: (related to Problem: Two New Magic Squares)
      - Magic Squares Of Primes (4)
        
        Solution: (related to Problem: A Magic Square Of Composites)
        
        Solution: (related to Problem: The Baskets Of Plums)
        
        Solution: (related to Problem: The Magic Knight's Tour)
        
        Solution: (related to Problem: The Mandarin's "T" Puzzle)
    - Measuring Weighing And Packing Problems (11)
      - Solution: (related to Problem: A Packing Puzzle)
      - Solution: (related to Problem: Gold Packing In Russia)
      - Solution: (related to Problem: Mixing The Tea)
      - Solution: (related to Problem: New Measuring Puzzle)
      - Solution: (related to Problem: The Barrel Puzzle)
      - Solution: (related to Problem: The Barrels Of Honey)
      - Solution: (related to Problem: The Doctor's Query)
      - Solution: (related to Problem: The Honest Dairyman)
      - Solution: (related to Problem: The Keg Of Wine)
      - Solution: (related to Problem: The Wassail Bowl)
      - Solution: (related to Problem: Wine And Water)
    - Moving Counter Problems (26)
      - Solution: (related to Problem: A Lodging-house Difficulty)
      - Solution: (related to Problem: A Railway Muddle)
      - Solution: (related to Problem: A Railway Puzzle)
      - Solution: (related to Problem: Arranging The Jampots)
      - Solution: (related to Problem: Boys And Girls)
      - Solution: (related to Problem: Catching The Mice)
      - Solution: (related to Problem: Central Solitaire)
      - Solution: (related to Problem: Plates And Coins)
      - Solution: (related to Problem: Round The Coast)
      - Solution: (related to Problem: The Eccentric Cheesemonger)
      - Solution: (related to Problem: The Educated Frogs)
      - Solution: (related to Problem: The Eight Engines)
      - Solution: (related to Problem: The Exchange Puzzle)
      - Solution: (related to Problem: The Grasshopper Puzzle)
      - Solution: (related to Problem: The Hat Puzzle)
      - Solution: (related to Problem: The Letter Block Puzzle)
      - Solution: (related to Problem: The Motor-garage Puzzle)
      - Solution: (related to Problem: The Nine Almonds)
      - Solution: (related to Problem: The Six Frogs)
      - Solution: (related to Problem: The Ten Apples)
      - Solution: (related to Problem: The Ten Prisoners)
      - Solution: (related to Problem: The Twelve Pennies)
      - Solution: (related to Problem: The Twickenham Puzzle)
      - Solution: (related to Problem: The Victoria Cross Puzzle)
      - Solution: (related to Problem: Torpedo Practice)
      - Solution: The Six Frogs - Solved (related to Problem: The Six Frogs)
    - Points And Lines Problems (8)
      - Solution: (related to Problem: A Plantation Puzzle)
      - Solution: (related to Problem: Cherries And Plums)
      - Solution: (related to Problem: The Burmese Plantation)
      - Solution: (related to Problem: The King And The Castles)
      - Solution: (related to Problem: The Ten Coins)
      - Solution: (related to Problem: The Twelve Mince-pies)
      - Solution: (related to Problem: The Twenty-one Trees)
      - Solution: (related to Problem: Turks And Russians)
    - Problems Concerning Games (14)
      - Solution: (related to Problem: "Strand" Patience)
      - Solution: (related to Problem: A Trick With Dice)
      - Solution: (related to Problem: Card Triangles)
      - Solution: (related to Problem: Dominoes In Progression)
      - Solution: (related to Problem: Slow Cricket)
      - Solution: (related to Problem: The "T" Card Puzzle)
      - Solution: (related to Problem: The Card Frame Puzzle)
      - Solution: (related to Problem: The Cross Of Cards)
      - Solution: (related to Problem: The Domino Frame Puzzle)
      - Solution: (related to Problem: The Five Dominoes)
      - Solution: (related to Problem: The Football Players)
      - Solution: (related to Problem: The Horse-race Puzzle)
      - Solution: (related to Problem: The Motor-car Race)
      - Solution: (related to Problem: The Village Cricket Match)
    - Puzzle Games (7)
      - Solution: (related to Problem: A Match Mystery)
      - Solution: (related to Problem: A War Puzzle Game)
      - Solution: (related to Problem: Puss In The Corner)
      - Solution: (related to Problem: The Cigar Puzzle)
      - Solution: (related to Problem: The Montenegrin Dice Game)
      - Solution: (related to Problem: The Pebble Game)
      - Solution: (related to Problem: The Two Rooks)
    - The Paradox Party (1)
      - Solution: (related to Problem: A Chessboard Fallacy)
    - Unclassified Problems (17)
      - Solution: (related to Problem: A Calendar Puzzle)
      - Solution: (related to Problem: A Chain Puzzle)
      - Solution: (related to Problem: A Wonderful Village)
      - Solution: (related to Problem: Find The Man's Wife)
      - Solution: (related to Problem: Jack And The Beanstalk)
      - Solution: (related to Problem: Pheasant-shooting)
      - Solution: (related to Problem: Placing Halfpennies)
      - Solution: (related to Problem: Such A Getting Upstairs)
      - Solution: (related to Problem: The Dovetailed Block)
      - Solution: (related to Problem: The Five Pennies)
      - Solution: (related to Problem: The Gardener And The Cook)
      - Solution: (related to Problem: The Hymn-board Poser)
      - Solution: (related to Problem: The Industrious Bookworm)
      - Solution: (related to Problem: The Ruby Brooch)
      - Solution: (related to Problem: The Sabbath Puzzle)
      - Solution: (related to Problem: The Tiring Irons)
      - Solution: (related to Problem: Who Was First?)
    - Unicursal And Route Problems (23)
      - Solution: (related to Problem: A Bank Holiday Puzzle)
      - Solution: (related to Problem: A Juvenile Puzzle)
      - Solution: (related to Problem: A Puzzle For Motorists)
      - Solution: (related to Problem: Hannah's Puzzle)
      - Solution: (related to Problem: Inspecting A Mine)
      - Solution: (related to Problem: The Cyclists' Tour)
      - Solution: (related to Problem: The Deified Puzzle)
      - Solution: (related to Problem: The Diamond Puzzle)
      - Solution: (related to Problem: The Dissected Circle)
      - Solution: (related to Problem: The Fifteen Turnings)
      - Solution: (related to Problem: The Fly On The Octahedron)
      - Solution: (related to Problem: The Grand Tour)
      - Solution: (related to Problem: The Honeycomb Puzzle)
      - Solution: (related to Problem: The Icosahedron Puzzle)
      - Solution: (related to Problem: The Level Puzzle)
      - Solution: (related to Problem: The Monk And The Bridges)
      - Solution: (related to Problem: The Motor-car Tour)
      - Solution: (related to Problem: The Sailor's Puzzle)
      - Solution: (related to Problem: The Tube Inspector's Puzzle)
      - Solution: (related to Problem: The Union Jack)
      - Solution: (related to Problem: The Voters' Puzzle)
      - Solution: (related to Problem: Visiting The Towns)
      - Solution: (related to Problem: Water, Gas, And Electricity)
- Graph Theory (2)
  - Solution: (related to Problem: Checking if `$K_5$` is Planar)
  - Solution: (related to Problem: Checking if `$K_{3,3}$` is Planar)
- Number Theory (2)
  - Solution: (related to Problem: Applications of the Jacobi Symbol)
  - Solution: (related to Problem: Calculating Quadratic Residues)
- Probability Theory And Statistics (2)
  - Solution: Application of the Law of Total Probability (related to Problem: Broken Items in the Box)
  - Solution: Application of the Urn Model Without Replacement (related to Problem: Broken Items in the Box II)
- Set Theory (1)
  - Solution: (related to Problem: To Construct a Partition of a Given Set)

History

Epochs (15)
- 11Th Century (1)
  - Epoch: 11th Century
- 12Th Century (1)
  - Epoch: 12th Century
- 13Th Century (1)
  - Epoch: 13th Century
- 14Th Century (1)
  - Epoch: 14th Century
- 15Th Century (1)
  - Epoch: 15th Century
- 16Th Century (1)
  - Epoch: 16th Century
- 17Th Century (1)
  - Epoch: 17th Century
- 18Th Century (1)
  - Epoch: 18th Century
- 19Th Century (1)
  - Epoch: 19th Century
- 20Th Century (1)
  - Epoch: 20th Century
- 21St Century (1)
  - Epoch: 21th Century
- Ancient World (1)
  - Epoch: Ancient World (from 4000 BC to 1 BC)
- Early Middle Ages (1)
  - Epoch: Early Middle Ages
- Late Ancient World (1)
  - Epoch: Late Ancient World (from 1 AD to 499 AD)
- Prehistory (1)
  - Epoch: Prehistory
Topics (7)
- Ancient World (5)
  - Topic: Ancient Chinese Mathematics
  - Topic: Babylonian Mathematics
  - Topic: Egyptian Mathematics
  - Topic: Indian Mathematics
  - Topic: Sumerian Mathematics
- Prehistory (2)
  - Topic: about 4000 BC: Clay Accounting Tokens
  - Topic: to 22 000 BC: Ishango Bone
Persons (3146)
- 11Th Century (12)
  - Person: Abraham Ibn Ezra, ben Meir
  - Person: Adelard Of Bath
  - Person: Al-Nasawi
  - Person: Al-Zarqali
  - Person: Brahmadeva
  - Person: Ha-Nasi, Abraham bar Hiyya
  - Person: Hemchandra, Acharya
  - Person: Hermann Of Reichenau
  - Person: Khayyam, Omar
  - Person: Kua, Shen
  - Person: Sripati
  - Person: Xian, Jia
- 12Th Century (11)
  - Person: Al-Samawal
  - Person: Al-Tusi, Sharaf al-Din
  - Person: Bhaskara (2)
  - Person: De Sacrobosco, Johannes
  - Person: Fibonacci, Leonardo Pisano
  - Person: Gherard Of Cremona
  - Person: Grosseteste, Robert
  - Person: Jabir Ibn Aflah
  - Person: Reinher Of Paderborn
  - Person: Scot, Michael
  - Person: Zhi, Li
- 13Th Century (19)
  - Person: Al-Banna
  - Person: Al-Farisi
  - Person: Al-Maghribi, Muhyi l&amp;#x27;din
  - Person: Al-Samarqandi, Shams al-Din
  - Person: Al-Tusi (2), Nasir al-Din
  - Person: Bacon, Roger
  - Person: Bradwardine, Thomas
  - Person: Campanus Of Novara
  - Person: Gerson, Rabbi Levi Ben
  - Person: Hui (2), Yang
  - Person: Ibn Tibbon, Jacob ben Machir
  - Person: Jiushao, Qin
  - Person: Llull, Ramon
  - Person: Magnus, Saint Albertus
  - Person: Nemorarius, Jordanus
  - Person: Shijie, Zhu
  - Person: Shoujing, Guo
  - Person: William Of Ockham
  - Person: Youqin, Zhao
- 14Th Century (11)
  - Person: Al-Kashi
  - Person: Al-Khalili
  - Person: Al-Rumi, Qadi Zada
  - Person: Albert Of Saxony
  - Person: Beg, Ulugh
  - Person: Brunelleschi, Filippo
  - Person: Madhava Of Sangamagramma
  - Person: Oresme, Nicole
  - Person: Pandit, Narayana
  - Person: Paramesvara
  - Person: Suri, Mahendra
- 15Th Century (30)
  - Person: Al Qalasadi, Abu&amp;#x27;l Hasan ibn Ali
  - Person: Al-Umawi
  - Person: Alberti, Leone Battista
  - Person: Apianus, Petrus
  - Person: Borgi, Piero
  - Person: Chuquet, Nicolas
  - Person: Copernicus, Nicolaus
  - Person: Da Vinci, Leonardo
  - Person: De Bouvelles, Charles
  - Person: De Ortega, Juan
  - Person: Della Francesca, Piero
  - Person: Dürer, Albrecht
  - Person: Ferro, del Scipione
  - Person: Fine, Oronce
  - Person: Lax, Gaspar
  - Person: Maior, John
  - Person: Maurolico, Francesco
  - Person: Nicholas Of Cusa
  - Person: Pacioli, Luca
  - Person: Peurbach, Georg
  - Person: Qushji, Ali
  - Person: Regiomontanus, Johann Müller
  - Person: Ries, Adam
  - Person: Roche, Estienne de La
  - Person: Rudolff, Christoff
  - Person: Somayaji, Nilakantha
  - Person: Stifel, Michael
  - Person: Tunstall, Cuthbert
  - Person: Werner, Johann
  - Person: Widman, Johannes
- 16Th Century (85)
  - Person: Al-Amili, Baha&amp;#x27; al-Din
  - Person: Allen, Thomas
  - Person: Bachet, Claude Gaspar
  - Person: Barocius, Franciscus
  - Person: Beaugrand, Jean
  - Person: Benedetti, Giovanni Battista
  - Person: Biancani, Giuseppe
  - Person: Bombelli, Rafael
  - Person: Brahe, Tycho
  - Person: Bramer, Benjamin
  - Person: Briggs, Henry
  - Person: Bruno, Giordano
  - Person: Bürgi, Jost
  - Person: Cardan, Girolamo
  - Person: Castelli, Benedetto Antonio
  - Person: Cataldi, Pietro Antonio
  - Person: Cavalieri, Bonaventura Francesco
  - Person: Clavius, Christopher
  - Person: Commandino, Frederico
  - Person: Danti, Egnatio Pellegrino Rainaldi
  - Person: Dawei, Cheng
  - Person: Dee, John
  - Person: Delgado, João
  - Person: Della Porta, Giambattista
  - Person: Desargues, Girard
  - Person: Descartes, René
  - Person: Digges, Thomas
  - Person: Faille, Jean Charles de La
  - Person: Faulhaber, Johann
  - Person: Ferrari, Lodovico
  - Person: Fincke, Thomas
  - Person: Frisius, Regnier Gemma
  - Person: Galilei, Galileo
  - Person: Gassendi, Pierre
  - Person: Gellibrand, Henry
  - Person: Ghetaldi, Marino
  - Person: Girard, Albert
  - Person: Golius, Jacobus
  - Person: Gregory Of Saint-Vincent
  - Person: Guangqi, Xu
  - Person: Guldin, Paul
  - Person: Gunter, Edmund
  - Person: Hardy, Claude
  - Person: Harriot, Thomas
  - Person: Hobbes, Thomas
  - Person: Hérigone, Pierre
  - Person: Jungius, Joachim
  - Person: Jyesthadeva
  - Person: Kepler, Johannes
  - Person: Lavanha, João Baptista
  - Person: Liddel, Duncan
  - Person: Magini, Giovanni Antonio
  - Person: Mayr, Simon
  - Person: Mercator, Gerard
  - Person: Mersenne, Marin
  - Person: Monte, del Guidobaldo Marchese
  - Person: Morin, Jean-Baptiste
  - Person: Mydorge, Claude
  - Person: Mästlin, Michael
  - Person: Napier, John
  - Person: Oughtred, William
  - Person: Pascal, Étienne
  - Person: Petit, Pierre
  - Person: Pitiscus, Bartholomeo
  - Person: Ramus, Peter
  - Person: Recorde, Robert
  - Person: Reinhold, Erasmus
  - Person: Rheticus, Georg Joachim von Lauchen
  - Person: Ricci, Matteo
  - Person: Riccioli, Giovanni Battista
  - Person: Salaciense, Pedro Nunes
  - Person: Savile, Sir Henry
  - Person: Scheiner, Christoph
  - Person: Schickard, Wilhelm
  - Person: Snell, Willebrord van Royen
  - Person: Stevin, Simon
  - Person: Tartaglia, Niccolò
  - Person: Turner, Peter
  - Person: Valerio, Luca
  - Person: Van Ceulen, Ludolph
  - Person: Van Lansberge, Johan Philip
  - Person: Van Roomen, Adriaan
  - Person: Vernier, Pierre
  - Person: Viète, François
  - Person: Wittich, Paul
- 17Th Century (145)
  - Person: &amp;#x27;sGravesande, Willem Jacob
  - Person: Aldrich, Henry
  - Person: Angeli, Stefano degli
  - Person: Apáczai, János
  - Person: Arbuthnot, John
  - Person: Arnauld, Antoine
  - Person: Auzout, Adrien
  - Person: Barrow, Isaac
  - Person: Bartholin, Erasmus
  - Person: Berkeley, George
  - Person: Bernoulli (2), Johann
  - Person: Bernoulli (3), Nicolaus
  - Person: Bernoulli (4), Nicolaus
  - Person: Bernoulli, Jacob
  - Person: Borelli, Giovanni Alfonso
  - Person: Bouguer, Pierre
  - Person: Boulliau, Ismael
  - Person: Boyle, Robert
  - Person: Bradley, James
  - Person: Brouncker, William
  - Person: Camus, Charles Étienne Louis
  - Person: Caramuel, Juan
  - Person: Carré, Louis
  - Person: Cassini (2), Jacques
  - Person: Cassini, Giovanni Domenico
  - Person: Castel, Louis Bertrand
  - Person: Ceva (2), Tommaso
  - Person: Ceva, Giovanni
  - Person: Clarke, Samuel
  - Person: Cocker, Edward
  - Person: Coley, Henry
  - Person: Collins, John
  - Person: Colson, John
  - Person: Cotes, Roger
  - Person: Craig, John
  - Person: Cunitz, Maria
  - Person: De Beaune, Florimond
  - Person: De Bessy, Bernard Frénicle
  - Person: De Billy, Jacques
  - Person: De Carcavi, Pierre
  - Person: De Fermat, Pierre
  - Person: De Fontenelle, Bernard le Bovier
  - Person: De L&amp;#x27;Hôpital, Guillaume
  - Person: De Lagny, Thomas Fantet
  - Person: De Maupertuis, Pierre Louis Moreau
  - Person: De Moivre, Abraham
  - Person: De Molières, Joseph Privat
  - Person: De Montmort, Pierre Rémond
  - Person: De Roberval, Gilles Personne
  - Person: De Sluze, René François Walter
  - Person: De Witt, Jan
  - Person: Dechales, Claude François Milliet
  - Person: Delamain, Richard
  - Person: Doppelmayr, Johann Gabriel
  - Person: Fabri, Honoré
  - Person: Fagnano, Giulio
  - Person: Flamsteed, John
  - Person: Fèvre, Jean Le
  - Person: Goldbach, Christian
  - Person: Gongora, Siguenza y
  - Person: Grandi, Luigi Guido
  - Person: Greaves, John
  - Person: Gregory (2), James
  - Person: Gregory (3), David
  - Person: Grimaldi, Francesco Maria
  - Person: Guarini, Guarino
  - Person: Hadley, John
  - Person: Halley, Edmond
  - Person: Hayes, Charles
  - Person: Heins, Valentin
  - Person: Hermann, Jakob
  - Person: Hevelius, Johannes
  - Person: Hire, Philippe de La
  - Person: Hooke, Robert
  - Person: Horrocks, Jeremiah
  - Person: Hudde, Johann van Waveren
  - Person: Huygens, Christiaan
  - Person: Jagannatha
  - Person: Jones, William
  - Person: Juecheng, Mei
  - Person: Kamalakara
  - Person: Katahiro, Takebe
  - Person: Keill, John
  - Person: Kirch, Maria Margarethe Winckelmann
  - Person: Koopman, Elisabetha
  - Person: Lamy, Bernard
  - Person: Machin, John
  - Person: Maclaurin, Colin
  - Person: Magnitsky, Leonty Filippovich
  - Person: Malebranche, Nicolas
  - Person: Manfredi (2), Gabriele
  - Person: Manfredi, Eustachio
  - Person: Meissner, Heinrich
  - Person: Mengoli, Pietro
  - Person: Mercator (2), Nicolaus
  - Person: Mohr, Georg
  - Person: Molyneux (2), Samuel
  - Person: Molyneux, William
  - Person: Moore, Jonas
  - Person: More, Henry
  - Person: Mouton, Gabriel
  - Person: Mylon, Claude
  - Person: Neile, William
  - Person: Newton, Sir Isaac
  - Person: Ozanam, Jacques
  - Person: Papin, Denis
  - Person: Pascal (2), Blaise
  - Person: Pell, John
  - Person: Picard, Jean
  - Person: Poleni, Giovanni
  - Person: Rahn, Johann Heinrich
  - Person: Rampinelli, Ramiro
  - Person: Raphson, Joseph
  - Person: Reyneau, Charles René
  - Person: Riccati, Jacopo Francesco
  - Person: Ricci (2), Michelangelo
  - Person: Richer, Jean
  - Person: Rolle, Michel
  - Person: Saccheri, Giovanni Girolamo
  - Person: Saunderson, Nicholas
  - Person: Saurin, Joseph
  - Person: Seki, Takakazu Shinsuke
  - Person: Seok-Jeong, Choi
  - Person: Sharp, Abraham
  - Person: Simson, Robert
  - Person: Stampioen, Jan Jansz de Jonge
  - Person: Stirling, James
  - Person: Tacquet, Andrea
  - Person: Taylor, Brook
  - Person: Tenneur, Jacques Alexandre Le
  - Person: Torricelli, Evangelista
  - Person: Van Heuraet, Hendrik
  - Person: Van Schooten, Frans
  - Person: Varignon, Pierre
  - Person: Verbiest, Ferdinand
  - Person: Viviani, Vincenzo
  - Person: Vlacq, Adriaan
  - Person: Von Leibniz, Gottfried Wilhelm
  - Person: Von Tschirnhaus, Ehrenfried Walter
  - Person: Wallis, John
  - Person: Ward, Seth
  - Person: Wending, Mei
  - Person: Whiston, William
  - Person: Wilkins, John
  - Person: Wren, Sir Christopher
- 18Th Century (252)
  - Person: Adrain, Robert
  - Person: Aepinus, Franz Maria Ulrich Theodosius
  - Person: Agnesi, Maria Gaëtana
  - Person: Ajima, Chokuyen Naonobu
  - Person: Ampère, André-Marie
  - Person: Arago, Dominique François Jean
  - Person: Arbogast, Louis François Antoine
  - Person: Argand, Jean Robert
  - Person: Atwood, George
  - Person: Babbage, Charles
  - Person: Banneker, Benjamin
  - Person: Barlow, Peter
  - Person: Bartels, Johann Christian Martin
  - Person: Bassi, Laura Maria Catarina
  - Person: Bayes, Thomas
  - Person: Bernoulli (5), Daniel
  - Person: Bernoulli (6), Johann
  - Person: Bernoulli (7), Johann
  - Person: Bernoulli (8), Jacob
  - Person: Bertins, Alexis Fontaine des
  - Person: Bessel, Friedrich Wilhelm
  - Person: Bidone, Giorgio
  - Person: Bienaymé, Jules
  - Person: Binet, Jacques Philippe Marie
  - Person: Biot, Jean Baptiste
  - Person: Bland, Miles
  - Person: Bliss, Nathaniel
  - Person: Bobillier, Étienne E
  - Person: Bolyai, Farkas
  - Person: Bolzano, Bernard Placidus Johann Nepomuk
  - Person: Bonnycastle, John
  - Person: Bordoni, Antonio Maria
  - Person: Boscovich, Ruggero Giuseppe
  - Person: Bossut, Charles
  - Person: Bouvard, Alexis
  - Person: Bowditch, Nathaniel
  - Person: Braikenridge, William
  - Person: Brashman, Nikolai Dmetrievich
  - Person: Brianchon, Charles Julien
  - Person: Bring, Erland Samuel
  - Person: Brinkley, John Mortimer
  - Person: Brisson, Barnabé
  - Person: Burckhardt, Johann Karl
  - Person: Buée, Adrien Quentin
  - Person: Bélanger, Jean-Baptiste
  - Person: Bézout, Étienne
  - Person: Calandrini, Jean-Louis
  - Person: Canard, Nicolas-François
  - Person: Carlyle, Thomas
  - Person: Carnot (2), Sadi
  - Person: Carnot, Lazare Nicolas Marguérite
  - Person: Casamayor, María Andresa
  - Person: Cassini (3), Dominique
  - Person: Castillon, Johann Francesco Melchiore Salvemini
  - Person: Cauchy, Augustin Louis
  - Person: Celsius, Anders
  - Person: Champollion, Jean-François
  - Person: Chasles, Michel
  - Person: Clairaut, Alexis Claude
  - Person: Clapeyron, Benoit Paul Émile
  - Person: Condamine, Charles Marie de La
  - Person: Cramer, Gabriel
  - Person: Crelle August Leopold
  - Person: Cruickshank, John
  - Person: D&amp;#x27;Alembert, Jean
  - Person: D&amp;#x27;Arcy, Patrick
  - Person: Da Cunha, José Anastácio
  - Person: Da Rocha, Monteiro
  - Person: Dandelin, Germinal Pierre
  - Person: Davies, Griffith
  - Person: De Boislaurent, Ferdinand François Désiré Budan
  - Person: De Borda, Jean Charles
  - Person: De Bougainville, Louis Antoine
  - Person: De Buffon, Georges Louis Leclerc Comte
  - Person: De Condorcet, Marquis
  - Person: De Coriolis, Gaspard Gustave
  - Person: De Coulomb, Charles Augustin
  - Person: De Fourcy, Louis Lefébure
  - Person: De Lacaille, Nicolas-Louis
  - Person: De Lalande, Joseph-Jérôme Lefrançais
  - Person: De Prony, Gaspard Clair François Marie Riche
  - Person: De Thury, César-François Cassini
  - Person: De Tinseau, D&amp;#x27;Amondans Charles
  - Person: De Wronski, Josef-Maria Hoëné
  - Person: Delambre, Jean Baptiste Joseph
  - Person: Deparcieux, Antoine
  - Person: Dirksen, Enno Heeren
  - Person: Du Châtelet, Émilie
  - Person: Du Séjour, Achille Pierre Dionis
  - Person: Duhamel, Jean Marie Constant
  - Person: Dupin, Pierre Charles François
  - Person: Emerson, William
  - Person: Encke, Johann Franz
  - Person: Euler, Leonhard
  - Person: Fagnano (2), Giovanni
  - Person: Fallows, Fearon
  - Person: Faraday, Michael
  - Person: Farey, John
  - Person: Fergola, Nicola
  - Person: Finck, Pierre-Joseph-Étienne
  - Person: Flauti, Vincenzo
  - Person: Fourier, Jean Baptiste Joseph
  - Person: Francoeur, Louis Benjamin
  - Person: Franklin, Benjamin
  - Person: Français (2), Jacques
  - Person: Français, François
  - Person: Fresnel, Augustin Jean
  - Person: Frisi, Paolo
  - Person: Fuller, Thomas
  - Person: Fuss, Nicolaus
  - Person: Gauss, Johann Carl Friedrich
  - Person: Gergonne, Joseph Diaz
  - Person: Germain, Marie-Sophie
  - Person: Gerstner, František Josef
  - Person: Giannini, Pietro
  - Person: Giordano, Annibale
  - Person: Girard (2), Pierre-Simon
  - Person: Glenie, James
  - Person: Gompertz, Benjamin
  - Person: Green, George
  - Person: Gregory (4), Olinthus
  - Person: Gräffe, Karl
  - Person: Gudermann, Christoph
  - Person: Hachette, Jean Nicolas Pierre
  - Person: Haldane, Robert
  - Person: Hallerstein, Augustin
  - Person: Hamilton, William
  - Person: Harlay, Marie-Jeanne Amélie
  - Person: Hatvani, István
  - Person: Hecht, Daniel Friedrich
  - Person: Hellins, John
  - Person: Herschel (2), Caroline
  - Person: Herschel (3), Caroline Lucretia
  - Person: Herschel, William
  - Person: Hindenburg, Carl Friedrich
  - Person: Holmboe, Bernt Michael
  - Person: Hopkins, William
  - Person: Horner, William George
  - Person: Hutton (2), Charles
  - Person: Hutton, James
  - Person: Ivory, James
  - Person: Jacquier, François
  - Person: Juan, Jorge
  - Person: Karsten, Wenceslaus Johann Gustav
  - Person: Klügel, Georg
  - Person: Kramp, Christian
  - Person: Kulik, Jakob Philipp
  - Person: Kästner, Abraham
  - Person: König, Samuel
  - Person: Lacroix, Sylvestre François
  - Person: Lagrange, Joseph-Louis
  - Person: Lambert, Johann Heinrich
  - Person: Lamé, Gabriel
  - Person: Landen, John
  - Person: Laplace, Pierre-Simon
  - Person: Lebesgue, Victor Amédée
  - Person: Legendre, Adrien-Marie
  - Person: Lepaute, Nicole-Reine Etable de Labrière
  - Person: Leslie, John
  - Person: Lexell, Anders Johan
  - Person: Lhuilier, Simon Antoine Jean
  - Person: Lloyd, Bartholomew
  - Person: Lobachevsky, Nikolai Ivanovich
  - Person: Lorgna, Antonio Maria
  - Person: Léger, Émile
  - Person: Malfatti, Gian Francesco
  - Person: Malus, Étienne Louis
  - Person: Marescotti, Pietro Abbati
  - Person: Mascheroni, Lorenzo
  - Person: Maseres, Francis
  - Person: Maskelyne, Nevil
  - Person: Mathieu, Claude-Louis
  - Person: Mayer, Tobias
  - Person: Mollweide, Karl Brandan
  - Person: Monge, Gaspard
  - Person: Montucla, Jean Étienne
  - Person: Morgan, William
  - Person: Morin (2), Arthur Jules
  - Person: Mourey, C. V.
  - Person: Mutis, José
  - Person: Méchain, Pierre
  - Person: Möbius, August
  - Person: Navier, Claude Louis Marie Henri
  - Person: Neumann, Franz
  - Person: Nicollet, Jean-Nicolas
  - Person: Ohm (2), Martin
  - Person: Ohm, Georg Simon
  - Person: Olivier, Théodore
  - Person: Osipovsky, Timofei Fedorovic
  - Person: Paman, Roger
  - Person: Paoli, Pietro
  - Person: Parseval, Marc-Antoine
  - Person: Peacock, George
  - Person: Petit (2), Aléxis Thérèse
  - Person: Pfaff, Johann Friedrich
  - Person: Piazzi, Giuseppe
  - Person: Plana, Giovanni Antonio Amedeo
  - Person: Playfair, John
  - Person: Poinsot, Louis
  - Person: Poisson, Siméon Denis
  - Person: Poncelet, Jean Victor
  - Person: Price, Richard
  - Person: Puissant, Louis
  - Person: Quetelet, Lambert Adolphe Jacques
  - Person: Ramsden, Jesse
  - Person: Reynaud, Antoine-André-Louis
  - Person: Riccati (2), Vincenzo
  - Person: Riccati (3), Giordano
  - Person: Richard, Louis
  - Person: Rittenhouse, David
  - Person: Robins, Benjamin
  - Person: Rodrigues, Benjamin Olinde
  - Person: Ruffini, Paolo
  - Person: Rui, Li
  - Person: Saint-Venant, Jean Claude
  - Person: Savart, Félix
  - Person: Savary, Felix
  - Person: Scherk, Heinrich Ferdinand
  - Person: Servois, François Joseph
  - Person: Simpson, Thomas
  - Person: Somerville, Mary Fairfax Greig
  - Person: Spence, William
  - Person: Steiner, Jakob
  - Person: Stewart (2), Dugald
  - Person: Stewart, Matthew
  - Person: Stone, Edmund
  - Person: Strong, Theodore
  - Person: Taurinus, Franz Adolph
  - Person: Terrot, Charles Hughes
  - Person: Tetens, Johannes Nikolaus
  - Person: Thomson, James
  - Person: Trail, William
  - Person: Troughton, Edward
  - Person: Vandermonde, Alexandre-Théophile
  - Person: Vilant, Nicolas
  - Person: Vince, Samuel
  - Person: Von Segner, Johann Andreas
  - Person: Von Staudt, Karl Georg Christian
  - Person: Von Vega, Georg Freiherr
  - Person: Wallace, William
  - Person: Walsh, John
  - Person: Waring, Edward
  - Person: Wessel, Caspar
  - Person: West, John
  - Person: Whewell, William
  - Person: Whish, Charles Matthew
  - Person: Wilson (2), John
  - Person: Wilson, Alexander
  - Person: Woodhouse, Robert
  - Person: Yasuaki, Aida
  - Person: Young, Thomas
  - Person: Yuan, Ruan
- 19Th Century (1211)
  - Person: Abbe, Ernst
  - Person: Abbott, Edwin
  - Person: Abel, Niels Henrik
  - Person: Abraham, Max
  - Person: Abramescu, Nicolae
  - Person: Ackermann, Wilhelm
  - Person: Adams (2), Edwin P.
  - Person: Adams (3), Doris
  - Person: Adams, John Couch
  - Person: Adler, August
  - Person: Afanassjewa, Tatiana Alexeyevna
  - Person: Ahrens, Wilhelm Ernst Martin Georg
  - Person: Airey, John Robinson
  - Person: Airy, George Biddell
  - Person: Aitken, Alexander Craig
  - Person: Aiyar, V. Ramaswami
  - Person: Alasia, Cristoforo
  - Person: Albanese, Giacomo
  - Person: Alexander (2), James Waddell
  - Person: Alexander, Archie
  - Person: Alison, John
  - Person: Allardice, Robert Edgar
  - Person: Allman, George Johnston
  - Person: Amaldi, Ugo
  - Person: Amberg, Ernst Julius
  - Person: Amoroso, Luigi
  - Person: Amsler, Jacob
  - Person: Anderson, Oskar Johann Viktor
  - Person: Andoyer, Henri
  - Person: Andreev, Konstantin Alekseevich
  - Person: Angelescu, Aurel
  - Person: Angheluta, Theodor
  - Person: Anstice, Robert Richard
  - Person: Antoine, Louis Auguste
  - Person: Appell, Paul Emile
  - Person: Archibald (2), Raymond Clare
  - Person: Archibald, James
  - Person: Aronhold, Siegfried Heinrich
  - Person: Arthur, William
  - Person: Artin, Emil
  - Person: Arvesen, Ole Peder
  - Person: Arzelà, Cesare
  - Person: Ascoli, Guido
  - Person: Augustus, De Morgan
  - Person: Ayrton, Phoebe Sarah Hertha Marks
  - Person: Ayyangar, A. A. Krishnaswami
  - Person: Bachelier, Louis
  - Person: Bachiller, Tomás Rodríguez
  - Person: Bachmann, Paul Gustav Heinrich
  - Person: Bacon (2), Clara
  - Person: Badoureau, Albert
  - Person: Bagnera, Giuseppe
  - Person: Baillaud, Édouard Benjamin
  - Person: Baire, René-Louis
  - Person: Baker (2), Bevan Braithwaite
  - Person: Baker, Henry Frederick
  - Person: Baldwin, Frank Stephen
  - Person: Ball (2), Robert Stawell
  - Person: Ball, Robert
  - Person: Balmer, Johann Jakob
  - Person: Banach, Stefan
  - Person: Banachiewicz, Tadeusz
  - Person: Barbier, Joseph Émile
  - Person: Barclay, Andrew Jeffrey Gunion
  - Person: Barker, Thomas
  - Person: Barkla, Charles Glover
  - Person: Barlow (2), Crossley
  - Person: Barnes, Ernest
  - Person: Bartel, Kazimierz Władysław
  - Person: Bashforth, Francis
  - Person: Basset, Alfred Barnard
  - Person: Basso, Giuseppe
  - Person: Bateman, Harry
  - Person: Battaglini, Giuseppe
  - Person: Bauer, Mihály
  - Person: Baxter, Agnes Sime
  - Person: Beale, Dorothea
  - Person: Beattie, John Carruthers
  - Person: Beatty, Samuel
  - Person: Behnke, Heinrich
  - Person: Bell (2), Eric Temple
  - Person: Bell, Robert J. T.
  - Person: Bellavitis, Giusto
  - Person: Beltrami, Eugenio
  - Person: Bendixson, Ivar Otto
  - Person: Bennett, Geoffrey Thomas
  - Person: Bergman, Stefan
  - Person: Bernays, Paul Isaac
  - Person: Bernstein (2), Sergei
  - Person: Bernstein, Felix
  - Person: Bertillon, Adolphe-Louis Jacques
  - Person: Bertini, Eugenio
  - Person: Bertrand, Joseph Louis François
  - Person: Berwald, Ludwig
  - Person: Berwick, William Edward Hodgson
  - Person: Berzolari, Luigi
  - Person: Besicovitch, Abram Samoilovitch
  - Person: Bessel-Hagen, Erich
  - Person: Betti, Enrico
  - Person: Beyel, Christian
  - Person: Bianchi, Luigi
  - Person: Bieberbach, Ludwig Georg Elias Moses
  - Person: Bigourdan, Guillaume
  - Person: Bilimovic, Anton Dimitrija
  - Person: Birkhoff, George David
  - Person: Bisacre, Frederick Francis Percival
  - Person: Bjerknes (2), Vilhelm
  - Person: Bjerknes, Carl
  - Person: Blackburn, Hugh
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- 20Th Century (1234)
  - Person: Aaboe, Asger Hartvig
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  - Person: Pless, Vera
  - Person: Plessner, Abraham Ezechiel
  - Person: Pogorelov, Aleksei Vasilevich
  - Person: Polkinghorne, John Charlton
  - Person: Polozii, Georgii Nikolaevich
  - Person: Pompilj, Giuseppe
  - Person: Pontryagin, Lev Semenovich
  - Person: Popken, Jan
  - Person: Pople, John Anthony
  - Person: Popov, Blagoj Sazdov
  - Person: Popoviciu (2), Elena Moldovan
  - Person: Popoviciu, Tiberiu
  - Person: Postnikov, Mikhail Mikhailovich
  - Person: Potapov, Vladimir Petrovich
  - Person: Potts, Renfrey Burnard
  - Person: Povzner, Aleksandr Yakovlevich
  - Person: Praeger, Cheryl Elisabeth
  - Person: Prager, William
  - Person: Preston, Gordon Bamford
  - Person: Prodi, Giovanni
  - Person: Prokhorov, Yurii Vasilevich
  - Person: Puri, Madan Lal
  - Person: Péter, Rózsa
  - Person: Quillen, Daniel Gray
  - Person: Quine, Willard Van Orman
  - Person: Rado, Richard
  - Person: Radó (2), Ferenc
  - Person: Rajagopal, Cadambathur Tiruvenkatacharlu
  - Person: Rallis, Stephen James
  - Person: Ramanathan, Kollagunta Gopalaiyer
  - Person: Ramanujam, Chidambaram Padmanabhan
  - Person: Ramsey, Frank Plumpton
  - Person: Rankin, Robert Alexander
  - Person: Rao, Calyampudi Radhakrishna
  - Person: Rapcsák, András
  - Person: Rasiowa, Helena
  - Person: Ratner, Marina
  - Person: Rayner, Margaret
  - Person: Ree, Rimhak
  - Person: Reeb, Georges Henri
  - Person: Rees (2), David
  - Person: Rees, Mina Spiegel
  - Person: Reichardt, Hans
  - Person: Reiner, Irving
  - Person: Reizins, Linards Eduardovich
  - Person: Rejewski, Marian Adam
  - Person: Rellich, Franz
  - Person: Rennie, Basil Cameron
  - Person: Reuter, Harry
  - Person: Rhodes, Ida
  - Person: Ribeiro, Pilar
  - Person: Ribenboim, Paulo
  - Person: Ricci (3), Giovanni
  - Person: Rigby, John Frankland
  - Person: Righini, Guglielmo
  - Person: Ringrose, John Robert
  - Person: Roach, Gary
  - Person: Robb, Richard Alexander
  - Person: Robbins, Herbert Ellis
  - Person: Robertson (2), Edmund
  - Person: Robertson, Howard Percy
  - Person: Robinson (2), Raphael
  - Person: Robinson (3), Abraham
  - Person: Robinson (4), Julia Bowman
  - Person: Robinson, G. de B.
  - Person: Rocard, Yves-André
  - Person: Rogers (2), Claude Ambrose
  - Person: Rohrbach, Hans
  - Person: Rokhlin, Vladimir Abramovich
  - Person: Romberg, Werner
  - Person: Room, Thomas Gerald
  - Person: Rota, Gian-Carlo
  - Person: Roth (2), Klaus
  - Person: Roth, Leonard
  - Person: Rothblum, Uriel George
  - Person: Routledge, Norman Arthur
  - Person: Roy, Samarendra Nath
  - Person: Rudin (2), Mary Ellen
  - Person: Rudin, Walter
  - Person: Rudolph, Daniel Jay
  - Person: Rund, Hanno
  - Person: Ruse, Harold Stanley
  - Person: Rutherford, Daniel Edwin
  - Person: Rutishauser, Heinz
  - Person: Rédei, László
  - Person: Rényi, Alfréd
  - Person: Różycki, Jerzy
  - Person: Sachs, Horst
  - Person: Sadler, Donald
  - Person: Sadosky (2), Cora
  - Person: Sadosky, Manuel
  - Person: Saitoti, George
  - Person: Samarskii, Alexander Andreevich
  - Person: Samelson, Hans
  - Person: Samoilenko, Anatoly Mykhailovych
  - Person: Samuel, Pierre
  - Person: Santaló, Luís Antoni
  - Person: Sargent, Winifred Lydia Caunden
  - Person: Sasaki, Shigeo
  - Person: Sato, Mikio
  - Person: Savage, Leonard Jimmie
  - Person: Sawyer, Warwick
  - Person: Schafer, Alice Turner
  - Person: Schatten, Robert
  - Person: Schattschneider, Doris
  - Person: Scheffé, Henry
  - Person: Schelp, Richard Herbert
  - Person: Schiffer, Menahem Max
  - Person: Schmetterer, Leopold
  - Person: Schmid, Hermann Ludwig
  - Person: Schmidt (4), Friedrich Karl
  - Person: Schmidt (5), Wolfgang
  - Person: Schneider, Theodor
  - Person: Schoen, Richard Melvin
  - Person: Schoenberg, Isaac Jacob
  - Person: Scholz (2), Arnold
  - Person: Schramm, Oded
  - Person: Schreier, Otto
  - Person: Schubert (2), Hans
  - Person: Schwartz (2), Laurent Moise
  - Person: Schwartz (3), Jacob T.
  - Person: Schwartz, Marie-Hélène
  - Person: Schwarz (2), Stefan
  - Person: Schwerdtfeger, Hans Wilhelm Eduard
  - Person: Schwinger, Julian Seymour
  - Person: Schäffer, Juan Jorge
  - Person: Schützenberger, Marcel-Paul
  - Person: Scott (5), Elizabeth
  - Person: Segal, Irving Ezra
  - Person: Segel, Lee
  - Person: Segre (2), Beniamino
  - Person: Seidel, Jaap
  - Person: Seidenberg, Abraham
  - Person: Seifert, Karl Johannes Herbert
  - Person: Selberg, Atle
  - Person: Selten, Reinhard
  - Person: Semple, John Greenlees
  - Person: Senechal, Marjorie
  - Person: Seress, Akos
  - Person: Serre, Jean-Pierre Albert Achille
  - Person: Serrin, James Burton
  - Person: Shabazz, Abdulalim
  - Person: Shafarevich, Igor Rostislavovich
  - Person: Shannon, Claude Elwood
  - Person: Sharkovsky, Oleksandr Mikolaiovich
  - Person: Shelah, Saharon
  - Person: Shephard, Geoffrey
  - Person: Shepherdson, John Cedric
  - Person: Sherif, Soraya
  - Person: Shields, Allen Lowell
  - Person: Shimura, Goro
  - Person: Shnirelman, Lev Genrikhovich
  - Person: Shoda, Kenjiro
  - Person: Sigmund, Karl
  - Person: Sikorski, Roman
  - Person: Silva, José Sebastião e
  - Person: Simon, Leon Melvyn
  - Person: Simpson (2), Mary
  - Person: Sims, Charles
  - Person: Sinai, Yakov Grigorevich
  - Person: Singer, Isadore Manuel
  - Person: Singh, Udita Narayana
  - Person: Skopin, Alexander Ivanovich
  - Person: Skorokhod, Anatolii Volodymyrovych
  - Person: Slater, Noel Bryan
  - Person: Sleeman, Brian
  - Person: Smale, Stephen
  - Person: Smith (3), John
  - Person: Smith (4), Karen
  - Person: Smithies, Frank
  - Person: Smullyan, Raymond Merrill
  - Person: Sneddon, Ian Naismith
  - Person: Sobolev, Sergei Lvovich
  - Person: Solitar, Donald Moiseyevitch
  - Person: Soueif, Laila
  - Person: Spanier, Edwin Henry
  - Person: Specht, Wilhelm Otto Ludwig
  - Person: Specker, Ernst Paul
  - Person: Speiser (2), Ambrosius Paul
  - Person: Spence (2), David
  - Person: Spencer (2), Anthony
  - Person: Spencer, Donald Clayton
  - Person: Sperner, Emanuel
  - Person: Spinadel, Vera
  - Person: Spitzer, Lyman
  - Person: Springer, Tonny Albert
  - Person: Srinivasan, Bhama
  - Person: Stallings, John Robert
  - Person: Stampacchia, Guido
  - Person: Stancu, Dimitrie D.
  - Person: Stark, Marceli
  - Person: Steele, Catherine Cassels
  - Person: Steenrod, Norman Earl
  - Person: Stefan (2), Peter
  - Person: Stein (2), Elias Menachem
  - Person: Steinfeld, Ottó
  - Person: Stephens, Clarence Francis
  - Person: Stewartson, Keith
  - Person: Stiefel, Eduard L
  - Person: Stone (2), Marshall Harvey
  - Person: Strassen, Volker
  - Person: Straus, Ernst Gabor
  - Person: Stromme, Stein Arild
  - Person: Stubblefield, Beauregard
  - Person: Stueckelberg, Ernst Carl Gerlach
  - Person: Subbotovskaya, Bella Abramovna
  - Person: Sullivan, Dennis Parnell
  - Person: Sultangazin, Umirzak
  - Person: Sunyer, Ferran
  - Person: Sutton, Oliver
  - Person: Suvorov, Georgii Dmitrievic
  - Person: Suzuki (2), Satoshi
  - Person: Suzuki, Michio
  - Person: Sverdrup, Erling
  - Person: Swart, Hendrika
  - Person: Szafraniec, Franciszek Hugon
  - Person: Szekeres, George
  - Person: Szele, Tibor
  - Person: Szemerédi, Endre
  - Person: Szmielew, Wanda Montlak
  - Person: Szász (2), Domokos
  - Person: Sós, Vera
  - Person: Słupecki, Jerzy
  - Person: Talbot (2), Walter R.
  - Person: Taleb, Nassim
  - Person: Tanaka, Hideo
  - Person: Taniyama, Yutaka
  - Person: Tanner, Cecily
  - Person: Tao, Terence Chi-Shen
  - Person: Tapia, Richard Alfred
  - Person: Tarski, Alfred
  - Person: Tate, John Torrence
  - Person: Taussky-Todd, Olga
  - Person: Taylor (6), Richard
  - Person: Teichmüller, Oswald
  - Person: Temple, George Frederick James
  - Person: Theilheimer, Feodor
  - Person: Thiêm, Lê Văn
  - Person: Thom (2), René
  - Person: Thomason, Robert Wayne
  - Person: Thompson (2), Robert C
  - Person: Thompson (3), John
  - Person: Thompson (4), Abigail
  - Person: Thurston, William Paul
  - Person: Tichy, Pavel
  - Person: Tietz, Horst
  - Person: Tiit, Ene-Margit
  - Person: Tikhonov, Andrei Nikolaevich
  - Person: Timms, Geoffrey
  - Person: Tims, Sydney Rex
  - Person: Tinbergen, Jan
  - Person: Tinney, Sheila Christina Power
  - Person: Tits, Jacques
  - Person: Todd (2), Jack
  - Person: Todd, John Arthur
  - Person: Trahtman, Avraham Naumovich
  - Person: Trakhtenbrot, Boris
  - Person: Trudinger, Neil Sidney
  - Person: Tucker (2), Albert
  - Person: Tukey, John Wilder
  - Person: Turing, Alan Mathison
  - Person: Turán, Paul
  - Person: Tutte, William Thomas
  - Person: Tverberg, Helge
  - Person: Tụy, Hoàng
  - Person: Ugbebor, Olabisi
  - Person: Uhlenbeck (2), Karen
  - Person: Uhlenbeck, George Eugene
  - Person: Ulam, Stanislaw Marcin
  - Person: Urbanik, Kazimierz
  - Person: Ursell, Fritz Joseph
  - Person: Vagner, Viktor Vladimirovich
  - Person: Vajda, Steven
  - Person: Valdivia, Manuel
  - Person: Valiant, Leslie Gabriel
  - Person: Van Dantzig, David
  - Person: Van Kampen, Egbert Rudolf
  - Person: Van Lint, Jacobus Hendricus
  - Person: Vanstone, Ray
  - Person: Varadhan, Sathamangalam Ranga Iyengar Srinivasa
  - Person: Varga (2), Richard Steven
  - Person: Varga, Ottó
  - Person: Vekua, Ilya Nestorovich
  - Person: Velez-Rodriguez, Argelia
  - Person: Verblunsky, Samuel
  - Person: Vernon, Siobhan O&amp;#x27;Shea
  - Person: Viazovska, Maryna
  - Person: Vidav, Ivan
  - Person: Vinti, Calogero
  - Person: Vitushkin, Anatoli Georgievich
  - Person: Vladimirov, Vasilii Sergeevich
  - Person: Voevodsky, Vladimir Aleksandrovich
  - Person: Von Neumann, John
  - Person: Vrănceanu, Gheorghe
  - Person: Waerden, Bartel Leendert van der
  - Person: Wald, Abraham
  - Person: Wales, Muriel Kennett
  - Person: Walker (3), Geoffrey
  - Person: Wall, Hubert
  - Person: Wallace (2), Alexander Doniphan
  - Person: Waller, Derek Arthur
  - Person: Walter, Marion Ilse
  - Person: Walton, Ernest
  - Person: Wang, Hsien Chung
  - Person: Warga, Jack
  - Person: Warner, Mary Wynne
  - Person: Warschawski, Stefan E
  - Person: Washington, Talitha
  - Person: Weber (4), Johanna
  - Person: Wegner, Udo Hugo Helmuth
  - Person: Weil, André Abraham
  - Person: Weise, Karl Heinrich
  - Person: Welchman, William Gordon
  - Person: Wenninger, Magnus Joseph
  - Person: Werner (2), Wendelin
  - Person: Whitehead (2), Henry
  - Person: Whiteside, Derek Thomas
  - Person: Whitney, Hassler
  - Person: Whitrow, Gerald
  - Person: Whittaker (2), John
  - Person: Whyburn (2), William Marvin
  - Person: Whyburn, William
  - Person: Wiegold, James
  - Person: Wielandt, Helmut
  - Person: Wigner, Eugene Paul
  - Person: Wiles, Andrew John
  - Person: Wilf, Herbert Saul
  - Person: Wilkins (2), J. Ernest
  - Person: Wilkinson, James Hardy
  - Person: Wilks, Samuel Stanley
  - Person: Williams (2), Evan James
  - Person: Williams (3), Lloyd
  - Person: Williamson, John
  - Person: Wintner, Aurel Friedrich
  - Person: Witt, Ernst
  - Person: Witten, Edward
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  - Person: Wolfowitz, Jacob
  - Person: Womersley, John
  - Person: Woods, Leslie Colin
  - Person: Wright (2), Edward Maitland
  - Person: Wright (3), Fred
  - Person: Wschebor-Wonsever, Mario Israel
  - Person: Wu (2), Sijue
  - Person: Wu, Wen-Tsun
  - Person: Wussing, Hans
  - Person: Wylie, Shaun
  - Person: Yamabe, Hidehiko
  - Person: Yano, Kentaro
  - Person: Yates, Frank
  - Person: Yau, Shing-Tung
  - Person: Yoccoz, Jean-Christophe
  - Person: Yosida, Kosaku
  - Person: Youden, William John
  - Person: Young (6), Laurence Chisholm
  - Person: Young (7), Lai-Sang
  - Person: Yuan (2), Wang
  - Person: Yushkevich, Adolph Andrei Pavlovich
  - Person: Zaanen, Adriaan Cornelis
  - Person: Zarankiewicz, Kazimierz
  - Person: Zassenhaus, Hans Julius
  - Person: Zeckendorf, Édouard
  - Person: Zeeman, Erik Christopher
  - Person: Zelmanov, Efim Isaakovich
  - Person: Zhautykov, Orymbek
  - Person: Zippin, Leo
  - Person: Zorn, Max August
  - Person: Zuse, Konrad
  - Person: Zygalski, Henryk
  - Person: Zygmund, Antoni Szczepan
  - Person: Ásgeirsson, Leifur
  - Person: Ávila, Artur
  - Person: Łoś, Jerzy Maria Michał
  - Person: Ślebarski, Tadeusz Boleslaw
  - Person: Świerczkowski, Stanisław
  - Person: Țarină, Marian
- Ancient World (57)
  - Person: Ahmes
  - Person: Anaxagoras Of Clazomenae
  - Person: Anaximander Of Miletus
  - Person: Antiphon
  - Person: Apastamba
  - Person: Apollonius Of Perga
  - Person: Archimedes Of Syracuse
  - Person: Archytas Of Tarentum
  - Person: Aristaeus the Elder
  - Person: Aristarchus Of Samos
  - Person: Aristotle
  - Person: Autolycus Of Pitane
  - Person: Baudhayana
  - Person: Bryson Of Heraclea
  - Person: Callippus Of Cyzicus
  - Person: Chrysippus Of Soli
  - Person: Conon Of Samos
  - Person: Democritus Of Abdera
  - Person: Dinostratus
  - Person: Diocles Of Carystus
  - Person: Dionysodorus
  - Person: Empedocles Of Acragas
  - Person: Eratosthenes Of Cyrene
  - Person: Euclid Of Alexandria
  - Person: Eudemus Of Rhodes
  - Person: Eudoxus Of Cnidus
  - Person: Gan De
  - Person: Geminus
  - Person: Heraclides Of Pontus
  - Person: Hipparchus Of Rhodes
  - Person: Hippasus of Metapontum
  - Person: Hippias Of Elis
  - Person: Hippocrates Of Chios
  - Person: Hong, Luoxia
  - Person: Hypsicles Of Alexandria
  - Person: Katyayana
  - Person: Leucippus Of Miletus
  - Person: Manava
  - Person: Menaechmus
  - Person: Nicomedes
  - Person: Oenopides Of Chios
  - Person: Panini
  - Person: Perseus
  - Person: Philon Of Byzantium
  - Person: Plato
  - Person: Pollio, Marcus Vitruvius
  - Person: Posidonius Of Rhodes
  - Person: Pythagoras Of Samos
  - Person: Thales Of Miletus
  - Person: Theaetetus Of Athens
  - Person: Theodorus Of Cyrene
  - Person: Theodosius Of Bithynia
  - Person: Thymaridas Of Paros
  - Person: Xenocrates Of Chalcedon
  - Person: Zeno Of Elea
  - Person: Zeno Of Sidon
  - Person: Zenodorus
- Early Middle Ages (47)
  - Person: Abu Kamil, ibn Aslam Shuja
  - Person: Al-Baghdadi, Abu Mansur ibn Tahir
  - Person: Al-Battani, Abu Abdallah Mohammad ibn Jabir
  - Person: Al-Biruni, Abu Arrayhan Muhammad ibn Ahmad
  - Person: Al-Hasan Banu Musa
  - Person: Al-Jawhari, al-Abbas ibn Said
  - Person: Al-Jayyani, Abu Abd Allah Muhammad ibn Muadh
  - Person: Al-Karaji, Abu Bekr ibn Muhammad ibn Al-Husayn
  - Person: Al-Khazin, Abu Jafar Muhammad ibn Al-Hasan
  - Person: Al-Khujandi, Abu Mahmud Hamid ibn al-Khidr
  - Person: Al-Khwarizmi, Abu Ja&amp;#x27;far Muhammad ibn Musa
  - Person: Al-Kindi, Abu Yusuf Yaqub ibn Ishaq al-Sabbah
  - Person: Al-Mahani, Abu Abd Allah Muhammad ibn Isa
  - Person: Al-Nayrizi, Abu&amp;#x27;l Abbas al-Fadl ibn Hatim
  - Person: Al-Quhi, Abu Sahl Waijan ibn Rustam
  - Person: Al-Sijzi, Abu Said Ahmad ibn Muhammad
  - Person: Al-Uqlidisi, Abu&amp;#x27;l Hasan Ahmad ibn Ibrahim
  - Person: Alcuin
  - Person: Alhazen, Abu Ali Al-Hasan ibn Al-Haytham
  - Person: Aryabhata The Ii
  - Person: Avicenna, Abu Ali al-Husain ibn Abdallah ibn Sina
  - Person: Banu Musa Brothers
  - Person: Bhaskara
  - Person: Brahmagupta
  - Person: Chunfeng, Li
  - Person: Gerbert Of Aurillac
  - Person: Govindasvami
  - Person: Hunayn Ibn Ishaq
  - Person: Ibn Yunus, Abu&amp;#x27;l-Hasan Ali Ibn Abd al-Rahman
  - Person: Ibn Yusuf, Ahmed
  - Person: Ibrahim Ibn Sinan
  - Person: Kushyar Ibn Labban
  - Person: Lalla
  - Person: Mahāvīra
  - Person: Mansur, Abu Nasr ibn Ali ibn Iraq
  - Person: Mohammad Abu&amp;#x27;L-Wafa, Al-Buzjani
  - Person: Musa (2), Ahmad Banu
  - Person: Musa, Jafar Muhammad Banu
  - Person: Prthudakasvami
  - Person: Sankara, Narayana
  - Person: Sinan, Abu ibn Thabit ibn Qurra
  - Person: Sridhara
  - Person: Thabit Ibn Qurra, Al-Sabi
  - Person: Varahamihira
  - Person: Vijayanandi
  - Person: Xiaotong, Wang
  - Person: Yativrsabha
- Late Ancient World (32)
  - Person: Anthemius Of Tralles
  - Person: Aryabhata The Elder
  - Person: Boethius, Anicius Manlius Severinus
  - Person: Chongzhi, Zu
  - Person: Cleomedes
  - Person: Diadochus, Proclus
  - Person: Diophantus Of Alexandria
  - Person: Domninus Of Larissa
  - Person: Eutocius Of Ascalon
  - Person: Geng, Zu
  - Person: Heng, Zhang
  - Person: Heron Of Alexandria
  - Person: Hong (2), Liu
  - Person: Hui, Liu
  - Person: Hypatia Of Alexandria
  - Person: Malchus, Porphyry
  - Person: Marinus Of Neapolis
  - Person: Menelaus Of Alexandria
  - Person: Nicomachus Of Gerasa
  - Person: Pandrosion
  - Person: Pappus Of Alexandria
  - Person: Ptolemy, Claudius
  - Person: Qiujian, Zhang
  - Person: Serenus
  - Person: Simplicius
  - Person: Sporus Of Nicaea
  - Person: Theon Of Alexandria
  - Person: Theon Of Smyrna
  - Person: Yang, Xiahou
  - Person: Yavanesvara
  - Person: Yue, Xu
  - Person: Zi, Sun

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