** Ludwig Schläfli**'s work was in geometry, arithmetic and function theory. He is best known for the so-called Schläfli symbols which are used to classify polyhedra.

- Although he was only fifteen years old when he entered the Gymnasium, Schläfli was already studying the differential calculus using Kästner's famous book Mathematische Anfangsgründe der Analysis des Unendlichen Ⓣ(Mathematical foundations of infinite analysis).
- In 1834 the University of Bern was founded and it incorporated the Theological School which was an old institution founded in 1528, so at this stage Schläfli automatically became a university student.
- After graduating with a degree in theology in 1836, Schläfli decided to become a school teacher since he had already decided not to pursue an ecclesiastical career.
- Schläfli worked for ten years as a school teacher in Thun.
- Schläfli was an expert linguist speaking many languages including Sanskritt and Rigveda but it was his fluency in French and Italian which proved important as this stage.
- In Bern in 1843 Schläfli met Steiner who was impressed with his language skills and also with his mathematical knowledge.
- Later that year Steiner, Jacobi and Dirichlet travelled to Rome and took Schläfli with them as an interpreter.
- Schläfli gained greatly from discussions with these leading mathematicians, in particular having a daily lesson in number theory from Dirichlet.
- The visit lasted for six months and during that time Schläfli translated some of his companions works into Italian.
- After six months in Italy, Schläfli returned to his teaching post in Thun but he continued to correspond with Steiner till 1856.
- After taking up his appointment at the University of Bern, Schläfli worked on two major investigations.
- The treatise was a long one and it was rejected by the Austrian Academy of Sciences, so Schläfli submitted it to the Berlin Academy of Science.
- In this work Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra.
- Schläfli introduced what is today aclled the Schläfli symbol.
- Most of Schläfli's work was in geometry, arithmetic and function theory.
- Schläfli made an important contribution to non-Euclidean (elliptic) geometry when he proposed that spherical three-dimensional space could be regarded as the surface of a hypersphere in Euclidean four-dimensional space.
- Schläfli knew how to find the volume of a tetrahedron not only in spherical space but also in hyperbolic space, although when he undertook this work in 1852 he was almost certainly unaware of Lobachevsky's work.
- Schläfli published the first complete description of the configuration in An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface.
- Although Schläfli never received full credit for his remarkable achievements during his lifetime, he was elected to the Istituto Lombardo di Scienze e Lettere in Milan (1868), the Göttingen Academy of Sciences (Königliche Gesellschaft der Wissenschaften) (1871), and the Accademia dei Lincei (1883).

Born 15 January 1814, Grasswil, Bern, Switzerland. Died 20 March 1895, Berne, Switzerland.

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Origin Switzerland

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive