**Ferdinand Minding** worked in differential geometry and the theory of surfaces.

- At this time it was typical for university students in this part of the world to spend parts of their undergraduate years at different universities and so, after his two semesters at Halle, Minding went to the University of Berlin where he continued his studies attending courses by Georg Wilhelm Friedrich Hegel (1770-1831) who at that time was giving courses on aesthetics, the philosophy of religion, the philosophy of history, and the history of philosophy.
- Ranke opposed the views of Hegel on the philosophy of history so Minding received an interestingly different approach from these two teachers.
- Except for attending a few lectures, Minding had not studied mathematics at university, so how did he become a mathematics teacher?
- Minding published his thesis, having made some minor changes to it, in Crelle's Journal für die reine und angewandte Mathematik, as Über die Berechnung des Näherungswertes doppelter Integrale Ⓣ(On the calculation of the approximation value of double integrals) (1830).
- In 1830 Minding became a mathematics lecturer at the University of Berlin where he taught the barycentric calculus as presented in the works of August Möbius and published Auflösung einiger Aufgaben der analytischen Geometrie mittels des barycentrischen Calculs Ⓣ(Dissolution of some problems of analytical geometry by barycentric calculus) (1830).
- Minding dropped the more delicate part of Gauss's theory of forms (genera, composition), but added things expected from the perspective of a textbook, for instance, linear Diophantine equations or continued fractions.
- Minding gave courses of lectures on the theory of curves, on analytical dynamics, and on analysis at the School of Architecture.
- In 1842 Lejeune Dirichlet proposed Minding for election to the Berlin Academy of Science but he was not elected at this time and this may have prompted Minding to seek a position away from Berlin.
- Moving to Dorpat meant that Minding became a colleague of Karl Eduard Senff (1810-1849).
- Sadly the collaboration between Minding and Senff was relatively short since Senff died in December 1849.
- However, they were able to jointly supervise the undergraduate studies of Karl Mikhailovich Peterson who later wrote his Candidate's Thesis Über die Biegung der Flächen Ⓣ(On bending of surfaces) advised by Minding.
- While mentioning Minding's famous students we should include Axel Harnack who studied with Minding while an undergraduate but went to Germany for his doctorate.
- At Dorpat, Minding taught algebra, analysis, geometry, probability, mechanics and physics.
- For example, in 1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area.
- Gauss had proved these results in 1825 before either Minding or Bonnet, but he had not published them.
- Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839.
- Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
- In a later article (1840), Minding arrived at another interesting result, though without perceiving its important implications.
- While Minding failed to notice that these formulas agree with those for the hyperbolic plane, established by Lobachevsky in his 'Imaginary geometry' (1837), Beltrami was aware of this fact, which he developed in his 'Attempt'.
- Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics.
- This work won Minding the Demidov prize of the St Petersburg Academy of Sciences in 1861.
- Papers published by Minding from 1868 until the end of his life include (we give English translations of the German or French titles): Proof of a theorem in statics (1868); A rule of forming denominators and numerators in the representation of a continued fraction by an ordinary fraction (1869); On a problem in the probability theory originating from meteor observations (1869); On the method of least squares (1871); On the mean curvature of surfaces (1875); On the curves of shortest circumference on surfaces of revolution (1876); On some isoperimetric problems (1877); Theory of shortest curves on curved surfaces (1878); and On the Theory of the shortest curves over rings with given area on curved surfaces (1878).
- Minding retired in 1883, near the start of this change forced on the university.
- As we mentioned above, Minding was awarded the prestigious Demidov Prize by the St Petersburg Academy of Sciences in 1861.

Born 23 January 1806, Kalisz, Russian Empire (now Poland). Died 3 May 1885, Dorpat, Russia (now Tartu, Estonia).

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Origin Poland

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