**Charles Hermite**'s work in the theory of functions includes the application of elliptic functions to the quintic equation. He published the first proof that $e$ is a transcendental number.

- Ferdinand Hermite was a trained engineer and he worked in this capacity in a salt mine near Dieuse.
- Charles was something of a worry to his parents for he had a defect in his right foot which meant that he moved around only with difficulty.
- Charles attended the Collège de Nancy, then went to Paris where he attended the Collège Henri.
- In some ways Hermite was similar to Galois for he preferred to read papers by Euler, Gauss and Lagrange rather than work for his formal examinations.
- If Hermite neglected the studies that he should have concentrated on, he was showing remarkable research ability publishing two papers while at Louis-le-Grand.
- Again like Galois, Hermite wanted to study at the École Polytechnique and he took a year preparing for the examinations.
- He was tutored by Catalan in 1841-42 and certainly Hermite fared better than Galois had done for he passed.
- After one year at the École Polytechnique Hermite was refused the right to continue his studies because of his disability.
- Hermite did not find these conditions acceptable and decided that he would not graduate from the École Polytechnique.
- Hermite made friends with important mathematicians at this time and frequently visited Joseph Bertrand.
- The letters he exchanged with Jacobi show that Hermite had discovered some differential equations satisfied by theta-functions and he was using Fourier series to study them.
- Hermite may have still been an undergraduate but it is likely that his ideas from around 1843 helped Liouville to his important 1844 results which include the result now known as Liouville's theorem.
- Hermite made important contributions to number theory and algebra, orthogonal polynomials, and elliptic functions.
- In 1849 Hermite submitted a memoir to the Académie des Sciences which applied Cauchy's residue techniques to doubly periodic functions.
- Another topic on which Hermite worked and made important contributions was the theory of quadratic forms.
- On 14 July 1856 Hermite was elected to the Académie des Sciences.
- However, despite this achievement, 1856 was a bad year for Hermite for he contracted smallpox.
- It was Cauchy who, with his strong religious conviction, helped Hermite through the crisis.
- This had a profound effect on Hermite who, under Cauchy's influence, turned to the Roman Catholic religion.
- Cauchy was also a very staunch royalist and Hermite was influenced by him to also become a royalist.
- We made comparisons with Galois earlier on in this article, but with royalist views, Hermite was now completely opposed to the views which the staunch republican Galois had held.
- The next mathematical result by Hermite which we must mention is one for which he is rightly famous.
- Although an algebraic equation of the fifth degree cannot be solved in radicals, a result which was proved by Ruffini and Abel, Hermite showed in 1858 that an algebraic equation of the fifth degree could be solved using elliptic functions.
- In 1862 Hermite was appointed maître de conférence at the École Polytechnique, a position which had been specially created for him.
- Hermite resigned his chair at the École Polytechnique in 1876 but continued to hold the chair at the Sorbonne until he retired in 1897.
- In the 1890s Hermite became much less interested in the new results found by the mathematicians of the next generation.
- The 1870s saw Hermite return to problems which had interested him earlier in his career such as problems concerning approximation and interpolation.
- In 1873 Hermite published the first proof that eee is a transcendental number.
- Using method's similar to those of Hermite, Lindemann established in 1882 that π was also transcendental.
- Many historians of science regret that Hermite, despite doing most of the hard work, failed to use it to prove the result on which would have brought him fame outside the world of mathematics.
- Hermite is now best known for a number of mathematical entities that bear his name: Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices.
- For Hermite certain areas of mathematics were much more interesting than other areas.
- Hermite's great love was for analysis and, not surprisingly, he had a great respect for Weierstrass.
- Poincaré is almost certainly the best known of Hermite's students.
- He once suggested that Hermite's mind did not proceed in logical fashion.
- Hadamard had great respect for Hermite as a teacher.
- Hermite, therefore, disliked Cantor's world, in which a new mathematical world was created.

Born 24 December 1822, Dieuze, Lorraine, France. Died 14 January 1901, Paris, France.

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Algebra, Analysis, Geometry, Number Theory, Special Numbers And Numerals

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