Charles Hermite

Charles Hermite (French pronunciation: [ʃaʁl ɛʁˈmit]) (December 24, 1822 – January 14, 1901) was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré.

He was the first to prove that e, the base of natural logarithms, is a transcendental number. His methods were later used by Ferdinand von Lindemann to prove that π is transcendental.

In a letter to Thomas Stieltjes in 1893, Hermite famously remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives."

Life

Born at Dieuze, Moselle, 24 December, 1822 he was the son of a salt mine engineer, Ferdinand Hermite. His mother was Madeleine Lallemand. The family moved to run a drapers business in Nancy in 1828 and his father also pursued ambitions as an artist. Charles was the sixth of his parents' seven children.

Charles had a defect in his right foot which meant that from boyhood he moved around with difficulty.

He studied at the Collège de Nancy and then, in Paris, at the Collège Henri IV and at the Lycée Louis-le-Grand.

Hermite wanted to study at the École Polytechnique and he took a year preparing for the examinations and was tutored by Catalan between 1841 and 1842.

In 1842 he entered the École Polytechnique, where he remained as a student for a short time. After one year at the École Polytechnique Hermite was refused the right to continue his studies because of his disability (Ecole Polytechnique is to this day a military academy). He had to fight to regain his place which he won but with strict conditions imposed. Hermite found this unacceptable and decided to leave the École Polytechnique without graduating.

As a boy he read some of the writings of Joseph Louis Lagrange on the solution of numerical equations, and of Carl Gauss on the theory of numbers. In 1842, his first original contribution to mathematics, in which he gave a simple proof of the proposition of Niels Abel concerning the impossibility of obtaining an algebraic solution for the equation of the fifth degree, was published in the "Nouvelles Annales de Mathématiques".

A correspondence with Carl Jacobi, begun in 1843 and continued in 1844, led to the insertion, in the complete edition of Jacobi's works, of two articles by Hermite, one concerning the extension to Abelian functions of one of the theorems of Abel on elliptic functions, and the other concerning the transformation of elliptic functions.

After spending five years working privately towards his degree, in which he befriended eminent mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, he took and passed the examinations for the baccalauréat, which he was awarded in 1847. He married Joseph Bertrand's sister, Louise Bertrand in 1848.

In 1848, Hermite returned to the École Polytechnique as répétiteur and examinateur d'admission. In 1856 he contracted smallpox. Through the influence of Augustin Cauchy and of a nun who nursed him, he resumed the practice of his religion. On 14 July, of that year, he was elected to fill the vacancy created by the death of Jacques Binet in the Académie des Sciences. In 1869, he succeeded Jean-Marie Duhamel as professor of mathematics, both at the École Polytechnique, where he remained until 1876, and in the Faculty of Sciences of Paris, which position he occupied until his death. From 1862 to 1873 he was lecturer at the École Normale Supérieure. Upon his seventieth birthday, on the occasion of his jubilee which was celebrated at the Sorbonne under the auspices of an international committee, he was promoted grand officer of the Légion d'honneur.

He died in Paris, 14 January, 1901, aged 78.

Contribution to mathematics

As a teacher Hermite was inspiring. His correspondence with Thomas Stieltjes testifies to the great aid he gave those entering scientific life. His efforts in teaching were directed not towards too rigorous minuteness, but towards exciting admiration for things simple and beautiful. His published courses of lectures have exercised a wide influence. His important original contributions to pure mathematics, published in the leading mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. In 1858 he solved the equation of the fifth degree by elliptic functions; and in 1873 he proved e, the base of the natural system of logarithms, to be transcendental. This last was used by Ferdinand von Lindemann to prove in 1882 the same for π.

Publications

The following is a list of his works.

* "Sur quelques applications des fonctions elliptiques.", Paris, 1855 Page images from Cornell
* "Cours professé à la Faculté des Sciences", edited by Andoyer, 4th ed., Paris, 1891 Page images from Cornell
* "Correspondance", edited by Baillaud and Bourget, Paris, 1905, 2 vols. PDF Copy from UMDL.

* "Oeuvres de Charles Hermite" were edited by Picard for the Academy of Sciences, 2 vols., Paris, 1905 and 1908. PDF copy from UMDL.

* Hermite, Charles. (1905–1917). Ouvres de Charles Hermite. Gauthier-Villars (reissued by Cambridge University Press, 2009; ISBN 9781108003285)

Quotations

"There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation."

"I shall risk nothing on an attempt to prove the transcendence of π. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort."