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.— Charles Hermite; cit. by Gaston Darboux, Eloges académiques et discours, Hermann, Paris 1912, p. 142.
Hermite was born in Dieuze, The Moselle on 24 December 1822, with a deformity in his right foot which would affect his gait for the rest of his life. He was the sixth of seven children of Ferdinand Hermite, and his wife Madeleine Lallemand. His father worked in his mother's family's drapery Business, and also pursued a career as an Artist. The drapery Business relocated to Nancy during 1828 and so did the family.
Hermite wanted to study at the École Polytechnique and during 1841 he took a year preparing for the examinations and was tutored by Eugène Charles Catalan. During 1842 he was admitted to the school. However, after one year Hermite was refused the right to continue his studies because of his disability (École Polytechnique is to this day a military academy). He had to struggle to regain his admission which he won but with strict conditions imposed. Hermite found this unacceptable and decided to quit the École Polytechnique without graduating.
During 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 during 1843 and continued the next year, resulted in 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 during 1847. He married Joseph Bertrand's sister, Louise Bertrand, during 1848.
An inspiring Teacher, Hermite strove to cultivate admiration for simple beauty and discourage rigorous minutiae. His correspondence with Thomas Stieltjes testifies to the great aid he gave those beginning scientific life. His published courses of lectures have exercised a great influence. His important original contributions to pure mathematics, published in the major mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. During 1858 he solved the equation of the fifth degree by elliptic functions; and during 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 during 1882 the same for π.
In a letter to Thomas Joannes Stieltjes during 1893, Hermite remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives."
During 1848, Hermite returned to the École Polytechnique as répétiteur and examinateur d'admission. During 1856 he contracted smallpox. Through the influence of Augustin-Louis Cauchy and of a nun who nursed him, he resumed the practice of his Catholic faith. On 14 July, of that year, he was elected for the vacancy created by the death of Jacques Binet in the Académie des Sciences. During 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 was a post 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.