Expelled over a deformed foot, Charles Hermite went on to prove e transcendental
The École Polytechnique turned Charles Hermite away after a single year because of a deformity in his right foot. He never graduated from it, yet came back as an examiner and professor, proved that the number e is transcendental, and gave his name to mathematical tools that later helped put quantum mechanics on rigorous footing.
Christmas Eve 1822 saw Hermite born in Dieuze, in Moselle, the sixth of seven children; his father worked in his wife's family drapery business while also painting. The family moved to Nancy in 1828. As a schoolboy in Nancy and then Paris he read Lagrange on solving equations and Gauss on number theory, and in 1842, still a student, he published a simple proof that fifth-degree equations have no general algebraic solution, the result known as the Abel–Ruffini theorem.
That same year he won entry to the École Polytechnique after a year of coaching from Eugène Catalan, only to be barred from continuing because of his foot. Refusing the strict conditions for readmission, he left and studied privately for five years, befriending Joseph Bertrand, Joseph Liouville and Carl Jacobi, with whom he corresponded on elliptic functions. He finally earned his baccalauréat in 1847, married Bertrand's sister Louise in 1848, and that year returned to the Polytechnique as an examiner and was elected to the Academy of Sciences.
His output was broad. In 1855 he proved that Hermitian matrices, those equal to their own conjugate transpose, always have real eigenvalues. Hilbert later extended the idea, and Hermitian operators became central to the mathematical formulation of quantum mechanics by Born, von Neumann and others. His 1864 polynomials, combined with a Gaussian, describe the quantum harmonic oscillator. In 1873 he showed in two different ways that e is transcendental, building on Liouville. He thought doing the same for pi was beyond him, but Ferdinand von Lindemann used similar methods to manage it in 1882.
A bout of smallpox in 1856 brought him back to his Catholic faith, under the influence of Cauchy and a nursing nun. He taught at the École Normale Supérieure and held chairs at the Polytechnique and the University of Paris, the latter until his death in Paris on 14 January 1901, aged 78. A crater near the Moon's north pole bears his name.
Source: Charles Hermite
