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Charles Hermite

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Charles Hermite

Charles Hermite (French pronunciation: [ʃaʁl ɛʁˈmit]) FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning 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 used later by Ferdinand von Lindemann to prove that π is transcendental.

Hermite was born in Dieuze, Moselle, on 24 December 1822, with a deformity in his right foot that would impair his gait throughout his life. He was the sixth of seven children of Ferdinand Hermite and his wife, Madeleine née Lallemand. Ferdinand worked in the drapery business of Madeleine's family while also pursuing a career as an artist. The drapery business relocated to Nancy in 1828, and so did the family.

Hermite obtained his secondary education at Collège de Nancy and then, in Paris, at Collège Henri IV and at the Lycée Louis-le-Grand. He read some of Joseph-Louis Lagrange's writings on the solution of numerical equations and Carl Friedrich Gauss's publications on number theory.

Hermite wanted to take his higher education at École Polytechnique, a military academy renowned for excellence in mathematics, science, and engineering. Tutored by mathematician Eugène Charles Catalan, Hermite devoted a year to preparing for the notoriously difficult entrance examination. In 1842 he was admitted to the school. However, after one year the school would not allow Hermite to continue his studies there because of his deformed foot. He struggled to regain his admission to the school, but the administration imposed strict conditions. Hermite did not accept this, and he quit the École Polytechnique without graduating.

In 1842, Nouvelles Annales de Mathématiques published Hermite's first original contribution to mathematics, a simple proof of Niels Abel's proposition concerning the impossibility of an algebraic solution to equations of the fifth degree.

A correspondence with Carl Jacobi, begun in 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.

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