Charles Hermite

Charles Hermite (1822–1901) was a French mathematician whose work connected algebra, number theory, and analysis. He proved that the number e is transcendental.

Transcendental number: A number that is not a root of any nonzero polynomial with integer coefficients. Hermite established that e belongs to this class, a landmark result in number theory.
Hermite's proof of the transcendence of e: A proof that e cannot satisfy any nonzero polynomial equation with integer coefficients. This is Hermite’s best-known result and the first proof that a familiar constant is transcendental.
Joseph Liouville: A French mathematician who contributed to number theory, analysis, and mathematical physics. Liouville’s work on transcendental numbers preceded Hermite’s proof for e.
Transcendence of e: The theorem that the base of the natural logarithm is not algebraic over the rational numbers. Hermite’s proof settled this question for e and opened a new phase in transcendence theory.
Algebraic number: A complex number that is a root of a nonzero polynomial with rational coefficients. Hermite’s proof distinguishes e from every number in this broader class.
Hermite interpolation: Polynomial interpolation that matches specified function values and derivative values at given points. The method shares Hermite’s name and illustrates the constructive algebra associated with his work.
Ferdinand von Lindemann: A German mathematician who proved that π is transcendental. Lindemann extended the transcendence methods associated with Hermite to prove π transcendental.
Lindemann–Weierstrass theorem: A theorem asserting linear independence properties of exponentials of distinct algebraic numbers. It generalizes the transcendence results that followed Hermite’s proof.
Exponential function: A function that is its own derivative and has value one at zero; its natural-base form is written eˣ. The constant whose transcendence Hermite proved is the exponential function’s natural base.
Approximation theory: The study of representing functions or data approximately with simpler mathematical objects. Hermite’s polynomial and series techniques belong to a broader tradition of approximation.

Linked from 9 pages