ANTICIPATION OF HILBERT'S SEVENTH PROBLEM

HILBERT, DAVID.

Über die Transcendenz der Zahlen e und pi.

Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In "Mathematische Annalen. Begründet 1868 durch Rudolf Friedrich Alfred Clebsch. 43. Band. 2. und 3. (Doppel-)Heft."Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 216-19. [Entire issue: Pp. 145-456].

First publication of Hilbert's important contribution to transcendental number theory which anticipates Hilbert's seventh problem, the seventh of twenty-three problems proposed by Hilbert in 1900 which became of seminal importance to 20th century mathematics.

A transcendental number is a number which is not algebraic-that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are pi and e.
Euler was the first person to define transcendental numbers - The name "transcendentals" comes from Leibniz in his 1682 paper where he proved sin x is not an algebraic function of x.

Order-nr.: 44495