‎"HILBERT, DAVID.‎
‎Über die Transcendenz der Zahlen e und pi. - [ANTICIPATION OF HILBERT'S SEVENTH PROBLEM]‎

‎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].‎

Reference : 44495

‎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.‎