Simplifying a proof of transcendence for \(e\): a letter exchange between Adolf Hurwitz, David Hilbert and Paul Gordan (Q6623908)

This historical survey deals with an analysis of the evolution of three proof variations given by Adolf Hurwitz (1859--1919), David Hilbert (1862--1943), and Paul Gordan (1837--1912) for the transcendence for Euler's number \(e\).\N\NSome attention is given by the author to the notions of algebraic and transcendental numbers, as well as to certain first proofs of the transcendence of numbers.\N\NOne can note the following sections of this paper in which descriptions are given with figures and schemes:\N\N-- \textit{Historical Context.}\N\N-- \textit{Three Variations of a Proof of Transcendence for \(e\).}\N\N-- \textit{Hessenberg's Analysis.}\N\NIn the section \textit{Letter Exchanges,} the main attention is given to the letter exchange, which accompanied the publication of the proofs, between Hurwitz, Hilbert and Gordan, as well as supplemented by references to Felix Klein and Charles Hermite.\N\NThe section \textit{Further Reception} deals with the reception of the mentioned proofs in teaching and research (until the 1970s).\N\NFor the entire collection see [Zbl 1537.01004].