“The Riddle of the Ages”: James Joseph Sylvester and the Transcendence of π

Abstract

The first proof of the transcendence of π by Ferdinand Lindemann in 1882 prompted the publication of a wave of further proofs, all attempting to elucidate, simplify, or generalize this epoch-making result. Modifications by the likes of Weierstrass, Gordan, and Hilbert all entered the literature. But one such proof sank without a trace and was almost completely ignored. This is surprising as, not only did it appear in a major journal with a large international readership, but it was also written by one of the most famous mathematicians of the time—James Joseph Sylvester. This paper tells its story.