The background of Kummer's proof of Fermat's last theorem for regular primes

Summary

This article contains a brief review of the circumstances which surrounded Kummer's proof of Fermat's Last Theorem for “regular” prime exponents. The often-told story that this proof developed out of an earlier proof which was fallacious is questioned, and a new document, an unknown letter from Liouville to Dirichlet which is related to this history, is presented. Also presented is the little-known fact that Kummer's theory of “ideal complex numbers”, which was the basis of the proof, contained a serious flaw which went uncorrected for ten years.