Modular Elliptic Curves and Fermat's Last Theorem

1995/05/01 by Andrew Wiles · 1 voice · 2,094 citations
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Computer science #Elliptic curve #Fermat's Last Theorem #History and Theory of Mathematics #Mathematics #Modular curve #Modular design #Modular elliptic curve #Programming language #Pure mathematics #Quarter period

paper · doi:10.2307/2118559

published in Annals of Mathematics 141(3), 443 (Princeton University)

openalex publication_date 1995/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n>2 such that a n + b n = c n. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.

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Discussions

• Seven years after #TheRoyale aired, Andrew Wiles made the episode out of date. https://doi.org/10.2307/2118559 #AllStarTrek #StarTrekTNG @startrek [bsky, 1 points, 0 comments]

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