Abstract

The statement of Fermat’s Last Theorem would have been comprehensible to Diophantus, who lived nearly 2000 years ago. The question was explicitly raised by Fermat in the 1600s, and was resolved by Wiles and Taylor in the 1990s, when I was a PhD student of Taylor. In 2023 I got an EPSRC grant to begin formalising the proof in the Lean theorem prover.

In my talk I’ll start with a history of the problem, and say something about the contributions made by computers in the pre-Wiles era. Without going into details, I’ll then say a little bit about the proof (due to Taylor) which I’m going to formalise, how it differs from Wiles’ original approach (it is broadly but not exactly the same), and what factors influenced the choice of route to the top. I’ll finish by talking about the infrastructure which I’ll be using in order to run the project as an open source multi-author collaborative experiment.

It is probably worth stressing that this talk is suitable for a general audience familiar with the idea of formalisation but with no background in modern number theory, and in particular it will not be a technical explanation of the route we’re taking.

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