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The Fermat's Last Theorem Project
Kevin Buzzard discusses the project to prove Fermat's Last Theorem in Lean. Introduction Fermat's Last Theorem (FLT) is the claim that some abstract equation has no solutions in positive integers. Th
One aspect of FLT is that the theorem is very simple to state($x^n+y^n=z^n$ has no solutions in positive integers if $n\geq3$), and yet it was incredibly hard to prove(indeed, it took the mathematical community over 350 years). Wiles might have been motivated by FLT, but ultimately his work comprised of a breakthrough in the Langlands Program, a broad collection of conjectures which are still mostly wide open, and very much of interest in 2024. Well before the project is finished, Lean will understand the concepts of automorphic forms and representations, Galois representations, potential automorphy, modularity lifting theorems, the arithmetic of varieties, class field theory, arithmetic duality theorems, Shimura varieties and many other concepts used in modern algebraic number theory; formalising the statements of what is happening in my own area of expertise will no longer be science fiction.
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