Machines Are on the Verge of Tackling Fermat’s Last Theorem—a Proof That Once Defied Them

Mathematician Kevin Buzzard is embarking on an ambitious project to translate Andrew Wiles’ 100-page proof of Fermat’s Last Theorem into computer code using the proof assistant tool Lean. Fermat’s Last Theorem, which states that no three positive integers can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2, remained unproven for centuries until Wiles’ proof in 1993. Buzzard, who teaches at Imperial College London, has been instrumental in developing Lean-based tools to aid in teaching mathematical proofs.

The project, supported by a research grant, aims to make complex mathematical proofs more accessible and verifiable, potentially revolutionizing how mathematicians work and collaborate. Lean, built on C++, allows for the codification and verification of induction proofs, bridging the gap between formal logic and prose arguments. This could enable a new generation of mathematicians to engage with computer-supported proofs and contribute to the field, even if they do not fully grasp the entire proof.

The endeavor also reflects a broader trend in mathematics where the lines between disciplines are becoming increasingly blurred. Tools like Lean can help mathematicians organize their ideas and make their work more comprehensible to others, fostering collaboration and further advancements in the field. Buzzard’s project is not just about proving a theorem; it’s about setting a precedent for the future of mathematical research and education.
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