AI Tools Formalize Key Lemmas of Fermat's Last Theorem in Days at London Workshop

The workshop deployed interactive theorem-proving environments augmented by large language models trained on Lean libraries to suggest and verify tactics. Participants reported rapid closure of gaps in the elliptic curve and modular form components that had stalled manual formalization efforts. This builds on prior Lean projects such as the Liquid Tensor Experiment and the formalization of the Odd Order Theorem, where human-AI pairing reduced verification time by factors of three to five. Cross-referencing with the 2024 AlphaProof results at the International Mathematical Olympiad shows consistent patterns: models excel at local tactic generation but require human oversight for global proof architecture.

Analysis of the event reveals a shift from isolated human proof construction toward iterative human-model refinement loops. Earlier attempts to formalize Wiles' 1995 proof stalled due to the sheer volume of commutative algebra and Galois representation lemmas; AI assistance addressed exactly these bottlenecks by surfacing relevant library entries and suggesting rewrites. The approach aligns with emerging meta-analyses in the field showing that hybrid systems outperform pure automation or pure human effort on proofs exceeding 10,000 lines.

Next steps include releasing the partial formalization as a Lean blueprint for community extension and testing whether scaling model context windows further reduces human intervention rates. A controlled comparison against unaided teams on similar subproblems would strengthen claims about acceleration.