Mathlib-integrated formalization of the modern FLT proof with reusable Galois-representation infrastructure

In progress. The Imperial project started in October 2024 with an EPSRC grant and a public blueprint. Buzzard's December 2024 report, two months in, describes formalizing a modern R = T (modularity lifting) argument building on Diamond, Fujiwara, Kisin, Taylor and Scholze, with ingredients such as crystalline cohomology and divided powers still missing from Mathlib, and stresses that the aim is the general theorems rather than FLT alone. On 4 September 2026 Anthropic's agentic formalization produced a 13-million-line certificate of FLT following the Darmon–Diamond–Taylor route; it compiles about twenty times slower than Mathlib and is not integrated with it. Buzzard checked its final statement with Comparator and judged that it tells us essentially nothing new mathematically. The integrated formalization of the modern proof, including reusable automorphic infrastructure, remains to be done and is not covered by the certificate.

Reusable formal infrastructure for the Langlands program (Galois representations, Hecke algebras, deformation rings) so that further arithmetic theorems can be formalized without rebuilding it. Also a test bed for scaling Mathlib development.

The Imperial blueprint is fully formalized with no sorry, merged into Mathlib or an agreed library compatible with it, the theorem FermatLastTheorem derived from the integrated library, and the library compiles within a stated budget (for example at most 3 times Mathlib's build time).