A complete machine-checked proof of Fermat's Last Theorem: the import closure of FinalCheck.lean - 1,450 definition modules (Definitions/), 29,511 statement modules (Theorems/), 29,511 proo...
fermats-last-theorem/FinalCheck.lean at aa2d8b34692b16c70f699536de0d8e75b9a3e9ef · anthropics/fermats-last-theorem
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fermats-last-theorem/README.md at aa2d8b34692b16c70f699536de0d8e75b9a3e9ef · anthropics/fermats-last-theorem
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pages build and deployment · anthropics/fermats-last-theorem@aa2d8b3
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Why I didn’t sign the Fields medallists’ letter
[This post has been cross-posted to Terence Tao’s blog.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem stateme…
Formalizing Fermat's Last Theorem
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Fermat's Library | Home
Fermat’s Library is a platform for illuminating academic papers. A new scientific paper annotated every week.
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
. · openai/ten-proofs@94bc0fe
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@94bc0fe
. · openai/ten-proofs@e9dce9a
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@e9dce9a
. · openai/ten-proofs@d0e1ae7
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@d0e1ae7
. · openai/ten-proofs@5a102c1
Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@5a102c1
Satisfiability Modulo Theories: A Beginner’s Tutorial — Satisfiability Modulo Theories: A Beginner's Tutorial documentation
Great minds have long dreamed of creating machines that can function as general-purpose problem solvers. Satisfiability modulo theories (SMT) has emerged as one pragmatic realization of this dream, providing significant expressive power and automation. This tutorial is a beginner’s guide to SMT. It includes an overview of SMT and its formal foundations, a catalog of the main theories used in SMT solvers, and illustrations of how to obtain models and proofs. Throughout the tutorial, examples and exercises are provided as hands-on activities for the reader. They can be run using either Python or the SMT-LIB language, using either the cvc5 or the z3 SMT solver.
Tutorial: Introduction to Formal Verification with Lean (Part 1) - HashCloak
A tutorial Formal Verification using Lean for cryptographic engineers. Implement and prove correctness of the One-Time pad following a cryptography book.