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Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@d0e1ae7

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Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@5a102c1

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Lean certificates accompanying proofs in mathematics and theoretical computer science - . · openai/ten-proofs@94bc0fe

Palomar – a registry of Lean verified mathematics

In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking tha…

Ten advances in mathematics and theoretical computer science

OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.

Theory Beyond Theorems and Proofs: A Guest Post

Scott’s foreword: I’m extremely grateful to my brilliant colleagues, Pravesh Kothari, Raghu Meka, and Prasad Raghavendra, for sharing the guest post below about how theoretical computer…

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.

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].

Palomar — Lean-verified mathematics

A public registry of Lean-verified mathematical results.

Anatomy of a Lean Proof for Software Engineers

Intro I recently worked through a problem from a theory of computation textbook that asked me to prove a property of a language using finite automata. The informal proof is a simple constructive proof where you build an automaton and show that it recognizes the language. This is kind of similar to program verification, so I thought it’d be interesting to see what it takes to formalize the proof. Lean is a good choice for this, because its Mathlib has all the theorems for the problem.

AI helped produce two proofs for the same cryptography problem

Last Thursday Massachusetts Institute of Technology graduate student Seyoon Ragavan sent a new quantum cryptography proof to his friend Yao-Ting Lin, a doctoral student at the University of California...

Terence Tao (@tao@mathstodon.xyz)

In traditional mathematics (or "Math 1.0"), a breakthrough proof of a long-standing open conjecture generates a large amount of subsequent activity and excitement in the field. The authors of the proof are invited to give many talks, and meet with other experts in the area. Workshops are set up to discuss the proof, as well as other recent developments. As a result, new connections and collaborations are formed, followup problems are shared, and other mathematicians (both junior and senior) are attracted to the field (including in some cases the authors themselves, if they initially came from a different subject). As a result of all this activity, the proofs naturally become digested, streamlined, placed in context with other results in the field, and ultimately become part of the textbooks and lecture notes for the next generation of mathematicians in the field. (1/4)