OpenAI generated formal mathematical proofs using Lean, an open-source programming language and proof assistant that checks logical correctness against strict rules.

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NEAR AI achieved first place by total solves on the Lean Eval v1 formalization leaderboard, solving 670 upstream PutnamBench problems alongside two corrected formalizations.

Mathematicians and computer scientists emphasize that automated formal checking in Lean does not eliminate the need for independent human evaluation of mathematical proofs and assumptions.

In its public GitHub repository, NEAR AI stated that replaying the PutnamBench benchmark usage at later listed DeepSeek off-peak prices would cost $331.

NEAR AI reported that its automated agent solved 672 Lean problems from the PutnamBench benchmark at a total submission-time model cost of $111.85, averaging approximately $0.17 per problem.

On October 6, 2026, OpenAI published 722 AI-generated mathematical research preprints covering 372 groups of results across fields including algebra, geometry, number theory, and mathematical logic.

Mathematician Hugo Duminil-Copin stated that every major open mathematical problem he had publicly cited in lectures, papers, or grant proposals was solved overnight by OpenAI's October 6, 2026 release.

Following its October 6, 2026 paper release, OpenAI revised 14 mathematical manuscripts to correct errors in proofs, statements, hypotheses, and citations.

Mathematician Matt Zaremsky reported that four years of incremental research by his team on the Boone-Higman conjecture was rendered obsolete by OpenAI's October 6, 2026 release.

OpenAI's October 6, 2026 mathematics release included proofs or partial proofs of open mathematical problems that each required approximately three hours of compute time.

Early-career researchers Tasmin Chu and Tristan Humbert were forced to rewrite active research grant proposals and postdoc applications after OpenAI's release solved their target mathematical problems.

On October 7, 2026, OpenAI withdrew three mathematical preprints after discovering a sign error that invalidated an argument in one paper and affected two related manuscripts.

In October 2026, an internal Anthropic research model using Claude took under 30 minutes to solve a 25-year-old cryptographic mystery regarding the origins of the NIST P-256 and other elliptic curve seeds supplied by the National Security Agency

Anthropic's Claude AI model traced the NIST P-256 seed to candidate number 1842 produced by lrand48, a standard Unix pseudorandom number generator initialized with a timestamp on August 16, 1997

Anthropic researchers tasked an internal Claude AI model to investigate the NIST P-256 and other elliptic curve seeds without telling the model the historical theory that the seeds originated from a forgotten phrase

Anthropic's investigation showed that seeds for NIST prime curves P-192, P-224, P-384, and P-521 matched pseudorandom generator timestamps from May 1997 through April 1998

OpenAI released findings on hundreds of newly solved math problems

OpenAI published machine-generated mathematical proofs formalized in Lean on October 6, 2026, which Ethereum researcher Justin Drake cited as evidence of advancing mathematical superintelligence

OpenAI released a collection of 722 mathematical results and proofs on October 6, 2026, produced by an internal frontier model and formalized in the computer-checkable Lean language

OpenAI tested OpenAI's internal frontier model, which produced 722 AI-generated math proofs, across thousands of mathematical problems, spending the equivalent of approximately three hours of ChatGPT Pro reasoning on the average result

OpenAI arranged OpenAI's 722 mathematical results into 372 families in a public GitHub repository