NEAR Protocol plans AI-assisted formal verification after solving 672 math problems for $112

Following OpenAI's October 6, 2026 release of 722 AI-generated mathematics papers, NEAR Protocol announced plans on October 16, 2026, to use AI-assisted formal verification to secure its network and smart contracts. NEAR AI demonstrated solving 672 PutnamBench math problems for $111.85 using Lean. While AI proof generation promises automated software verification, mathematicians raise concerns over errors—evidenced by OpenAI retracting three papers and revising 14 others.

NEAR Protocol plans formal verification using Lean

• ▪NEAR Protocol co-founder Illia Polosukhin stated that formal verification research aims to provide mathematical guarantees for software behavior to mitigate security risks from AI-generated code and attacker exploitation tools.
• ▪NEAR Protocol explained that production formal verification requires mathematically representing software, specifying required security properties, and constructing proofs that cover deployed code implementations.
• ▪On October 16, 2026, NEAR Protocol announced plans to apply AI-assisted formal verification to its network protocol, core smart contracts, and developer tools using Lean.

NEAR AI benchmark performance and costs

• ▪NEAR AI achieved first place by total solves on the Lean Eval v1 formalization leaderboard, solving 670 upstream PutnamBench problems alongside two corrected formalizations.
• ▪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.
• ▪In its public GitHub repository, NEAR AI stated that replaying the PutnamBench benchmark usage at later listed DeepSeek off-peak prices would cost $331.

Certora review of Templar protocol

• ▪Security firm Certora conducted a manual review of Templar's Rust contracts during its March 30, 2026 assessment of the protocol.
• ▪Security firm Certora completed a formal specification and verification of the market contract for Templar, a lending protocol deployed on NEAR Protocol, on March 30, 2026.

Limits of automated formal verification

• ▪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 May 2026, Ethereum co-founder Vitalik Buterin cautioned that proving one software layer does not establish that an entire system behaves as intended.

OpenAI releases mathematical research preprints

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

Mathematicians react to OpenAI releases

• ▪Fields Medal winners Hugo Duminil-Copin and Tim Gowers, along with mathematicians Steven Strogatz and Terence Tao, expressed distress over OpenAI's sudden release of hundreds of AI-generated mathematics proofs.
• ▪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.
• ▪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.
• ▪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.

Errors found in OpenAI mathematics preprints

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