AxiomMath's AI Prover Formalizes the 246 Prime Gap Theorem in Lean4

新智元 · wechat · 2026-08-22

On August 17, AxiomMath—founded by 25-year-old Carina Hong—announced its AxiomProver system completed a formal verification of the prime gap '246 theorem': the proof holds with no logical errors. The 246 theorem is the closest result to the twin prime conjecture, tightened from Yitang Zhang's 70 million (2013) through Maynard's 600 (Fields Medal) and Polymath8b's 246 (with Tao), unimproved for over a decade.

How it works: AxiomProver proves nothing new; it translates the human proof into machine-checkable form. The multi-agent system uses an Auto-formalizer to fill gaps into Lean4 code, a Conjecturer for missing lemmas, a search engine for full proofs, and an Auto-informalizer to translate back for human review. The verification spans 14 chapters and 132 pages, built on the GPY method and Maynard's multi-dimensional sieve—a 50-dimensional optimization (k=50, ε=1/25) with the crucial variational constant M₅₀,₁/₂₅≈4.0043>4—depending only on Bombieri-Vinogradov and the prime number theorem externally. The library is open-source on GitHub and locally verifiable.

The company: Hong finished MIT math/physics dual degrees in 3 years with 9 papers and the Morgan Prize, dropped out of a Stanford PhD in March 2025 to found AxiomMath, recruiting her MIT advisor Ken Ono as founding mathematician. It raised $64M seed and a $200M Series A at a $1.6B valuation, with prior results including a perfect Putnam score and 42/42 at IMO. Ono stresses the broader stakes: AI generates code faster than humans can review, and number theory underpins cryptography—the same formal verification tech can check AI-written code. Verification is easier than creation, but just as valuable.

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