突发！OpenAI下一代AI攻克10项菲尔兹奖级难题
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TL;DR - A WeChat repost (转自新智元) reporting that OpenAI's unreleased next-gen model "Astra" produced a 249-page write-up claiming breakthroughs on 10 long-open math problems, with Lean 4 formalization and open-sourced proofs. If it survives peer scrutiny, it would mark a step-change in AI's capacity for original mathematical research.
- Claimed results span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics; the article highlights three: construction of a finitely presented non-sofic group (refuting Gromov's 1999-era conjecture, via the unit group of the binary Leavitt algebra plus Kun-Thom expander graphs and Thompson's group V), a new exponential decay rate for the Cohn-Elkies LP bound on asymptotic sphere packing (first improvement on the 1978 Kabatiansky-Levenshtein bound), and a disproof of Connes' rigidity conjecture via a countably infinite family of pairwise non-isomorphic groups with identical von Neumann algebras.
- Verification claim: proofs formalized in Lean 4 with machine-checkable certificates, released at github.com/openai/ten-proofs, alongside a proofs PDF and a separate reasoning-walkthrough PDF.
- Cost framing: total inference cost reportedly under $2,000 (~$200/problem) at Sol API pricing, obtained as a byproduct of evaluating an unreleased model — the piece's central argument that test-time compute for research math is far from saturated.
- Caveats stated in the article itself: the 10 problems were cherry-picked by OpenAI after other attempts; Noam Brown acknowledges no Millennium-Prize-class problem (e.g. Riemann) has been solved. Third-party reactions cited (Kontorovich, Thomas Bloom, Elliot Glazer) are enthusiastic but predate full community review. Some model names referenced in the post appear garbled/unverifiable.
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突发！OpenAI下一代AI攻克10项菲尔兹奖级难题
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TL;DR - A WeChat repost (转自新智元) reporting that OpenAI's unreleased next-gen model "Astra" produced a 249-page write-up claiming breakthroughs on 10 long-open math problems, with Lean 4 formalization and open-sourced proofs. If it survives peer scrutiny, it would mark a step-change in AI's capacity for original mathematical research.
- Claimed results span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics; the article highlights three: construction of a finitely presented non-sofic group (refuting Gromov's 1999-era conjecture, via the unit group of the binary Leavitt algebra plus Kun-Thom expander graphs and Thompson's group V), a new exponential decay rate for the Cohn-Elkies LP bound on asymptotic sphere packing (first improvement on the 1978 Kabatiansky-Levenshtein bound), and a disproof of Connes' rigidity conjecture via a countably infinite family of pairwise non-isomorphic groups with identical von Neumann algebras.
- Verification claim: proofs formalized in Lean 4 with machine-checkable certificates, released at github.com/openai/ten-proofs, alongside a proofs PDF and a separate reasoning-walkthrough PDF.
- Cost framing: total inference cost reportedly under $2,000 (~$200/problem) at Sol API pricing, obtained as a byproduct of evaluating an unreleased model — the piece's central argument that test-time compute for research math is far from saturated.
- Caveats stated in the article itself: the 10 problems were cherry-picked by OpenAI after other attempts; Noam Brown acknowledges no Millennium-Prize-class problem (e.g. Riemann) has been solved. Third-party reactions cited (Kontorovich, Thomas Bloom, Elliot Glazer) are enthusiastic but predate full community review. Some model names referenced in the post appear garbled/unverifiable.