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Benefit Ledger · provisional · Mathematics

Pre-release GPT-6 Astra solves five Bloom-curated Erdős problems in Lean

On 1 September 2026 Epoch AI reported that a pre-release GPT-6 Astra system was the only model to score on FrontierMath Erdős, a Lean benchmark of 68 significant unsolved Erdős problems. It solved problems 74 and 126 under the official $300 protocol, and problems 1, 548, and 571 in extra attempts.

1 Sep 2026Tier 2 NotableMethodology 0.1

Current score

+0.46

3 base · Notable (tier 2 of 5, 3 pts)
× 0.8500 attribution · Primary causal contribution
× 0.5000 evidence · External expert evaluation
× 0.5500 realization · Experimentally validated
× 0.6500 durability
Event-level product before credit split: 0.46

Lean-checked solutions to Bloom-curated Erdős problems are notable mathematics (tier 2), not a field-defining cluster. Attribution is to pre-release Astra (0.85). Evidence is Epoch’s public protocol and paper (0.50). Realization is verified Lean, with extra solves outside the official score (0.55).

What happened

Thomas Bloom selected 68 Erdős problems that were open as of August 2026. Epoch ran GPT-6 Astra (pre-release), GPT-5.6 Sol, GPT-5.5, and Claude Fable 5/5.1 at $300 and 72 hours per problem. Only Astra scored: a counterexample to problem 74 and a proof of problem 126 (3%). Additional, non-protocol attempts with larger budgets also yielded a disproof of problem 1 and proofs of 548 and 571. Those extras are not a benchmark score. This is recorded as realized Lean-checked mathematics on named Erdős problems, not as a 3% exam result. It is distinct from the May unit-distance disproof (problem 90) and from the August ten-advances cluster.

Model attribution

+0.46

GPT-6

Pre-release GPT-6 Astra run by Epoch on FrontierMath Erdős; the only scored model in the official protocol.

Epoch names a pre-release GPT-6 Astra as the solver. That is the named Astra line, not the August internal ten-proofs system or the September Navier–Stokes search model.

Attribution 0.8500 · Credit share 100% · OpenAI

Claims

  • Under Epoch’s $300 protocol, pre-release GPT-6 Astra produced Lean-verified solutions to Erdős problems 74 and 126, for a 3% score; Sol and Fable scored 0%.

    outcome · supported

  • Additional larger-budget attempts also yielded Lean solutions to problems 1, 548, and 571; those are not part of the official 3% score.

    outcome · supported

Sources

primary sources

independent sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 → 0.46

    Imported events under methodology 0.1.