OpenAI model disproves Erdős's 1946 unit-distance conjecture
OpenAI said an internal general-purpose reasoning model, not trained specifically for maths, constructed planar point sets with at least n^(1+δ) unit-distance pairs, refuting the long-standing n^(1+o(1)) conjecture. The argument uses algebraic number theory (class field towers); external mathematicians checked it and wrote a companion paper, and Noga Alon and Tim Gowers praised it publicly.
Why it matters
OpenAI called it the first time a prominent open problem central to a field of mathematics was solved autonomously by AI, and Gowers called it a milestone, shifting AI from solving obscure problems to famous ones.
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- DevelopmentOpenAI claims Navier-Stokes blow-up proof; mathematicians dispute credit8 Sep 2026 · Research · USLed to: Escalation from an Erdős problem to a Millennium problem
- DevelopmentDeepMind study: most AI 'solutions' to open Erdős problems were already in the literature29 Jan 2026 · Research · GB, USContrasts with: Low-novelty sweep versus a single historically significant result
What led here
Earlier developments on the same thread
- DevelopmentOpenAI agrees to deploy its models on Department of War classified networks28 Feb 2026 · Deal · US
- DevelopmentOpenAI, Anthropic and Google offer frontier AI to US agencies for about $1 via GSA6 Aug 2025 · Procurement · US
- DevelopmentGemini Deep Think earns officially graded gold-medal score at IMO 202521 Jul 2025 · Research · GB, US
- DevelopmentGoogle DeepMind's AlphaEvolve agent improves algorithms and open maths bounds14 May 2025 · Research · GB, US
What happened next
Later developments on the same thread
- DevelopmentGPT-6 Astra jumps to 62.7% on ARC-AGI-3, six months after models scored 0.5%3 Sep 2026 · Report · US
- DevelopmentClaude completes first end-to-end Lean formal proof of Fermat's Last Theorem4 Sep 2026 · Research · US, GB
- DevelopmentOpenAI ties large reasoning-distillation campaign to people linked to Moonshot AI30 Sep 2026 · Incident · US, CN
- DevelopmentOpenAI publishes a batch of new maths results from an internal model, with Lean proofs6 Oct 2026 · Research · US
Same story elsewhere
What other countries and bodies did on this
- DevelopmentAI systems from Huawei and Xiaohongshu reported to score 42/42 at IMO 202623 Jul 2026 · Research · CN, INTL
- DevelopmentIndia hosts AI Impact Summit in New Delhi, first in the series in the Global South16 Feb 2026 · Statement · IN, INTL
- DevelopmentEU publishes General-Purpose AI Code of Practice ahead of AI Act model duties10 Jul 2025 · Rule change · EU
- DevelopmentDeepSeek releases R1 reasoning model with open weights under MIT licence20 Jan 2025 · Model release · CN
Threads by topic: Mathematics Frontier models