OpenAI model disproves 80-year-old Erdős conjecture in maths milestone

TL;DR:

• OpenAI says one of its general-purpose reasoning models has disproved a 1946 conjecture from Hungarian mathematician Paul Erdős on the planar unit distance problem, by uncovering a family of constructions that beats the long-assumed square-grid arrangement.
• The work has been validated by mathematician Thomas Bloom, who maintains the Erdős problems site and publicly criticised OpenAI’s last Erdős claim as recycled literature; Tim Gowers calls the result “a milestone in AI mathematics”.
• Bloom stresses the proof was “significantly improved by the human researchers at OpenAI and the many other mathematicians involved”, a clearer co-authorship framing than OpenAI used last year.

OpenAI’s announcement matters less for the maths and more for how the company has handled it. Last year’s claim — that a model had cracked an Erdős problem — collapsed once researchers found the result was already in the literature the model had ingested. This time the company brought Bloom inside the work and let him publish a companion paper alongside the blog post, which is a different posture from the marketing-led releases that drew the earlier criticism.

A UK researcher reads the result as a signal, not a single result

Andrew Rogoyski of the Institute for People-Centred AI at the University of Surrey told the Guardian the announcement showed AI is giving humans “new ways to look at problems” and was becoming “a fundamental tool of future scientific research”. That framing matters for UK universities: the Royal Society, UKRI and the Alan Turing Institute have all been arguing for AI-for-science investment, and a credibly-validated reasoning win is exactly the demonstration that strengthens those funding cases — even if the underlying Erdős conjecture remains technically open, since OpenAI’s model showed only that the proposed limit is too low rather than producing a tight new bound.

The bigger question for UK research leaders is what counts as an “AI proof” in practice. Bloom’s caveat — the AI’s original proof was valid but humans materially improved it, and humans still play a “vital role in discussing, digesting and improving” the work — is the honest answer the field needs as labs race to claim mathematical firsts. It also lowers the bar for an awkward conversation UK funders will have to have: how to attribute credit, allocate authorship and audit reproducibility when frontier models become co-authors on serious research papers.

Looking forward

Expect more Erdős-style claims from frontier labs over the coming months — Google DeepMind has been investing heavily in AlphaProof, Anthropic has hinted at reasoning-model maths work, and the validated-by-Bloom standard now exists as a public benchmark. For UK research-intensive SMEs and AI-for-science startups (BenevolentAI, Isomorphic Labs, Materials Discovery Lab spinouts), the practical takeaway is that human-AI co-authorship is becoming the credible pattern; the failed solo-AI claim is the warning.