The redemption proof

In October 2025, OpenAI claimed its model had "solved" ten open problems from Erdős's famous list. Thomas Bloom, who maintains the canonical archive of those problems, pointed out within days that the model had merely found already-published solutions. Demis Hassabis called the episode embarrassing; the executive who made the claim deleted his post. This May, the same Thomas Bloom put his name on a paper verifying that an OpenAI model had done the real thing.

"This is a disproof, not a proof, which would have been more impressive." — OpenAI's own write-up

The problem is deceptively simple to state. Scatter n points on a sheet of paper and count how many pairs sit exactly one unit apart. Erdős conjectured in 1946 that you can never get many more such pairs than a plain square grid gives you. Given only that sentence — no hints — an internal OpenAI reasoning model returned a construction that beats the bound, an infinite family of point sets squeezing out polynomially more unit-distance pairs than the conjecture allows. It got there not through geometry but by detouring into algebraic number theory, a move the circulating reasoning trace makes around its 39th page.

Nine mathematicians, including the Fields Medalist Tim Gowers, digested and rewrote the argument and posted it to arXiv. Gowers said that had humans submitted it to a top journal he would recommend acceptance without hesitation. That is the line being cleared: not a competition problem fed to a dedicated theorem-prover, not an evolutionary search bolted to a custom solver, but a general model producing a result the field judges worth publishing on its own terms.

The honest footnotes matter. It is a disproof — one counterexample is easier than a proof — and it generalizes a construction Erdős himself wrote down; the working parts were already scattered through the literature. The model's contribution was being first to assemble them. And the model is unnamed and unreleased, so the capability behind the headline is one no outside reader can run or even identify. What survives all of that is still the thing the field had been waiting for: the first time a general-purpose AI cleared the bar of producing original mathematics that working mathematicians found worth keeping.