An internal OpenAI reasoning model has disproved a famous 1946 conjecture from Paul Erdős, the first time AI has settled a major open problem in mathematics.
Key Points:
- An OpenAI model disproved the Erdős unit distance conjecture, open for 80 years.
- The proof leaned on algebraic number theory and passed external review.
- It is the first major open problem solved autonomously by AI.
OpenAI Cracks Erdős Conjecture
The company announced on May 20 that its model produced a counterexample to the unit distance problem, which asks how many pairs among many points can sit exactly one unit apart. For decades, researchers had treated a square grid as close to the best layout. The puzzle is easy to state, yet it had shrugged off eighty years of effort from leading mathematicians.
The model went another way, building a more intricate pattern that drew on algebraic number theory to fit in more unit distances than a grid allows, a structure no human had seriously pursued.
A panel of outside experts checked the proof before the company made it public.
Princeton's Will Sawin soon refined the argument. His version showed the number of unit distances grows at least as fast as n raised to the 1.014 power, a polynomial edge over the old grid bound. The upper limit still sits near n to the 1.333, so a gap remains.
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Gowers Hails A Math Milestone
Tim Gowers, a Fields Medal winner, called the work a landmark and said no earlier AI proof had come close. Daniel Litt of the University of Toronto described it as the first AI result he found genuinely exciting on its own terms, not just as a sign of things to come.
Experts stressed why the route mattered. Most mathematicians had spent years trying to prove the conjecture rather than break it, and few would grind through such a tedious build without a sign it would pay off. An AI weighs that gamble differently, working through countless dead ends until one improbable path holds.
OpenAI's Rocky Erdős Record
The breakthrough did not stand alone. Days later, Google reported that one of its systems had resolved nine lesser problems from Erdős's list, two of them open for more than 50 years.
The careful rollout answered an earlier stumble. In October, the company claimed a model had solved ten Erdős problems, only for reviewers to show it had merely surfaced old solutions rather than proving anything new. That episode pushed the company toward outside review this time.
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