@wjmzbmr1: 1/ Today, an internal @OpenAI model has refuted Erdős’s unit distance conjecture — a research result that one could rec…
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An internal OpenAI model has disproved Erdős's unit distance conjecture, solving a famous open problem in mathematics and demonstrating AI's potential to contribute to high-level research.
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Cached at: 05/21/26, 10:14 AM
1/ Today, an internal @OpenAI model has refuted Erdős’s unit distance conjecture — a research result that one could recommend “acceptance without any hesitation” to the Annals of Mathematics, one of the most prestigious journals in mathematics.
We came across it in a side quest to push our model on the hardest problems.
2/ It is an elegant conjecture that remained unsolved for 80 years:
Draw n points on a piece of paper. What is the largest possible number of pairs at distance exactly 1?
Erdős conjectured that the answer is almost linear, i.e. n^(1+o(1)). Our model gives a counterexample, drawing on ideas from algebraic number theory, showing that one can have n^(1+δ) such pairs for some small δ > 0.
3/ I started working on reasoning at OpenAI in early January this year, exactly because I believed AI would have a huge impact on mathematics and science in general. But I did not expect a solution to a major open problem in mathematics to arrive as early as May.
4/ The speed of AI progress is truly staggering. I still remember being shocked last summer, as a former IOI gold medalist, by the news that AI could win IMO/IOI gold. But clearly the pace is not slowing down.
5/ Mathematics is one of the cleanest settings for demonstrating scientific progress. But our model is a general-purpose reasoning model: it was not designed or trained specifically for mathematics, nor did it use specialized scaffolding for proof search.
With this level of reasoning ability — check out the model’s chain of thought here [https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf…] — and broad knowledge across scientific domains, I would not be surprised if we soon see landmark results in other scientific fields as well.
6/ Echoing my remarks in the video: one small “downside” of working at OpenAI is that once in a while, there are days when it is very hard to sleep — not from pressure, but from excitement :)
Every day here brings something exciting: getting to participate in training the model, coding again after years of theoretical research, and witnessing breakthroughs happen in real time.
It is an amazing time to be alive!
7/ Finally, see also @HongxunWu’s post for some of our thoughts after discovering the solution.
And this plot is just beautiful — test-time compute is magic:
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