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An internal OpenAI model has disproved one of the most well-known Erdős problems: the unit distance problem. This is, without doubt, the most impressive achievement of AI in mathematics so far.
https://x.com/thomasfbloom/status/2057177152894771631
An OpenAI model has achieved a major breakthrough in mathematics, by disproving a central conjecture in discrete geometry that was first posed by Paul Erdős in 1946. This is the first time AI has autonomously solved a prominent open problem central to a field of mathematics.
https://x.com/gdb/status/2057182650784452925
An OpenAI model has disproved a central conjecture in discrete geometry | OpenAI
https://openai.com/index/model-disproves-discrete-geometry-conjecture/
just quick napkin math on how long this took (unless i missed where they said): the published CoT summary is 111,145 tokens long. it’s really hard to say how much they summarized, assume 3x-20x reduction in tokens? and i’m assuming this is gpt-5.6 pro, so taking Artifical
https://x.com/willdepue/status/2057213893857165701
The proof came from a general-purpose reasoning model, not a system built specifically to solve math problems or this problem in particular, and represents an important milestone for the math and AI communities.
https://x.com/OpenAI/status/2057176203166171317
Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that
https://x.com/OpenAI/status/2057176201782075690
unfortunately openai didn’t publish the unsummarized chain of thought, but the summary is 125 pages! the model reaches the crucial idea (which it describes as ‘frightening,’ i would love to read the unabridged chain of thought here…) on page 39
https://x.com/voooooogel/status/2057198687307362642
unit-distance-remarks.pdf
Click to access unit-distance-remarks.pdf
Very proud that an OpenAI model disproved Erdős’s longstanding unit distance conjecture, with an elegant and intricate proof that brings sophisticated ideas from algebraic number theory to bear on geometry. For whatever reason, mathematics has been the field most amenable to
https://x.com/markchen90/status/2057517045575774598
If you are a mathematician, then you may want to make sure you are sitting down before reading further.
https://x.com/wtgowers/status/2057175727271800912
Philosophy Eats AI
https://sloanreview.mit.edu/article/philosophy-eats-ai/
🧵(1/8) An @OpenAI internal reasoning LLM achieved an AI Math milestone: solving an open problem central to its mathematical subfield– in this case, the unit distance problem of discrete geometry. We came across it in a side quest to truly push our model on the hardest problems.
https://x.com/HongxunWu/status/2057176383106027567
1/ Ten months ago, I was ecstatic that AI could win IMO gold. Today, that excitement feels quaint: an internal @OpenAI model has refuted Erdos’s unit distance conjecture–a research result that one could recommend “acceptance without any hesitation” to the Annals of Mathematics.
https://x.com/alexwei_/status/2057182873208369485
Did we ever learn what model won gold at the IMO from OpenAI? It was a year ago and it was called an unreleased internal general purpose model back then. Has GPT-5.5 Pro Extended caught up with whatever it was?
https://x.com/emollick/status/2057196459259301933
AI has now solved a major open problem — one of the best known Erdos problems called the unit distance problem, one of Erdos’s favourite questions and one that many mathematicians had tried.
https://x.com/wtgowers/status/2057175729008153069
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