OpenAI announced on May 20 that one of its internal reasoning models autonomously disproved an 80-year-old mathematical conjecture. The Erdős unit distance conjecture, an open problem in discrete geometry formulated by legendary mathematician Paul Erdős in 1946, has stumped human mathematicians for decades.
What Happened
The model produced a 125-page formal proof disproving the conjecture using techniques from algebraic number theory. This wasn’t a guided process — the model developed the proof autonomously, not by following human-provided step-by-step instructions.
Fields Medal winner Tim Gowers reviewed the proof and confirmed it as correct. He called it a milestone for AI in mathematics.
Why This Matters
Until now, AI models have mostly helped with math by verifying existing proofs or speeding up known solution approaches. A model independently discovering a new proof — for a problem that human mathematicians haven’t cracked in 80 years — is qualitatively different.
It demonstrates that reasoning models can generate genuinely new mathematical insights, not just reproduce existing patterns. This is exactly the kind of capability that OpenAI and other labs view as a stepping stone toward AGI.
My Take
Let’s keep this in perspective. Erdős left behind hundreds of open problems, and they’re not all equally hard. The unit distance conjecture is well-known but it’s not a Millennium Prize Problem. Still — an autonomous 125-page proof with correct algebraic number theory? Nobody thought that was possible a year ago.
For the race between the major labs, this is a strong signal. While Anthropic is breaking valuation records, OpenAI is showing it’s still at the cutting edge when it comes to pure reasoning capabilities.
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