The Verification Problem (On OpenAI's Erdős Disproof)
OpenAI's recent announcement claimed that its model had disproved Erdős's planar unit-distance conjecture, marking a significant achievement in mathematical problem-solving. However, a previous claim about solving ten Erdős problems was criticized for merely surfacing existing solutions rather than providing new insights. The verification of the latest result involved collaboration with mathematicians, highlighting the importance of rigorous proof in the field.
- ▪OpenAI's model was initially criticized for misrepresenting existing solutions to Erdős problems.
- ▪The recent disproof of the planar unit-distance conjecture was verified by nine mathematicians, including Thomas Bloom.
- ▪The model's approach utilized advanced algebraic number theory to achieve a polynomial improvement over previous beliefs.
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May 23, 2026 · 11 min read The Verification Problem aimathematicsverification Contents What the model actually did The texture of the reasoning Why verification was the expensive part The part the field isn’t ready for What it was really for Footnotes In October, OpenAI said its model had solved ten open Erdős problems. It hadn’t.1 The model had surfaced existing solutions buried in the literature and presented them as fresh conquests, and Thomas Bloom — who runs erdosproblems.com and would know — said so publicly and without much patience for the framing.2 Last week OpenAI announced that an internal model had disproved Erdős’s planar unit-distance conjecture.3 This time the announcement came with a companion paper written by nine mathematicians, and one of the nine was Thomas Bloom.4…
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