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AI Out-Counterexamples Human Mathematicians

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Recent months have seen AI systems generating significant counterexamples in mathematics, challenging human mathematicians. On May 20th, 2026, ChatGPT disproved the Erdős Unit Distance conjecture. While initially met with human verification, the proof's formalization in Lean was later achieved by Logical Intelligence, a company co-founded by Yan Le Cun.

Further advancements came on June 26th, 2026, when OpenAI's Sol model, steered by Boris Alexeev, produced a complete formalization of the Erdős counterexample, generating 1.2 million lines of Lean code in three weeks. This demonstrated the potential for large-scale AI-driven mathematical development.

In July, a counterexample to Grothendieck's question about finite free group schemes was discovered by Sol, autoformalized by Fable, and verified within minutes. This rapid generation and formalization of complex mathematical proofs highlight AI's growing role and capabilities in mathematical research.