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articleJanuary 7, 2026

AI Solves Erdős Problem #728

The breakthrough in AI-assisted mathematics isn't just solving problems—it's the emerging capability to rapidly write and rewrite expositions of solutions.

Summary

Terence Tao announces that an AI system solved Erdős Problem #728 with minimal human intervention. The problem itself was unusual because Erdős's original formulation was incorrect—a proper reconstruction was only recently completed.

The Real Breakthrough

Tao's main interest isn't the solution itself. He emphasizes a different capability: "the emerging AI-powered capability to rapidly write and rewrite expositions of the solution." This ability to generate and iterate on mathematical explanations may prove more significant than solving individual problems.

What Makes This Different

Unlike most prior AI solutions to Erdős problems, this solution hasn't been located in existing literature. The AI appears to have produced genuinely novel work rather than rediscovering known results.

Key Takeaway

Problem-solving captures attention, but exposition generation changes the game. An AI that can explain a solution clearly and revise those explanations on demand transforms how mathematical knowledge spreads and builds.