GPT-5.2 Pro Solves Erdős Problem #281 – First Confirmed Autonomous AI Solution of an Open Mathematical Problem

Summary

The AI model GPT-5.2 Pro has solved Erdős Problem #281 from number theory – a breakthrough that mathematician Terence Tao calls "perhaps the clearest example" of an AI solution to an open mathematical problem. Neel Somani reported this success, with Tao confirming that the model's proof differs significantly from earlier solution approaches. However, Tao warns against a distorted perception of AI capabilities: a new database shows that the actual success rate for AI attempts on Erdős problems is only one to two percent.

People

• Neel Somani
• Terence Tao
• Paata Ivanisvili
• Mehmet Mars Seven
• Matthias Bastian

Topics

• AI breakthrough in mathematics
• Erdős problems and number theory
• AI success rates on mathematical problems
• Distorted perception of AI capabilities
• Publication bias in AI research

Detailed Summary

The AI model GPT-5.2 Pro played a significant role in solving Erdős Problem #281 from number theory. According to Neel Somani, it was possible with the support of this model to solve another long-standing open mathematical problem.

Renowned mathematician Terence Tao evaluates this achievement as "perhaps the clearest example" that an AI has solved an open mathematical problem. However, Tao notes that earlier proofs for this problem may have already existed, which could have influenced the model's answer. Tao emphasizes, however, that the proof provided by GPT-5.2 Pro is "quite different" from the earlier proofs, suggesting a genuine independent solution approach.

At the same time, Tao warns against an overly optimistic assessment of AI capabilities. Negative results are rarely published, while positive results quickly go viral – a classic publication bias that leads to a distorted public perception.

A new database by Paata Ivanisvili and Mehmet Mars Seven systematically documents all AI attempts on Erdős problems. The reality is considerably more sobering than media hype might suggest: the actual success rate is only one to two percent and concentrates on easier problems. Nevertheless, AI is recognized as a supporting tool, even if average difficulty Erdős problems have not yet been automatically solvable.

The first autonomous solution of an Erdős problem confirmed by Tao dates to January 4, 2026.

Key Takeaways

• GPT-5.2 Pro has solved Erdős Problem #281 – a breakthrough confirmed by Terence Tao
• The AI proof differs significantly from earlier solution approaches
• The real success rate of AI on Erdős problems is only one to two percent
• Positive AI results are published disproportionately frequently, leading to distorted expectations
• AI functions as a supporting tool, not as an autonomous solver for difficult mathematical questions
• A systematic database now documents all AI attempts on Erdős problems

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