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Why the Legendary Erdős Problems Are Falling to AI
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OpenAI's internal AI models have produced novel mathematical results on long-standing problems posed by Paul Erdős, including a counterexample to the 1946 unit distance problem and solutions to three additional Erdős problems via an unreleased model called Astra.
AI is demonstrating the ability to generate genuinely novel mathematical insights by connecting distant branches of math that humans hadn't successfully applied, not just verifying or computing known approaches. For engineers working on formal verification or proof-adjacent systems, this signals that AI collaboration on hard analytical problems is becoming viable, though the models remain unreleased and their outputs still require substantial human refinement.
Written by elseif from the cluster below · every claim links back to a sourceThe three things worth knowing
An internal OpenAI model produced a counterexample to Erdős's 1946 unit distance problem, described as the first historically significant proof from an AI model.
The unreleased Astra model made 10 mathematical advances including solutions to three more Erdős problems.
The AI's approach was innovative in that it brought in ideas from a distant branch of math that no human had successfully applied to these problems.
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