A method the literature missed for ninety years
Tao, Jared Duker Lichtman and six co-authors resolved Erdős Problem #1196 on primitive sets. The idea that carried it — bounding Erdős sums via Markov chains with von Mangoldt weights — was suggested by output from GPT-5.4 Pro and, the authors note, appears to have been overlooked since Erdős's seminal 1935 paper. This is the collaboration mode that is hardest to dismiss: the machine supplied a direction, the people supplied the proof.
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What's new (Tao)
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Tao, Jared Duker Lichtman and six co-authors resolved Erdős Problem #1196 on primitive sets.
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The idea that carried it — bounding Erdős sums via Markov chains with von Mangoldt weights — was suggested by output from GPT-5.4 Pro and, the authors note, appears to have been overlooked since Erdős's seminal 1935 paper. This is the collaboration mode that is hardest to dismiss: the machine supplied a direction, the people supplied the proof.
- 01What's new (Tao)
- 02arXiv:2605.00301