An amateur used ChatGPT to prove an Erdős conjecture via a method no expert had ever tried, surprising mathematicians who study the problem.
Key Takeaways
ChatGPT proved a conjecture in number theory (primitive sets domain) using a novel proof approach no human mathematician had previously attempted.
Experts believe the method is not a one-off – it may generalize to further unsolved problems beyond this conjecture.
Raw ChatGPT output was poor quality; an expert had to sift through and distill the core insight before the proof was usable.
The result suggests some Erdős problems may have persisted due to human mental blocks, not irreducible mathematical depth.
Hacker News Comment Review
Headline accuracy was disputed: “amateur solves” overstates what ChatGPT delivered directly, since expert translation of messy output was required before the key insight was recoverable.
A sudden unexplained use of the von Mangoldt function in the reasoning trace, with no prior mention in the run, raised serious questions about proof provenance and whether the trace is complete.
The problem’s persistence was reframed: commenters argued AI may be structurally better at cross-domain technique transfer because it has no peer-pressure incentive to avoid unfamiliar tools.
Notable Comments
@adamgordonbell: Shares the actual prompt – explicit no-search instruction, “number theory and primitive sets” framing, followed by 80m 17s of unguided thinking.
@crsn: “One-shotting a problem like this would have been nearly unthinkable in 2025” – flags the zero-turn completion as the real technical milestone.
@meken: Even if AI progress stalls here, clearing mentally-blocked problems from the backlog is a standalone win for math research.
