In 1964, a Hungarian mathematician named Tibor Gallai posed a problem about graph colorings that seemed, at first glance, like a straightforward exercise in combinatorics. Sixty-two years later, it remains unsolved in the professional mathematics literature. Last week, a retired high school teacher in rural Oregon named David Strom submitted a proof to the arXiv preprint server that, if verified, resolves the problem completely. Strom's primary collaborator was a publicly available AI assistant.

The story of how Strom arrived at the proof is as interesting as the proof itself. A lifelong amateur mathematician, Strom had been working on recreational math problems for decades, the kind of puzzles that appear in popular science magazines and mathematical hobbyist communities. He encountered the Gallai problem through a YouTube video about unsolved mathematics and became, as he described it in a blog post, unreasonably obsessed with it.

What changed this time was the availability of AI tools capable of engaging with mathematical reasoning at a high level. Strom spent several months in dialogue with an AI assistant, using it as a mathematical sparring partner — proposing approaches, having them critiqued, exploring alternative framings, and gradually building toward a proof strategy that neither he nor the AI could have developed independently.

"I would describe the AI as a very patient, very knowledgeable collaborator who never got tired and never made me feel stupid for asking basic questions. It could not solve the problem. But it could tell me why my approaches were failing, and that was invaluable."

— David Strom, amateur mathematician

The mathematical community's response has been cautious but genuinely interested. Three professional mathematicians who have reviewed preliminary versions of the proof have described it as plausible and worth serious examination. None have yet committed to a formal verification, which for a proof of this complexity could take months. The arXiv submission has attracted unusual attention — over 40,000 views in its first 48 hours, an extraordinary number for a combinatorics preprint.

The implications of Strom's work extend well beyond the specific mathematical result. For decades, the sociology of mathematical research has been organized around graduate programs, research universities, and the informal networks of professional mathematicians who evaluate and validate each other's work. Amateur contributions to serious mathematics are vanishingly rare — the last notable example was probably Yitang Zhang's 2013 breakthrough on prime gaps, and Zhang was a professional mathematician working in isolation, not a retiree with no formal training beyond a bachelor's degree.

AI is beginning to change this dynamic. The same tools that allow a retired teacher to engage productively with a 60-year-old unsolved problem are also being used by professional mathematicians to accelerate their own research. DeepMind's AlphaProof system has demonstrated the ability to generate formal proofs for competition-level mathematics problems. Anthropic's Claude Opus 4.7 has been used by several research groups to check and extend existing proofs. The question of where human mathematical insight ends and AI assistance begins is becoming genuinely difficult to answer.

For the mathematical community, this raises uncomfortable questions about attribution, credit, and the nature of mathematical discovery. If a proof is generated through an extended human-AI dialogue, who deserves credit? How should journals handle submissions that acknowledge substantial AI assistance? These questions do not yet have consensus answers, and the Strom case is likely to accelerate the conversation.

"The question is not whether AI can do mathematics. It clearly can, at least in some domains. The question is what that means for the humans who have built their identities and careers around being mathematicians."

— Professor of Mathematics, Princeton University

Strom himself is philosophical about the attribution question. In his blog post, he describes the proof as a genuine collaboration and expresses no interest in claiming sole credit. He is, by his own account, simply delighted that a problem he found beautiful has been resolved, and that he was able to play a role in resolving it. Whether the mathematical establishment shares that equanimity remains to be seen.