A model cracks a problem mathematicians have chewed on for over 50 years — in less than an hour. That’s exactly what OpenAI claims: GPT-5.6 Sol Ultra allegedly produced a proof of the Cycle Double Cover Conjecture. The PDF has been sitting on OpenAI’s servers since July 10, with the model itself listed as the sole author.
What it’s about
The conjecture was posed independently by George Szekeres (1973) and Paul Seymour (1979). Simplified, it says: for any graph without «bridges» — edges whose removal would split the graph — you can find a collection of cycles that covers every edge exactly twice. Sounds harmless, but it’s one of the well-known open problems in graph theory.
The striking part is the approach: OpenAI ran 64 subagents in parallel. Instead of a single train of thought, it was a whole swarm breaking down subproblems, discarding approaches, and stitching results together.
The important caveat
The proof has not been peer-reviewed. It has not been confirmed by the field. And this is exactly where the real work begins: on Hacker News and in math circles, people are already scrutinizing whether the proof is truly airtight or whether an error hides somewhere.
That’s not a footnote. A «machine-verified» proof sounds like certainty — but humans verifying an AI output takes weeks to months.
My take
If the proof holds, this is a bigger moment than any benchmark win. Winning games, writing code — models have shown that already. Cracking a genuine, unsolved mathematical problem would be a different league: original intellectual work instead of pattern matching.
But I’m staying cautious. The history of AI is full of «breakthroughs» that shrank under closer inspection. The interesting thing isn’t the press release — it’s what the mathematicians say over the coming weeks. That’s where I’m looking.
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