Briefs · Frontier Science
A machine may have solved a 50-year-old puzzle in under an hour
OpenAI says its new model has proved the Cycle Double Cover Conjecture, a problem that has resisted mathematicians for half a century, in under an hour. Say that again slowly: half a century, under an hour.
The conjecture, posed by Szekeres in 1973 and Seymour in 1979, claims every bridgeless graph can be covered by cycles so that each edge is used exactly twice. It sounds like a parlour trick; it is, in fact, one of graph theory’s deepest open questions.
GPT-5.6 Sol Ultra, released to the public on 9 July, was told to spend at least eight hours before giving up. It used up to 64 parallel subagents, wrote the proof with Codex, and published both the proof and the prompt. A Lean formalisation, machine-checkable, followed.
One caution, and it matters: this is a claim, not a verdict. The proof had not been peer-reviewed when announced, and the history of mathematics is littered with brilliant proofs that turned out to be wrong.
Conclusion: the machine has not settled mathematics, but rather issued it a challenge, and the referees are now holding the pen.
Summary in our own words. The original belongs to its publisher.