GPT-5.6 Sol Ultra Proved a 50-Year-Old Conjecture in an Hour
The Cycle Double Cover Conjecture has been open since 1973. Szekeres posed it, Seymour re-posed it in 1979, and five decades of graph theorists could not close it. This week OpenAI closed it — or at least claims to. One day after GPT-5.6 Sol Ultra went generally available, OpenAI published a proof of the conjecture produced by the model itself: 64 subagents working in parallel, just under one hour of wall-clock time. They released the prompt and the full proof PDF.
The mechanism is the story as much as the result. Sol Ultra's ultra mode is not a bigger model, it is multi-agent orchestration — the system decomposes the problem and throws dozens of subagents at the pieces. A famous open problem in graph theory falling to a swarm of subagents in an hour is the cleanest demonstration yet that the unit of mathematical work is shifting from the lone genius to the orchestrated fleet.
One caveat worth keeping: the proof still has to survive review by actual graph theorists, and AI-generated proofs of famous conjectures have died in review before. OpenAI publishing the full PDF and prompt is the right move — it makes the claim checkable rather than a press release.
The trajectory is hard to argue with either way. In May an OpenAI model disproved an Erdos unit-distance conjecture. Now a 50-year-old conjecture gets a claimed proof in under an hour. If even half of these hold up, research mathematics just became an agent workload.
Proof PDF: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf
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The mechanism is the story as much as the result. Sol Ultra's ultra mode is not a bigger model, it is multi-agent orchestration — the system decomposes the problem and throws dozens of subagents at the pieces. A famous open problem in graph theory falling to a swarm of subagents in an hour is the cleanest demonstration yet that the unit of mathematical work is shifting from the lone genius to the orchestrated fleet.
One caveat worth keeping: the proof still has to survive review by actual graph theorists, and AI-generated proofs of famous conjectures have died in review before. OpenAI publishing the full PDF and prompt is the right move — it makes the claim checkable rather than a press release.
The trajectory is hard to argue with either way. In May an OpenAI model disproved an Erdos unit-distance conjecture. Now a 50-year-old conjecture gets a claimed proof in under an hour. If even half of these hold up, research mathematics just became an agent workload.
Proof PDF: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf
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