OpenAI's GPT-5.6 Sol Ultra solved a 50-year-old math problem in under an hour

A 50-year-old mathematical puzzle has fallen to an AI — and it took less time than most people spend on lunch.

On Thursday, OpenAI announced that its GPT-5.6 Sol Ultra model produced a complete proof of the Cycle Double Cover Conjecture in under an hour. The model used 64 parallel subagents to crack the problem, which has been an open question in graph theory since the 1970s.

The conjecture was first posed by mathematician George Szekeres in 1973 and independently by Paul Seymour in 1979. It asks a deceptively simple question: for any bridgeless graph — one where you can’t remove a single edge and disconnect it — can you always find a set of cycles such that every edge appears in exactly two of them?

OpenAI published the proof and the exact prompts used to generate it as a PDF on its CDN. Company researcher Ethan Knight announced the result on X, writing that the model used 64 subagents working in parallel, with the system dynamically managing each agent’s workload.

The prompt instructed the model to keep research directions diverse in early stages — different agents tried different mathematical representations, algebraic approaches, and structural induction. A separate team of “adversarial agents” looked for holes and edge cases. The system was also told not to search the web, not to settle for partial proofs, and to run adversarial checks for common math errors.

The system was given up to eight hours of compute time. It finished in roughly one. The proof works by reducing the conjecture to a cubic graph problem, applying the 8-flow theorem, and using linear algebra over GF(3) — the finite field with three elements — to construct an edge labeling that guarantees every edge belongs to exactly two cycles.

Thomas Bloom, a mathematician at the University of Manchester, was among the first to evaluate the proof publicly. He called it “a very beautiful proof” — concise, elementary, and built from tools that have been around for decades. If someone had thought of it back then, Bloom said, it could have been done in the 1980s.

Bloom said the AI’s real advantage wasn’t coming up with new mathematical ideas, but its patience. “A human mathematician will try a natural approach, and if it fails, will probably give up,” he wrote. “The AI doesn’t get discouraged.”

But the proof has a clear blind spot: it cites no prior literature. A well-known 1983 paper by Bermond, Jackson, and Jaeger that ought to appear in the references is nowhere to be found. Bloom noted this is a recurring problem with AI-generated math papers.

The proof hasn’t been peer-reviewed. Uploading a PDF to a company CDN is not the same as publishing in a math journal, as several outlets and mathematicians were quick to point out. The Cycle Double Cover Conjecture has seen many claimed proofs over the years — several appeared on arXiv only to be retracted after flaws were found. The mathematical community is approaching this one with caution.

The proof also wasn’t verified with Lean or any other formal proof assistant. Several experts noted that the existing formal math libraries for graph theory aren’t sophisticated enough to handle a proof of this complexity, so automated verification isn’t an option in the short term.

The compute cost for the run was estimated at $275 to $485 on OpenAI’s Sol pricing, or up to $13,000 on the Cerebras platform.

If the proof holds up to scrutiny, it would be the first time a large language model has independently solved a problem listed on Wikipedia’s “Unsolved Mathematical Problems” page. Previous AI results in math — DeepMind’s work on the Cap Set Problem, breakthroughs in Knot Theory — were human-AI collaborations, not fully independent proofs.

Bloom argued the result also raises questions about the nature of mathematical discovery. Because the proof uses mostly classical tools from decades ago, the AI’s strength wasn’t originality — it was brute-force persistence, the ability to try thousands of variations without getting bored.

Graph theory specialists are expected to review every step of the proof over the coming days and weeks. Only after that process is complete will the result be accepted by the mathematical community.