OpenAI Says GPT-5.6 Sol Ultra Proved the 50-Year-Old Cycle Double Cover Conjecture in Under an Hour

A day after making GPT-5.6 Sol Ultra generally available, OpenAI announced that the model had produced a proof of the Cycle Double Cover Conjecture — a graph theory problem that has resisted mathematicians for roughly half a century — in just under one hour, using 64 concurrent subagents.

The problem

The conjecture, posed independently by Szekeres and Seymour in the 1970s, claims that for every bridgeless graph — one with no edge whose removal disconnects it — there exists a collection of cycles that together cover every edge exactly twice. It is easy to state, notoriously hard to prove, and central to a web of related problems in graph theory.

How the proof was generated

According to OpenAI, the prompt instructed Sol Ultra to deploy up to 64 subagents and manage them "aggressively and dynamically." Early rounds were designed for diversity: agents pursued different mathematical formulations, algebraic angles and structural inductions independently before the orchestrating model consolidated promising lines. The company published both the prompt and the resulting proof, released as a PDF with authorship attributed entirely to the model.

OpenAI says the proof is machine-verified. That claim is doing significant work: formal verification in a system like Lean would make the result essentially indisputable, while "verified" in a looser sense — checked by other models or partially formalized — would leave the burden on human referees.

The scrutiny begins

Mathematicians have begun the slow work of validation, and the field's recent history counsels patience — several celebrated AI "solutions" to open problems have dissolved under expert review, while others, like AI-assisted progress on Erdős problems, have held up.

If the proof survives, it would arguably be the most significant standalone AI achievement in mathematics to date — not a competition problem or a bounded benchmark, but an open conjecture with a 50-year pedigree, solved by orchestrated parallel reasoning. If it fails, it becomes the sharpest cautionary tale yet about trusting fluent, machine-generated mathematics without formalization.

Either way, the method — dozens of diverse subagents managed dynamically over a one-hour horizon — is a template the rest of the field will now copy.