OpenAI's GPT-5.6 Sol Ultra Solves 50-Year-Old Math Conjecture in Under an Hour

OpenAI has announced that GPT-5.6 Sol Ultra, its latest flagship model, has generated a complete proof of the Cycle Double Cover Conjecture — a fundamental open problem in graph theory that had remained unproven for approximately 50 years. The model accomplished the task in under an hour, deploying 64 subagents working in parallel.

The conjecture addresses a basic question in graph theory: in any network of vertices and edges, can a set of cycles always be found such that each edge is traversed exactly twice? Formulated independently by several mathematicians in the 1970s, it had seen only partial solutions for special cases with no generally accepted proof.

Mathematician Thomas Bloom of the University of Manchester reviewed the proof and called it a very nice proof, noting the solution is short, elementary, and could have been discovered in the 1980s. It requires no new mathematical theories, but cleverly combines existing tools.

Bloom suggested the reason humans missed it was a subtle, counterintuitive twist in the reasoning. He wrote that a human would try the natural approach, see it fail, and think the problem must be harder than expected — while the AI does not get discouraged and keeps trying small variations until one clicks.

However, Bloom also offered sharp criticism: OpenAI's paper contains no citations to prior work that the proof builds upon — specifically a 1983 paper by Bermond, Jackson, and Jaeger. He noted this is a frequent issue with AI-generated proofs: they use ideas and proof strategies from the literature without proper citation.

The mathematician doubts the AI came up with the solution entirely on its own, given that its first problem-solving instinct is generally to search for all related papers on a problem and read them. This reignites the ongoing debate about whether reasoning models merely recombine existing knowledge or produce genuinely novel work.

The human-written prompt played a crucial role. It instructed the model to assume a complete proof exists (cutting off the easy answer that the conjecture is open), banned web searches about whether the problem has been solved, and directed 64 agents to work independently. The model was told to compute for at least eight hours before giving up — it finished in one.