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

In July 2026, OpenAI announced that its flagship model, GPT-5.6 Sol Ultra, had successfully proven the Cycle Double Cover Conjecture in graph theory. Since its proposal in the 1970s, only partial special cases had been solved over 50 years. The model used 64 sub-agents running in parallel and completed the proof in under an hour.

Mathematician Thomas Bloom of the University of Manchester praised the proof in his preliminary assessment as 'very beautiful,' noting it is 'short, elementary, and could have been discovered in the 1980s.' The proof introduced no new theory but cleverly combined existing tools. Bloom believed the key step contained a counterintuitive twist, where human mathematicians might give up after trying natural approaches, while the AI kept trying small variations until it succeeded.

Prompt engineering was crucial to this success: the model was told to 'assume a complete proof exists,' prohibited from searching the internet, and had to reject partial results or reductions to other unsolved conjectures. It was required to compute for at least 8 hours before giving up, but actually only took 1 hour.

Bloom also offered sharp criticism: the core mathematical idea in the proof at least dates back to a 1983 paper by Bermond, Jackson, and Jaeger, but the OpenAI paper contains no citation at all. He pointed out that this is a common issue with AI-generated proofs—they use ideas and strategies from the literature without proper attribution.

Bloom doubts the AI independently invented the solution. 'Given that its first instinct in problem-solving is often to search all relevant papers and read them,' he thinks the proof is more likely a recombination of existing ideas rather than a true creative leap. This fuels the ongoing debate about whether AI possesses genuine creativity: does it merely recombine existing information, or can it produce something entirely new?

Bloom compares this breakthrough to OpenAI's previous solution of the Unit Distance Conjecture. Both are 'major open problems that turned out to be much easier than expected—requiring no major new theory, and one could imagine that in many alternative histories these proofs would have been discovered decades ago.' He believes AI excels at such problems: the necessary theory already exists, requiring only a great deal of patience and persistence.

However, Bloom warns that such problems likely represent only 'a small fraction' of all unsolved problems, and they cannot be identified in advance. AI systems, by attacking a large number of problems simultaneously in a 'strange new world' (and only reporting successes), will give us a better sense of which problems have 'always been within our reach.' This also means the statistical significance of breakthroughs may be skewed by selective corporate reporting.

The most important uncertainty at present is that full verification by the math community has not been completed. Bloom's assessment is the most detailed public analysis so far, but it is not peer review. The full correctness of the proof still needs official confirmation. Furthermore, OpenAI only reports successful cases, which may lead to optimistic estimates of AI capabilities.

Another open question is whether AI systems can solve problems that require genuinely novel theory. Bloom believes that under the current paradigm, AI may crack more conjectures that 'only need existing theory plus patience' in the future, but deeper problems—those requiring entirely new conceptual frameworks—may remain beyond its reach.

The achievement of GPT-5.6 Sol Ultra is both a milestone and a caution. It demonstrates the AI's ability to discover hidden simple solutions through sheer stubborn exploration—a quality difficult for humans to replicate. At the same time, the missing citation issue highlights the limitations of AI output: it cannot consciously integrate into the academic integrity system.

This incident suggests that we may need new citation standards for AI-generated research. More importantly, it reveals that a subset of 'hard' problems actually just lack a bit of persistent effort. AI is helping us discover these overlooked simple paths, but true creative breakthroughs—those requiring the construction of entirely new theoretical frameworks—may remain the last bastion of human intelligence.