OpenAI's GPT-5.6 Sol Ultra proves 50-year-old graph theory problem in one hour

OpenAI announced on July 10 that its GPT-5.6 Sol Ultra model completed a full proof of the Cycle Double Cover Conjecture in under an hour. This is a major unsolved problem in graph theory that has stumped mathematicians for over 50 years. The conjecture, proposed by George Szekeres in 1973 and Paul Seymour in 1979, asks whether every bridgeless graph has a set of cycles covering each edge exactly twice.

OpenAI researcher Ethan Knight shared on X that the model used 64 sub-agents working together, with adversarial agents checking for errors. It finished in about an hour, even though the system had eight hours reserved. The proof involved reducing the problem to cubic graphs, using the 8-flow theorem, and linear algebra over GF(3).

Mathematician Thomas Bloom from the University of Manchester called the proof "elegant and basic," highlighting AI's patience in trying many variations. But he noted it lacks any references to existing literature, like a key 1983 paper. The proof hasn't been peer-reviewed or formally verified, so the math community is cautious.

If validated, this would be the first time a large language model independently solved a problem from Wikipedia's list of unsolved math problems. Previous AI breakthroughs in math, like DeepMind's work on the cap set problem, were human-AI collaborations. Graph theory experts will review the proof in the coming days to weeks.