OpenAI's GPT-5.6 Sol Ultra is reported to have proven the cyclic double cover conjecture, a long-standing unsolved problem in graph theory, within one hour. This conjecture states that every bridgeless graph can be covered by a set of cycles such that each edge is included exactly twice. It is considered one of the most notable unsolved problems, having been studied by the mathematical community since the 1970s without a complete proof for about 50 years.

This result is explained as having been derived by GPT-5.6 Sol Ultra operating 64 sub-agents in parallel. The key aspect is that multiple agents worked by simultaneously exploring different approaches and comparing and integrating proof strategies. Mathematician Thomas Bloom evaluated the proof as exhibiting a surprisingly elementary structure. However, he criticized the lack of sufficient citations to existing research, known theorems, and prior results. This demonstrates that the source, scope of contribution, and judgment of originality remain important in the verification process of mathematical proofs produced by AI.

This case is reigniting the discussion regarding the role artificial intelligence can play in mathematical research. The key issue is whether AI is merely a tool that recombines existing knowledge to quickly identify paths missed by humans, or an entity that actually generates new mathematical ideas. In particular, if AI has presented a valid proof for a long-unsolved problem like the cyclic double cover conjecture, significant changes are expected in future methods of theorem proof, paper review, and research hypothesis generation. While the final evaluation must undergo rigorous verification by the mathematical community, the case of GPT-5.6 Sol Ultra is expected to be recorded as an event that simultaneously revealed the possibilities and limitations of AI-based mathematical research.