OpenAI has announced a groundbreaking achievement in the fields of artificial intelligence and mathematics. The new GPT-5.6 Sol model has successfully proven the Cycle Double Cover Conjecture, a problem that remained unsolved for over half a century. The successful proof was achieved simultaneously with the release of the new AI model version.
The Puzzle of Graph Theory
Formulated in the 1970s, this hypothesis belongs to the field of graph theory, which studies vertices and the edges connecting them. It states that almost any graph admits a cycle double cover, where every edge belongs to exactly two closed cycles. Previously, as noted by the authoritative popular science magazine Scientific American, mathematicians had only managed to prove this for specific classes of graphs, but a general solution remained elusive.
Solution from AI
The proof generated by GPT-5.6 Sol demonstrates that any graph satisfying the hypothesis conditions can be covered by no more than eight specifically selected cycles. According to Noga Alon, a mathematician from Princeton University, this result is further evidence that artificial intelligence tools are beginning to significantly influence modern mathematical research.
How It Was Done
To obtain the proof, OpenAI used a special prompt published alongside the results. Specifically, the model was instructed to distribute the solution among 64 agents working in parallel and to continue searching for a solution even if the task was considered unsolved. Additionally, developers recommended that the model dedicate at least eight hours to searching for the proof before abandoning further attempts.
The Future of Mathematical Research
Andrew Sutherland, a mathematician from the Massachusetts Institute of Technology (MIT), suggested that similar cases may occur in the future. According to him, some problems acquire a reputation for being exceptionally difficult, causing researchers to pay them less attention, whereas large language models are capable of combining existing methods to find relatively simple solutions for long-standing mathematical hypotheses.
