GPT-5.6 has reportedly proven a 50-year-old hypothesis in graph theory
Sh0ny
12 июля 20261 min read
In short
A day after the release of GPT-5.6 Sol Ultra, OpenAI announced that the model had found proof of the double-covering cycle hypothesis—an open problem in graph theory that had remained unsolved for nearly half a century. According to OpenAI employee Ethan Knight, the calculations took less than an hour and required 64 parallel subagents.
On July 10, one day after the public launch of GPT-5.6 Sol Ultra, OpenAI announced that its flagship language model had solved a problem that had remained unsolved in graph theory for nearly half a century. This refers to the double-covering cycle conjecture—one of the most well-known unsolved problems in this field.
According to OpenAI employee Ethan Knight, the model found a proof in less than an hour. To achieve this, an approach using 64 parallel subagents was employed—that is, the problem was processed by a set of independently operating copies of the model working in coordination.
Status of the Proof
Errors in the models’ mathematical reasoning are not uncommon, so this claim should be treated with caution. At this time, the presented proof is being reviewed by mathematicians, and its correctness has not yet been confirmed.
The Method Takes Center Stage
Even if the formal proof does not withstand peer review, OpenAI’s approach to solving a complex scientific problem is of greater interest. The large-scale use of parallel subagents demonstrates how a large language model can be applied to tasks requiring multi-step logical reasoning and task decomposition.