GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]

cdn.openai.com

July 10, 2026

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Summary

GPT-5.6 Sol Ultra has successfully produced a proof for the Cycle Double Cover Conjecture. The proof is documented in a PDF file available online.

Coverage & discussions

Hacker News · cdn.openai.com

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Analysis ready

Community Sentiment

Positive

Positives

AI has now solved one of the most famous open problems in graph theory, using an off the shelf model, in one hour — this is a monumental milestone in AI capabilities!
The proof is not just concise but elegantly combines previously known properties, showcasing a level of insight that rivals human mathematicians.
Commenters are excited that AI's ability to tackle complex problems could accelerate scientific advancements, hinting at a future where AI researchers significantly enhance human efforts.

Concerns

There's skepticism about the significance of solving a problem that few seem to care about, raising doubts about AI's impact on meaningful advancements.
Some commenters worry that if AI can outperform humans in mathematics, it could lead to existential questions about human value and job security.
Critics argue that AI has yet to prove itself beyond basic tasks, with no recent advancements in artistic or writing sensibilities, suggesting a plateau in creative capabilities.