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GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
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Overview
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.
Summary from cdn.openai.com.
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- Praise: 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!
- Praise: The proof is not just concise but elegantly combines previously known properties, showcasing a level of insight that rivals human mathematicians.
- Praise: 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.
- Concern: 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.
- Concern: Some commenters worry that if AI can outperform humans in mathematics, it could lead to existential questions about human value and job security.
- Concern: 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.