GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf] (cdn.openai.com)

Article summary

A recent announcement revealed that GPT-5.6 Sol Ultra produced a proof of the Cycle Double Cover Conjecture. The model was given a prompt and worked on it for at least 8 hours. The discussion around this achievement focuses on the model's ability to track time and its implications for solving complex problems. The cost of the result and the specifics of the model's configuration are also being debated.

Main themes

• LLM problem-solving capabilities
• Temporal awareness in AI models
• Mathematical proof generation
• Model configuration and cost
• Human-AI collaboration

What commenters say

• The model's ability to track time and work on a problem for an extended period is a key factor in its ability to produce a proof of the Cycle Double Cover Conjecture.
• The use of a prompt that instructs the model to work on a problem for at least 8 hours is a novel strategy that can incentivize the model to produce a solution.
• Some commenters believe that the model's achievement is a significant breakthrough, while others argue that it is not a surprise given the model's capabilities and the amount of computational resources used.
• There is disagreement about the potential for LLMs to solve other famous open problems in mathematics, such as the Riemann Hypothesis, with some arguing that it is unlikely and others believing that it is possible with sufficient computational resources and clever prompting.
• The cost of using LLMs to solve complex problems is a significant factor, with some estimates suggesting that the cost of the result could be in the hundreds of thousands or even millions of dollars.
• Some commenters argue that the model's ability to produce a proof of the Cycle Double Cover Conjecture is evidence that LLMs can do real math and make significant contributions to the field.
• Others argue that the Riemann Hypothesis is a fundamentally different type of problem that may require new mathematical tools and techniques to solve, and that LLMs are unlikely to make a breakthrough in this area.