# OpenAI Claims GPT-5.6 Sol Ultra Solved 50-Year-Old Math Conjecture in Under an Hour > Source: > Published: 2026-07-11 22:45:34+00:00 # OpenAI Claims GPT-5.6 Sol Ultra Solved 50-Year-Old Math Conjecture in Under an Hour - OpenAI published a claimed proof of the Cycle Double Cover Conjecture generated by GPT-5.6 Sol Ultra in under one hour using 64 parallel subagents [[1]](https://the-decoder.com/openais-gpt-5-6-sol-ultra-reportedly-solves-a-50-year-old-math-problem-in-under-an-hour/) - Mathematician Thomas Bloom called the proof 'very nice' and 'elementary,' noting it could have been discovered in the 1980s [[2]](https://x.com/thomasfbloom/status/2075855061494706240) - The proof has not undergone peer review, and the conjecture has attracted multiple flawed proofs over the decades [[3]](https://www.developersdigest.tech/blog/gpt-56-sol-ultra-cycle-double-cover-proof) - OpenAI released both the full proof and the prompt used to generate it as public PDFs [[4]](https://x.com/__eknight__/status/2075643450196971805) - Bloom criticized the proof's lack of citations for foundational prior work, including a 1983 paper by Bermond, Jackson, and Jaeger [[2]](https://x.com/thomasfbloom/status/2075855061494706240) OpenAI said on July 10 that its GPT-5.6 Sol Ultra model generated a complete proof of the Cycle Double Cover Conjecture — a 50-year-old unsolved problem in graph theory — in under one hour. The company published the proof and the prompt used to produce it as PDFs on its content delivery network, attributing the mathematics entirely to the model [1]. The Cycle Double Cover Conjecture, posed independently by George Szekeres in 1973 and Paul Seymour in 1979, asks whether every bridgeless graph contains a collection of cycles such that each edge appears in exactly two cycles. It is widely considered one of the most important open problems in graph theory [3]. OpenAI's Ethan Knight announced the result on X, writing: "Yesterday, we made GPT-5.6 Sol Ultra generally available. Today, we're sharing that it produced a proof of the 50-year-old Cycle Double Cover Conjecture using 64 subagents in just under one hour" [4]. The announcement coincided with the model's public launch. ## How the Proof Was Generated The prompt instructed GPT-5.6 Sol Ultra to deploy up to 64 concurrent subagents, managing them 'aggressively and dynamically.' Early rounds were designed to maintain diversity, with agents pursuing different mathematical formulations, algebraic angles, and structural inductions independently. Adversarial agents were assigned to hunt for edge cases and errors [1]. The instructions prohibited internet searches, rejected partial solutions and special-case proofs, and required adversarial verification against typical mathematical errors. The model was allocated eight hours but completed the task in roughly one [1]. The proof reduces the conjecture to cubic graphs, leverages the 8-flow theorem, and constructs edge labelings that force each edge into exactly two cycles through linear algebra over GF(3) [3]. ## Early Mathematician Reactions Thomas Bloom, a mathematician at the University of Manchester, provided the first substantive public evaluation. He called it 'a very nice proof' that is 'short, elementary, and could have been discovered in the 1980s' [2]. Bloom identified what he described as a key advantage of the AI approach: the model's willingness to persist through small variations of an approach that a human mathematician might have abandoned after early failures. 'One can imagine trying the natural labelling first... and when that failed shrugging... while the AI does not get discouraged,' he wrote [2]. However, Bloom criticized the proof's complete lack of citations, noting that a foundational 1983 paper by Bermond, Jackson, and Jaeger went unmentioned. He flagged this as a recurring problem with AI-generated mathematical work [2]. ## Verification Remains Pending The proof has not undergone formal peer review. Multiple outlets and commentators have emphasized the distinction between a PDF published on a company's CDN and a peer-reviewed mathematical result [5]. The Cycle Double Cover Conjecture has a history of attracting claimed proofs — including several posted to arXiv over the years — that were later found to contain gaps or were withdrawn. This history has made the mathematical community particularly cautious about premature celebration [3]. The proof was not formalized in Lean or any other proof assistant. Online commentators noted that existing graph theory libraries in formal verification systems remain insufficient for research-level theorems, making automated verification impractical in the near term [3]. Cost estimates for the compute required ranged from $275 to $485 at standard Sol pricing, with some estimates reaching $13,000 on Cerebras infrastructure [3]. ## What It Means for AI and Mathematics If verified, the result would represent the first time a large language model has independently solved a problem famous enough to appear on Wikipedia's list of unsolved mathematical problems. Previous AI mathematical achievements, including DeepMind's work on the cap set problem and knot theory, involved significant human-AI collaboration rather than fully autonomous proof generation [3]. The achievement also raises questions about the nature of mathematical discovery. Bloom's observation that the proof is 'elementary' — relying on techniques available for decades — suggests the AI's advantage lay in computational persistence rather than conceptual novelty [2]. Professional verification is expected to take days to weeks. Graph theorists will need to stress-test each step of the argument before the result can be considered settled [5]. ## Companies mentioned ## Further sources [[1] The Decoder — OpenAI's GPT-5.6 Sol Ultra reportedly solves a 50-year-old math p… ↗](https://the-decoder.com/openais-gpt-5-6-sol-ultra-reportedly-solves-a-50-year-old-math-problem-in-under-an-hour/) [[2] Thomas Bloom on X — reaction thread on the Cycle Double Cover Conjecture proof ↗](https://x.com/thomasfbloom/status/2075855061494706240) [[3] Developers Digest — GPT-5.6 Sol Ultra Produces Proof of the Cycle Double Cover … ↗](https://www.developersdigest.tech/blog/gpt-56-sol-ultra-cycle-double-cover-proof) [[4] Ethan Knight (OpenAI) on X — announcement of the Cycle Double Cover Conjecture … ↗](https://x.com/__eknight__/status/2075643450196971805) [[5] AI Weekly — OpenAI Attributes Cycle Double Cover Proof to GPT-5.6 Sol Ultra ↗](https://aiweekly.co/alerts/openai-attributes-cycle-double-cover-proof-to-gpt-56-sol-ultra) The stories that matter, in one email. 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