OpenAI AI Claims Three Big Math and Physics Proofs
OpenAI says its AI models produced three new proofs in maths, computer science and physics, but none is peer reviewed yet. What was claimed and what comes next.
OpenAI says its AI models have produced three new scientific results, one each in mathematics, computer science and physics. The company announced the results on October 26 and said it is working with outside academic experts to check them. None of the three claims has been peer reviewed or independently confirmed yet, so they should be read as claims, not settled science.
What OpenAI announced
In a post titled "Working with academic communities to build scientific understanding", OpenAI said its models produced the results and that it is handing the job of verifying and explaining them to groups of outside academics. The company said the experts take part voluntarily, are unpaid, sign no non-disclosure agreements, and keep their independence. OpenAI also said it does not seek academic credit for the discoveries. The three results got three different treatments. For the mathematics result, OpenAI published the AI output and left researchers to organise their own efforts to explain it. For the computer science result, an outside group formed to explain the work while the output was made public. For the physics result, the outside group asked OpenAI to hold back the AI-produced material and write the result up itself.
The computer science claim: a famous hypothesis disproved
The computer science result concerns the Exponential Time Hypothesis, a long-standing idea about how fast certain hard problems can be solved. The hypothesis says that a well-known problem called 3-SAT cannot be solved in subexponential time, meaning much faster than current methods allow. Researchers have relied on this idea for decades, and OpenAI says it has been used in hundreds of papers to set limits on how efficiently problems in graph theory, computational biology, databases and computational geometry can be solved. OpenAI says its system produced a natural-language disproof of the hypothesis on October 16, and that the result was formalised in Lean, a computer language used to check mathematical proofs, on October 17. The company says the finding reopens questions about how much faster these tasks could become. It also cautions that finding such algorithms, and turning theory into practical improvements, will require significant further research. A disproof here does not mean computers can suddenly solve everything quickly, and it does not by itself settle the famous P versus NP question. A group led by Russell Impagliazzo and Ramamohan Paturi of the University of California San Diego, two of the researchers who first proposed the hypothesis, along with Ryan Williams of the Massachusetts Institute of Technology, will shepherd the verification of this result.
The mathematics claim: waves in every dimension
The mathematics result is a proof of the local smoothing conjecture, proposed by Christopher Sogge in 1991. In simple terms, it concerns how waves concentrate over time. OpenAI says its models proved the conjecture in every dimension, using a new auxiliary partial differential equation, and that this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. Earlier work had reached less far: researchers proved local smoothing in two dimensions in 2019, and proved the Kakeya conjecture in three dimensions in 2025. OpenAI says the AI output came on October 18 and was formalised in Lean on October 19. Both the natural-language writeup and the Lean proof are posted in the company's public GitHub repository.
The physics claim: the building blocks of matter
The physics result is a mathematically rigorous existence proof for certain interacting quantum field theories in four dimensions, including quantum chromodynamics, the theory of the strong force that holds atomic nuclei together. OpenAI says the work also covers a unified completion of the Standard Model of particle physics, and includes a proof concerning the existence of pure Yang-Mills theory, which is part of a long-standing Millennium Prize problem set by the Clay Mathematics Institute. OpenAI says its models produced a proof of Yang-Mills existence on September 9 and a quantum chromodynamics proof on September 18, and that the Lean formalisation of the Yang-Mills proof was completed on October 16. A group led by David Gross, a Nobel laureate in physics, will lead the work on this result. Unlike the other two results, the physics material has not been released publicly yet, because the outside group is writing it up itself.
Why it matters, and what is not yet proven
If the claims hold up, they would touch three central open problems at once. The computer science result would reopen questions about the limits of efficient computation. The mathematics result would extend earlier work from two or three dimensions to every dimension. The physics result would put parts of quantum field theory on a firmer mathematical footing. But the key word is "if". OpenAI itself describes the manuscripts as a form of raw research data rather than finished science. A Lean formalisation checks the exact statements that were formalised, and independent experts still need to confirm that those statements match the original conjectures in full. Until peer review and independent verification are complete, the results remain unverified claims, however striking they sound. OpenAI links the work to a recently announced 5 million dollar contribution to the Simons Foundation, which will manage the money for workshops, conferences and special programs to help researchers understand and build on AI-produced results. The company says it does not yet know which of its three release approaches will prove most useful, and that its process continues to evolve in response to feedback from academic communities.
What happens next
The next step belongs to the outside experts. The computer science and mathematics groups will examine the published proofs and explain their implications, while the physics group prepares its own writeup. Only after that scrutiny will the wider scientific community know whether these are genuine breakthroughs, partial results, or claims that do not survive checking. For now, the story is as much about how AI research is shared as about the results themselves: openly, with outside shepherds, and before the verdict is in.
Sources
Economic Times CIO - https://cio.economictimes.indiatimes.com/news/artificial-intelligence/openais-ai-proves-exponential-time-hypothesis-false-shifts-scientific-discovery-landscape/135226369?utm_source=top_news&utm_medium=sectionListing Unite.AI - https://www.unite.ai/openai-says-its-models-produced-three-proofs-in-math-cs-and-physics/ Le360 - https://en.le360.ma/technology/openai-announces-three-ai-generated-discoveries-in-mathematics-computer-science-and-physics_LD3HBJQQ4JHXFOUAUMF3TODF7U/