OpenAI Claims Major Progress on 372 Math Problems but Experts Want Proof

OpenAI has released hundreds of mathematical research papers containing claims about problems that have challenged researchers for decades, including some of the most famous unsolved questions in mathematics. The collection covers 372 open problems and has triggered intense debate over whether artificial intelligence is beginning to transform mathematical research or producing more work than humans can reasonably verify.

The release is particularly striking because OpenAI says most of the results were generated by an internal AI model that has not been made publicly available. While some researchers see the potential for major discoveries, others are questioning the quality of the proofs, the lack of transparency and the growing pressure on mathematicians to examine an enormous volume of machine-generated research.

OpenAI Has Released 722 Papers Covering 372 Mathematical Problems

The latest release from OpenAI contains 722 papers relating to 372 open problems across mathematics and theoretical computer science. The collection spans several disciplines, including algebra, geometry, mathematical analysis and computer algorithms, with some papers claiming progress on questions that have resisted previous attempts by human researchers.

According to OpenAI, almost every result was produced by an internal frontier model in response to a single prompt provided to one AI agent. The company says the average result used computing resources equivalent to approximately three hours of ChatGPT Pro thinking, a figure that suggests the approach could eventually make advanced mathematical research considerably more accessible.

The announcement follows another major mathematical claim from OpenAI involving the Navier-Stokes problem. That earlier effort reportedly relied on a swarm of approximately 10,000 AI agents and millions of dollars in computing resources, making the latest collection particularly interesting to researchers watching the cost of AI-assisted discovery.

If the company’s description accurately reflects how the results were produced, the technology could offer a substantially cheaper route to investigating difficult mathematical questions. However, the model responsible for the work remains unreleased, which means outside researchers cannot independently reproduce the entire process using the same system.

OpenAI published the collection through a GitHub repository, alongside selected summaries of the model’s reasoning, computational estimates and information about the number of attempted problems. The company has also shared formalised versions of many proofs using Lean, a programming language designed to help computers check mathematical reasoning.

OpenAI says the release is intended to push the frontier of human knowledge and enable further progress in mathematics. The difficult question is whether the collection can deliver that goal without placing an unreasonable burden on the researchers expected to evaluate it.

Some Results Target Mathematics’ Most Famous Unsolved Questions

Several papers in the collection concern major mathematical challenges, including the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. Both are among the seven Millennium Prize Problems established by the Clay Mathematics Institute, with each carrying a $1 million prize for an accepted solution.

The Riemann hypothesis is particularly significant because of its connection to the distribution of prime numbers. It concerns the locations of certain zeros of the Riemann zeta function, and a complete proof would represent a major achievement in number theory.

The Birch and Swinnerton-Dyer conjecture concerns elliptic curves, mathematical objects with important connections to number theory and other areas of mathematics. Its implications have made it one of the most closely studied problems in modern mathematical research.

OpenAI’s release also includes a claimed solution to the four-dimensional Kakeya conjecture, alongside results involving improvements to important algorithms. These claims have attracted attention because they concern questions with substantial histories of research behind them.

However, there is an important distinction between making progress on an open problem and solving it completely. A paper might establish a useful special case, introduce a new technique or prove a related theorem without resolving the original question in its entirety.

That distinction is especially important when evaluating claims involving Millennium Prize Problems. A paper’s appearance in an AI-generated research collection does not establish that a famous conjecture has been solved, and a prize cannot be claimed merely because a model has produced a proposed proof.

Each result must be assessed on its own mathematical merits. Researchers need to establish precisely what has been proved, whether the reasoning is sound and whether the result represents a genuinely new contribution.

Mathematicians Are Questioning the Quality of the Evidence

The sheer size of the collection has created excitement, but it has also raised concerns about the reliability and presentation of the work. Mathematicians must determine whether the papers contain valid proofs and original insights, or whether some arguments combine existing techniques without successfully establishing their conclusions.

Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology, expressed reservations about claims that difficult problems could be solved through a single prompt and one AI agent. Speaking to Scientific American, he said, “Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified.”

Sutherland added, “We should ask for receipts.” His comments reflect a central principle of mathematical research: claims need to withstand independent scrutiny before the wider community can accept them as established results.

Transparency becomes particularly important when researchers cannot access the model responsible for the work. Without sufficient information about the system and its methods, outside experts face difficulties reproducing the results and understanding how the model reached its conclusions.

The presentation of the papers has created another problem. A mathematician quoted in the second reference described encountering a paper concerning a problem he had studied, only to find its explanation so difficult to follow that he believed it would have been rejected had he received it as a journal submission.

A technically correct result can still be difficult to evaluate if its proof is poorly explained. Researchers need clear definitions, logical steps and sufficient context to determine how a conclusion follows from the assumptions.

The concern is therefore not limited to whether AI can produce correct mathematics. It also involves whether the resulting work can be understood, checked and incorporated into the body of mathematical knowledge.

OpenAI Has Already Retracted Papers and Corrected Errors

The initial collection has undergone corrections since publication. According to the second reference, OpenAI has retracted three papers following an elementary error and amended several others after mistakes invalidated their results.

These developments do not demonstrate that every paper in the collection is unreliable. They do, however, show why the claims need careful examination before being treated as established mathematical discoveries.

Mathematics relies on proofs that can be inspected and checked, rather than the reputation of the person or organisation presenting them. Even a sophisticated AI model can generate an argument that contains a subtle logical gap, applies a theorem incorrectly or reaches a conclusion that its reasoning does not support.

Errors also vary in significance. A minor presentation problem may leave the underlying mathematics intact, while a missing assumption or invalid inference can undermine an entire proof.

The number of papers makes the task more demanding because each result requires its own assessment. Researchers cannot assume that a proof is correct simply because another paper from the same model has survived scrutiny.

OpenAI has acknowledged the need to improve how it presents mathematical results. The company says it plans to improve citations, mathematical exposition and the presentation of its research in future releases.

For mathematicians, those changes could make the work easier to assess. However, improved presentation will need to be accompanied by reliable proofs and sufficient transparency for independent verification.

Can Lean Help Verify Hundreds of AI-Generated Proofs?

One tool central to OpenAI’s approach is Lean, a programming language that allows mathematical proofs to be formalised and checked by a computer. Rather than relying solely on a human reader to follow every step, researchers can express an argument within a formal system built around mathematical definitions and logical rules.

OpenAI says it has formalised around 300 of the main results in the collection at the time of the reported release. The company has also said it will continue adding formalised proofs as the work progresses.

Formal verification could be particularly useful when AI produces research at a scale that would be difficult for individual mathematicians to examine manually. A correctly formalised proof can provide strong assurance that the encoded logical steps follow from the stated assumptions.

However, formalisation does not automatically settle every question about a mathematical claim. The formal version must accurately represent the intended argument, and researchers still need to determine whether the theorem being proved genuinely addresses the original problem.

An AI system can also make mistakes when translating mathematical reasoning into a formal language. The second reference notes that previous AI-generated formalisations, including work associated with the Navier-Stokes problem, have raised concerns about whether the formalised argument faithfully captures the intended result.

This means automated checking and expert review have different but complementary roles. Software can help identify logical errors within a formal proof, while mathematicians assess the significance, originality and relevance of the result.

Lean may therefore become an important part of AI-assisted research, but its usefulness depends on how carefully the proofs are formalised and how transparently the process is documented.

The Navier-Stokes Dispute Has Increased Pressure for Transparency

OpenAI’s latest release follows controversy surrounding its earlier claimed solution involving the Navier-Stokes problem, another Millennium Prize Problem. Mathematicians Tristan Buckmaster and Levent Alpöge alleged that OpenAI had accessed their data and used their ideas in developing the work, while OpenAI denied the allegations.

The dispute intensified questions about how AI companies obtain mathematical insights, what information they disclose and how researchers can independently evaluate their claims. It also contributed to calls for clearer standards governing the publication of AI-generated research.

On September 21, OpenAI announced that it was assembling an independent advisory group of mathematicians to develop recommendations for responsibly releasing AI-generated mathematical results. According to the first reference, the recommendations called for companies to disclose the model, exact prompt and computational resources behind each result.

OpenAI says it has drawn on the group’s advice in preparing the latest collection. However, the company has not provided every detail recommended, and the model responsible for the results remains unavailable to the public.

The company has argued that it takes the recommendations seriously while maintaining that it is not bound by them. It has also said it is working towards releasing the model responsibly.

That leaves researchers with a difficult balance. Making AI-generated results available could accelerate discovery, but releasing large collections without enough supporting information may make independent evaluation more difficult.

Some mathematicians believe the results should be shared rather than kept secret, even if they require substantial checking. Daniel Litt, a mathematician at the University of Toronto, told Scientific American, “If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us.”

Litt added, “To me, it’s going to be a good thing for mathematics.” His position captures the argument that imperfectly presented research can still contain useful ideas, provided the community has an opportunity to examine them.

AI Could Change Mathematical Research Beyond Recognition

The latest release also raises questions about the role of mathematics in evaluating the broader capabilities of artificial intelligence. Solving difficult mathematical problems requires complex reasoning, careful handling of assumptions and the ability to construct arguments that withstand logical examination.

For AI developers, these challenges make advanced mathematics a useful way to evaluate whether models are becoming more capable at research-level tasks. Strong results could support claims that AI systems are progressing towards artificial general intelligence, a hypothetical form of AI able to perform a broad range of cognitive tasks at human or higher levels.

However, a large collection of mathematical papers is not proof that artificial general intelligence has been achieved. The reliability, reproducibility and significance of the individual results still need to be established.

The release also creates practical concerns for students and early-career researchers. If AI can generate large volumes of potentially useful research, human mathematicians may face greater pressure to find original problems, evaluate machine-generated work and demonstrate the value of their own contributions.

Terence Tao has criticised the pace at which frontier AI laboratories are producing mathematical results, according to the first reference. His concerns reflect a broader debate over whether the speed of AI-assisted research is outstripping the community’s ability to evaluate it responsibly.

OpenAI says it plans to fund workshops, conferences and other programmes to help researchers understand major results produced by its models. Such initiatives could help mathematicians assess the most significant work and identify methods worth developing further.

Still, the workload cannot disappear simply because the initial research becomes cheaper. If AI produces hundreds of papers, someone must still determine which arguments are correct and which findings deserve a place in the mathematical literature.

The Real Test Will Be What Survives Independent Review

OpenAI’s collection could contain valuable discoveries that help researchers solve difficult problems and develop new mathematical techniques. It could also include incomplete arguments, errors and claims whose significance becomes less impressive after detailed examination.

The distinction will emerge through independent review, reproducibility and the willingness of researchers to challenge the work rather than accept the company’s claims at face value.

If AI systems can consistently produce correct, original and understandable proofs, they could become powerful research tools for mathematicians around the world. If the papers remain difficult to verify, however, their volume could create as much work as it saves.

The next milestone is therefore not another massive release of AI-generated mathematics. It is the point at which independent experts can confirm which results are correct, explain why they matter and build further discoveries on a foundation that others can trust.