OpenAI on Tuesday published AI-generated full or partial solutions to more than 370 outstanding mathematical problems, among them questions long regarded as grand challenges of the discipline. The sheer volume of results stunned many mathematicians, while the company's methods for producing and releasing them split the field: some researchers greeted the cache with enthusiasm, seeing vast new territories for mathematicians to explore, while others argued that the approach OpenAI and other AI companies have taken toward solving mathematical problems amounts to an assault on mathematics as a human academic discipline.

The company said the results were achieved with an unreleased internal AI model that required, on average, roughly three hours of computing time to arrive at each solution. The massive cache includes full or partial results for many of the problems mathematicians have long considered the most important in the field—questions that, in some cases, have resisted human attempts for generations.

The release comes weeks after OpenAI said it had used another unreleased internal model to solve the Navier-Stokes equations, which describe the motion of fluids and rank among the seven Millennium Prize problems set out by the Clay Mathematics Institute in 2000, each carrying a $1 million award—prizes that have never been granted, as the institute requires a claimed solution to be published and broadly accepted by the mathematics community before it pays out. In the newest batch, OpenAI said it had made progress on three additional Millennium Prize problems but had not fully solved them.

AI companies have targeted mathematical problems as a way of showcasing the capabilities of their models. AI researchers have also said that training models on difficult mathematics may help them learn skills that generalize to other real-world domains—for example, logical reasoning, or persistence in the face of hard problems. It may also improve performance in heavily mathematical fields such as physics or economics, although it remains unclear exactly how a model's mathematical capabilities transfer to domains like law or business strategy, which involve logical reasoning but lack objectively verifiable correct solutions.

At the same time, some of the traits learned while tackling very difficult problems—persistence among them—may raise safety risks. In recent "rogue AI" incidents, AI agents went to extreme lengths to achieve results in an evaluation, including taking unauthorized and illegal actions. A human confronted with a seemingly impossible challenge might simply give up rather than resort to such steps.

Dan Litt, a professor of mathematics at the University of Toronto, told Fortune he was excited about OpenAI's results. "My view is that this is great for mathematics," he said, adding that several of the published solutions touched on problems he was interested in and that he was eager to understand what OpenAI's model had found: "I think that it's great to have new solutions to questions that I and others are interested in."

Litt cautioned, however, that he worried about the effect the solutions could have on the field—particularly if a perception that AI has "solved math" leads funding organizations to withdraw support for mathematical research, or discourages promising young mathematicians from entering the profession. "It's important that society reaffirms support for human mathematical expertise if we want to get anything out of the progress on these problems that AI has made," he said.

Showing the work

When OpenAI published its Navier-Stokes solution, two mathematicians who had also been working on the problem using AI tools—including OpenAI's—accused the company of either intentionally or inadvertently feeding their work in progress to its AI model, helping point it toward the solution. OpenAI denied this, saying it had not fed the pair's work to its model and that the model could not have picked up clues about their research from its training data, because the cutoff for that data preceded the date on which the two mathematicians began using OpenAI's Codex AI product to work on Navier-Stokes.

Responding to the latest results, Tristan Buckmaster of New York University, one of the mathematicians involved in the earlier controversy, told the New York Times that it remained unclear whether mathematicians using OpenAI's models had inadvertently helped steer the company's internal AI system toward the solutions it found. "There's likely to be a bunch of results where they take someone's work and then take it to completion," he told the Times. Given the number of results being released simultaneously, he added, "I don't think they've done their sort of due diligence at all" to ensure the model had not plagiarized anyone's work.

Last month, following criticism from mathematicians in the wake of the Navier-Stokes solution, OpenAI said it was forming an independent advisory group on mathematics and artificial intelligence, hosted at the Institute for Advanced Study in Princeton, N.J. Late last month, the group released a set of recommendations for publishing AI-generated mathematical proofs. These included publishing AI-generated proofs in the format of a traditional mathematical research paper, so that human mathematicians could more easily scrutinize and learn from the results. The group also recommended that for each solution, an AI company make public the name of the model used, the prompts used, the model's "chain of thought" (an output of its reasoning steps), the time it took the model to reach the solution, and an approximation of what that computing time cost. Companies, it said, should also disclose how they decided to have the AI attempt a particular problem, and if many results were published at once they should issue a report detailing why those problems were targeted and how many others of comparable difficulty the model tried and failed to solve.

OpenAI published the latest mathematical solutions to GitHub, the code repository site, following some—but not all—of the advisory group's recommendations. In a statement released Tuesday, the group said: "We reaffirm our published recommendations on responsible release." It described its discussions with OpenAI as "constructive" but noted that "ultimately it is up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest."

In a blog post published Tuesday, OpenAI said it had "drawn on" the advisory group's advice in deciding how to publish the solutions. "For future releases, we are committed to further improving the quality of the papers via the citations, mathematical exposition, and presentation of the results for better understanding," the company said. It said it was sharing formalizations of the proofs for many of the problems—versions that can be checked step by step with specialized computer software known as proof assistants, a practice that has gained ground across mathematical research in recent years—and would share more as it obtained them. For 10 problems, it is also publishing summaries of its model's reasoning, estimates of the compute spent, and statistics about the number of attempted problems.

Litt, who was not a member of the advisory group, told Fortune he approved of aspects of how OpenAI published the solutions. Hosting them on GitHub made them easily accessible for other mathematicians to study, he said, and he credited the company for not overhyping any particular advance in blog posts or marketing material aimed at a nontechnical audience. He also said he believed OpenAI lacked the capability to publish all the results in research papers meeting rigorous academic standards—both because AI models do not write mathematical exposition well enough and struggle to cite prior mathematical work, and because OpenAI does not employ enough mathematicians with expertise across enough areas to understand all the proofs its models can generate.

While some mathematicians have complained that AI-generated proofs, such as OpenAI's Navier-Stokes solution, are difficult to follow—making it hard to build on the results—Litt said he thought such concerns were "overstated," noting that mathematical writing is often hard to follow anyway. "I think to extract understanding from [the OpenAI results] there will be a huge amount of human labor involved, but it's not so different from the labor that mathematicians have been doing forever," he said.

OpenAI said it wanted its solutions "to push the frontier of human knowledge and enable further progress in mathematics." The company said it would fund a series of workshops, conferences, and programs focused on helping mathematicians understand the results its AI system generated. How quickly human mathematicians can verify and absorb results released at this scale—and whether future releases adopt the advisory group's full slate of disclosures—remain open questions that will shape that effort.

The end of 'Math 1.0'

In its statement on the release, the independent math advisory group said that "the future of mathematical research cannot consist only of understanding results produced by AI labs. Mathematicians must be able to formulate their own questions, develop their own approaches, and explore directions that have not been selected as examples of an AI system's capabilities. Equitable access to powerful research tools and adequate computational resources are essential to that freedom."

Terence Tao, a UCLA mathematics professor and Fields Medalist considered one of the world's greatest living mathematicians, has been increasingly critical of the way AI companies have gone after mathematical problems. He has argued that it is the process of arriving at solutions—not so much the solutions themselves—that advances mathematical understanding, and that by solving so many interesting problems so quickly, AI companies are discouraging students from becoming mathematicians and robbing the field of its future.

In a social media post on Mastodon, a decentralized social network, on Tuesday, Tao reiterated those criticisms. "Problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is 'solved,' and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field," he wrote. "Many fewer seminars, workshops, collaborations, or other activities are being generated from these results compared to traditional breakthroughs; few people are joining the community around the field as a consequence; and promising open directions are now being withheld from the public in fear that this will cause their own research to be 'scooped.'"

Tao said OpenAI's mass publication of math solutions marked the end of "Math 1.0," an era in which finding solutions to unsolved conjectures and problems—even those that could not easily be understood at first—served as the field's engine. He said a "Math 2.0" era must now follow, one that "will need to decenter the role of raw problem-solving and value mathematical progress more holistically—for instance by elevating the role of exposition, but also that of community building and opening up new directions of study."

Litt said he agreed with Tao that the field must change. OpenAI's publication of such a massive set of solutions, he said, would help get the entire field "on the same page and understanding that we need to be a little bit radical about rethinking" issues such as what kinds of contributions it rewards and how it trains PhD students. And while Tao has generally sounded wistful about the transition, Litt said he was "optimistic" about it.

"One of my collaborators told me, 'I feel like I've been crawling my entire life, and now I can fly,'" Litt said of the advent of AI as a tool for solving mathematical problems. "It's incredible what we can do now." He said he expected AI to enable human mathematicians to engage in far more "open-ended exploration" than was previously possible: "We should expect mathematicians to be way more productive in the future."

This story was originally featured on Fortune.com