OpenAI’s latest mathematical milestone has quickly become mired in controversy. Today, the company announced that its agents have solved one of the Millennium Prize Problems, some of the most important open problems in mathematics. Under normal circumstances, that solution would be a huge feather in OpenAI’s cap.

But the announcement has been overshadowed by accusations that OpenAI used NYU mathematician Tristan Buckmaster’s and Anthropic employee Levent Alpöge’s AI-assisted work on the problem as a jumping-off point and failed to credit them. OpenAI has denied the accusations.

It remains uncertain if OpenAI’s models made use of the work completed by Buckmaster and Alpöge, though Sébastien Bubeck, a member of the technical staff at OpenAI, said in a press briefing that the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge’s efforts. But whether or not OpenAI’s models took advantage of Buckmaster and Alpöge’s research, this episode may mark a turning point in the history of mathematics.

AI models now seem essential for making progress on the most important mathematical problems of our time, and solving them may demand resources only available at a couple of frontier AI companies, which often defy the norms of academic collaboration that undergird most mathematical progress. If that’s the future we are headed for, it is unclear how human mathematicians will fit into it. 

The problem that OpenAI claims to have solved is known as the Navier–Stokes existence and smoothness problem. It is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. Solutions come with a one million dollar prize; before today, only one other Millennium Prize Problem had been solved. 

The Navier–Stokes problem concerns a set of equations that describes how fluids, such as water and air, flow over time. The equations are widely used in the field of fluid dynamics, and they have proven powerful, but physicists and mathematicians didn’t understand them completely. In particular, it was unknown until today whether the equations might, under some conditions, break down and predict an impossible state of affairs—such as a fluid having infinite velocity.

On Monday, NYU’s Buckmaster posted a proof on the social media site Mastodon showing that a simplified version of the Navier–Stokes equations can indeed break down—a major step forward on the Millennium Problem. He and Alpöge had worked on the problem for almost a year, using publicly available models from both OpenAI and Anthropic.

Then today, OpenAI presented a proof showing that the full Navier–Stokes equations can break down as well. The proof was obtained using an internal model that dramatically outperforms the already-impressive Astra model, which was only released last week. The company says it does not plan to claim the million-dollar prize for solving the problem.

These mathematical achievements are indisputably impressive, but they have attracted far less attention than the controversy about their origins. Along with the proof, Buckmaster posted a document detailing his interactions with OpenAI employees after he heard rumors about their work and reached out to one of them. According to him, OpenAI employees presented two possibilities to him: Either he and Alpöge could post their work and OpenAI would post their Navier-Stokes solution the following day, or he could work with OpenAI on a Navier-Stokes paper that excluded Alpöge from authorship, due to his affiliation with Anthropic, OpenAI’s biggest rival.

Buckmaster also wrote that he asked the employees whether the agents had obtained access to transcripts of the work that he and Alpöge had done with OpenAI models, which they denied; and whether OpenAI models had been trained on those transcripts, to which they offered no response. MIT Technology Review reached out to Buckmaster for comment, but didn’t hear back before publication.

The clear implication of the document is that OpenAI’s models somehow made use of Buckmaster and Alpöge’s work. That scenario is plausible on its face. The Buckmaster/Alpöge and OpenAI proofs both make use of an approach to the Navier-Stokes problem pioneered by the mathematicians Diego Córdoba and Luis Martínez-Zoroa.

According to Javier Gómez-Serrano, a mathematics professor at Brown University, this approach was one of several that was thought to hold promise for solving the Navier-Stokes problem. So, while it’s by no means impossible that both teams could have arrived at this approach independently, it’s also conceivable that Buckmaster and Alpöge’s work could have influenced OpenAI’s.

In the press briefing, Mark Chen, OpenAI’s chief research officer, again denied that any agents or OpenAI employees accessed Buckmaster and Alpöge’s transcripts—but given what has been revealed about the Hugging Face hack, it’s clear that OpenAI is not always entirely aware of what its agents are doing. 

If OpenAI’s models did train on Buckmaster and Alpöge’s work, or if its agents somehow gained access to it, then the company’s failure to track down the truth and assign those researchers appropriate credit reflects poorly on it. But there might be a thin silver lining to that version of the story for mathematicians, because it would suggest that the hard work of two humans, one of whom is a prominent expert on Navier-Stokes, was essential to the agents’ ability to solve the Millennium Problem.

Experts have long identified “research taste,” or the ability to choose promising research questions and directions, as a major obstacle for AI in science and mathematics. If the OpenAI agents did indeed choose to follow the Córdoba–Martínez-Zoroa approach because Buckmaster and Alpöge had done the same, then human research taste played an essential role in OpenAI’s success.

Even so, the bigger picture here is sobering. The progress that Buckmaster and Alpöge made over almost a year of collaboration with publicly available models speaks to the promise of human–AI collaboration. But they were not able to achieve a full solution. Meanwhile, OpenAI brute-forced a solution in a few days using an internal model, and their successful solution came at an astronomical cost: In the press briefing, Bubeck and Chen said the team was only able to solve the problem by running about 10,000 agents concurrently, at a cost of millions of dollars.

Over the past few months, I’ve heard from several researchers that mathematicians are becoming depressed, and it’s not difficult to see why. Mathematics is quickly becoming the province of frontier AI companies with impressive internal-only models, money to burn, and a lack of collaborative spirit. “Whether AI companies will decide to spend their money on doing one thing or another, I truly don’t know,” says Gómez-Serrano. “What is clear is that very few mathematicians will have resources of that scale.”

If OpenAI and Anthropic keep striving for more and more impressive mathematical accolades, there might not be any open problems left for human mathematicians outside of those companies to wrestle with. That would dramatically change the field of mathematics.

Last week, UCLA mathematician Terence Tao wrote a Mastodon thread describing how important mistakes, wrong directions, and incomplete solutions are for the field. “In most cases in pure mathematics, the problems are posed not because we desperately want the solution to these problems in and of themselves, but because we have seen from past experience that human-directed efforts to solve these problems tend to spur further development of the field,” Tao wrote.

“Prematurely solving the problem by purely AI-powered methods—particularly without full transparency into the solution process—can contaminate this process to the point where it actually becomes a net negative for the progress of mathematics as a whole.”

Humans might take longer than agents to solve mathematical problems, but in the process, they uncover new mathematical approaches and ideas that might inspire their peers and even birth their own subfields.

But when AI agents solve those problems instead—and when private companies keep the agents’ wrong turns from public view—those benefits disappear. It remains to be seen what else will vanish in the process. 

During Tuesday’s Google I/O keynote, Demis Hassabis, the CEO of Google DeepMind, proclaimed that we are currently “standing in the foothills of the singularity.” It was a striking statement—the singularity is the theoretical future moment when AI rapidly exceeds human intelligence and dramatically transforms the world. But what struck me as I listened in the audience was the context in which he said those words. 

He was on stage to close out the session with a segment on scientific AI, the centerpiece of which was a video detailing how the company’s weather prediction software provided an advance alert about Hurricane Melissa’s catastrophic landfall in Jamaica last year—and potentially saved lives. If that software, called WeatherNext, helped anyone escape the storm or better fortify their home, that’s an enormous and meaningful achievement. But it’s hardly evidence of an impending singularity.

The juxtaposition of Hassabis’ lofty rhetoric with the real-world results of WeatherNext highlighted the tension between two very different approaches to AI for science. The first focuses on AI tools, like WeatherNext, that are designed and trained to solve specific scientific problems. The second is agentic, LLM-based systems that could one day execute cutting-edge research projects without human involvement.

This second vision powers a great deal of AI enthusiasm right now, including recent excitement around recursive self-improvement, or the idea that AI systems could eventually become the primary drivers of AI advancement—a process that would get faster and faster as the AI systems grow smarter. And agentic systems are now making real research contributions, sometimes with limited human guidance.

Just this week, Pushmeet Kohli, Google Cloud’s chief scientist, published a piece in a special AI and science issue of the journal Daedalus, writing: “We are moving toward AI that doesn’t just facilitate science but begins to do science.” With autonomous AI scientists on the horizon, it’s harder to justify massive efforts to develop super-specialized tools—even one like AlphaFold, for which DeepMind scientists won a Nobel Prize, or a potentially life-saving system like WeatherNext. It also heralds a far stranger future for science, in which humans and AI systems collaborate as peers—or AI even makes scientific progress on its own.

To be clear, Google does not appear to be abandoning its work on specialized AI for science tools. AlphaGenome and AlphaEarth Foundations, which are trained for genetics and Earth science applications respectively, were released last summer, and the newest version of WeatherNext came out in November.

What’s more, such tools remain extremely popular among scientists. Last year, for instance, Google reported that protein structure predictions from AlphaFold have been used by over three million researchers worldwide. And Isomorphic Labs, a Google subsidiary that aims to use AlphaFold and related technologies to develop new drugs, just raised a $2 billion Series B funding round.

But there are concrete signs of realignment, in both enthusiasm and resources. Last month, the Los Angeles Times reported that Google fellow John Jumper, who won the Nobel for AlphaFold, is now working on AI coding, not on science-specific AI tools. It’s not surprising that Google is assigning its best minds to the coding problem, as the company has recently taken a reputational hit because its coding tools don’t currently stand up to those offered by Anthropic and OpenAI. But it may also signal a prioritization of agentic science on Google’s part, as coding abilities are key to the success of some of those systems. 

Across the industry, agentic researcher systems are showing real potential. This week, OpenAI announced that one of their models had disproved an important mathematics conjecture—perhaps the most meaningful contribution that generative AI has made to mathematics so far, according to some mathematicians.

Importantly, the model used by OpenAI is not specialized for solving mathematical problems, or even for research; according to the company, it’s a general-purpose reasoning model in the vein of GPT-5.5. If general agents can make independent contributions to mathematical research, they might soon be able to do the same in science (though the fact that ideas in science must be verified experimentally makes it a tougher domain for AI).

Google is certainly devoting a lot of attention toward an agent-driven scientific future. The big scientific announcement at I/O was the new Gemini for Science package, which unites several of the company’s LLM-based scientific systems under one brand.

This includes the hypothesis-generating AI Co-Scientist and algorithm-optimizing AlphaEvolve, which are still not publicly available—but as Google is now allowing any researcher to apply for access to Gemini for Science, they may soon see wider adoption in the scientific community. Scientists who were involved in early testing are enthusiastic about their potential: Gary Peltz, a Stanford geneticist, compared using the AI Co-Scientist to “consulting the oracle of Delphi” in a Nature Medicine article.

Gemini for Science isn’t incompatible with specialized tools; to the contrary, agentic systems can be designed to call on such tools when they might be useful. And no agentic system can predict the structure that a protein will fold into without AlphaFold’s help (at least not yet). But the company seems to be shifting its public image—and at least some resources and personnel, such as Jumper—away from specifically developing those kinds of tools. Though it has only been five years since AlphaFold solved the protein-folding problem, both the technology and the discourse have quickly moved beyond that once-revolutionary achievement.

Google has been careful to position this new set of scientific agents as an accelerant for human scientists, rather than a replacement for them—the choice of the name AI Co-Scientist as opposed to AI Scientist, for instance, appears quite deliberate. Hassabis uses that same human-centric framing when he talks about changes in the landscape of scientific AI. “For the next decade or so, we should think about AI as this amazing tool to help scientists,” Hassabis said in an interview published in the Daedalus issue. “Beyond that timeframe, it is hard to say with any certainty, but perhaps these systems will become more like collaborators.”

But no one can be an effective scientific collaborator without also being a skilled scientist in their own right. And if Hassabis is anywhere near the mark when he talks about the “foothills of the singularity,” then AI scientists could eventually exceed the capabilities of their human counterparts.

In a discussion with the journalist Mike Allen at I/O, Hassabis spoke of how he was initially inspired to pursue AI when he observed how progress in physics had stagnated since the 1970s; he wondered whether the human mind had reached its limits in that domain, and if AI could help to overcome that barrier. Superhuman agentic scientists would certainly fit that bill. We might not ever get anywhere near there, but Google seems to be aiming itself toward that summit.

Earlier this month, Microsoft launched Copilot Health, a new space within its Copilot app where users will be able to connect their medical records and ask specific questions about their health. A couple of days earlier, Amazon had announced that Health AI, an LLM-based tool previously restricted to members of its One Medical service, would now be widely available. These products join the ranks of ChatGPT Health, which OpenAI released back in January, and Anthropic’s Claude, which can access user health records if granted permission. Health AI for the masses is officially a trend. 

There’s a clear demand for chatbots that provide health advice, given how hard it is for many people to access it through existing medical systems. And some research suggests that current LLMs are capable of making safe and useful recommendations. But researchers say that these tools should be more rigorously evaluated by independent experts, ideally before they are widely released. 

In a high-stakes area like health, trusting companies to evaluate their own products could prove unwise, especially if those evaluations aren’t made available for external expert review. And even if the companies are doing quality, rigorous research—which some, including OpenAI, do seem to be—they might still have blind spots that the broader research community could help to fill.

“To the extent that you always are going to need more health care, I think we should definitely be chasing every route that works,” says Andrew Bean, a doctoral candidate at the Oxford Internet Institute. “It’s entirely plausible to me that these models have reached a point where they’re actually worth rolling out.”

“But,” he adds, “the evidence base really needs to be there.”

Tipping points 

To hear developers tell it, these health products are now being released because large language models have indeed reached a point where they can effectively provide medical advice. Dominic King, the vice president of health at Microsoft AI and a former surgeon, cites AI advancement as a core reason why the company’s health team was formed, and why Copilot Health now exists. “We’ve seen this enormous progress in the capabilities of generative AI to be able to answer health questions and give good responses,” he says.

But that’s only half the story, according to King. The other key factor is demand. Shortly before Copilot Health was launched, Microsoft published a report, and an accompanying blog post, detailing how people used Copilot for health advice. The company says it receives 50 million health questions each day, and health is the most popular discussion topic on the Copilot mobile app.

Other AI companies have noticed, and responded to, this trend. “Even before our health products, we were seeing just a rapid, rapid increase in the rate of people using ChatGPT for health-related questions,” says Karan Singhal, who leads OpenAI’s Health AI team. (OpenAI and Microsoft have a long-standing partnership, and Copilot is powered by OpenAI’s models.)

It’s possible that people simply prefer posing their health problems to a nonjudgmental bot that’s available to them 24-7. But many experts interpret this pattern in light of the current state of the health-care system. “There is a reason that these tools exist and they have a position in the overall landscape,” says Girish Nadkarni, chief AI officer​ at the Mount Sinai Health System. “That’s because access to health care is hard, and it’s particularly hard for certain populations.”

The virtuous vision of consumer-facing LLM health chatbots hinges on the possibility that they could improve user health while reducing pressure on the health-care system. That might involve helping users decide whether or not they need medical attention, a task known as triage. If chatbot triage works, then patients who need emergency care might seek it out earlier than they would have otherwise, and patients with more mild concerns might feel comfortable managing their symptoms at home with the chatbot’s advice rather than unnecessarily busying emergency rooms and doctor’s offices.

But a recent, widely discussed study from Nadkarni and other researchers at Mount Sinai found that ChatGPT Health sometimes recommends too much care for mild conditions and fails to identify emergencies. Though Singhal and  some other experts have suggested that its methodology might not provide a complete picture of ChatGPT Health’s capabilities, the study has surfaced concerns about how little external evaluation these tools see before being released to the public.

Most of the academic experts interviewed for this piece agreed that LLM health chatbots could have real upsides, given how little access to health care some people have. But all six of them expressed concerns that these tools are being launched without testing from independent researchers to assess whether they are safe. While some advertised uses of these tools, such as recommending exercise plans or suggesting questions that a user might ask a doctor, are relatively harmless, others carry clear risks. Triage is one; another is asking a chatbot to provide a diagnosis or a treatment plan. 

The ChatGPT Health interface includes a prominent disclaimer stating that it is not intended for diagnosis or treatment, and the announcements for Copilot Health and Amazon’s Health AI include similar warnings. But those warnings are easy to ignore. “We all know that people are going to use it for diagnosis and management,” says Adam Rodman, an internal medicine physician and researcher at Beth Israel Deaconess Medical Center and a visiting researcher at Google.

Medical testing

Companies say they are testing the chatbots to ensure that they provide safe responses the vast majority of the time. OpenAI has designed and released HealthBench, a benchmark that scores LLMs on how they respond in realistic health-related conversations—though the conversations themselves are LLM-generated. When GPT-5, which powers both ChatGPT Health and Copilot Health, was released last year, OpenAI reported the model’s HealthBench scores: It did substantially better than previous OpenAI models, though its overall performance was far from perfect. 

But evaluations like HealthBench have limitations. In a study published last month, Bean—the Oxford doctoral candidate—and his colleagues found that even if an LLM can accurately identify a medical condition from a fictional written scenario on its own, a non-expert user who is given the scenario and asked to determine the condition with LLM assistance might figure it out only a third of the time. If they lack medical expertise, users might not know which parts of a scenario—or their real-life experience—are important to include in their prompt, or they might misinterpret the information that an LLM gives them.

Singhal, the OpenAI health lead, notes that the company’s current GPT-5 series of models, which had not yet been released when the original HealthBench study was conducted, do a much better job of soliciting additional information than their predecessors. However, OpenAI has reported that GPT-5.4, the current flagship, is actually worse at seeking context than GPT-5.2, an earlier version.

Ideally, Bean says, health chatbots would be subjected to controlled tests with human users, as they were in his study, before being released to the public. That might be a heavy lift, particularly given how fast the AI world moves and how long human studies can take. Bean’s own study used GPT-4o, which came out almost a year ago and is now outdated. 

Earlier this month, Google released a study that meets Bean’s standards. In the study, patients discussed medical concerns with the company’s Articulate Medical Intelligence Explorer (AMIE), a medical LLM chatbot that is not yet available to the public, before meeting with a human physician. Overall, AMIE’s diagnoses were just as accurate as physicians’, and none of the conversations raised major safety concerns for researchers. 

Despite the encouraging results, Google isn’t planning to release AMIE anytime soon. “While the research has advanced, there are significant limitations that must be addressed before real-world translation of systems for diagnosis and treatment, including further research into equity, fairness, and safety testing,” wrote Alan Karthikesalingam, a research scientist at Google DeepMind, in an email. Google did recently reveal that Health100, a health platform it is building in partnership with CVS, will include an AI assistant powered by its flagship Gemini models, though that tool will presumably not be intended for diagnosis or treatment.

Rodman, who led the AMIE study with Karthikesalingam, doesn’t think such extensive, multiyear studies are necessarily the right approach for chatbots like ChatGPT Health and Copilot Health. “There’s lots of reasons that the clinical trial paradigm doesn’t always work in generative AI,” he says. “And that’s where this benchmarking conversation comes in. Are there benchmarks [from] a trusted third party that we can agree are meaningful, that the labs can hold themselves to?”

They key there is “third party.” No matter how extensively companies evaluate their own products, it’s tough to trust their conclusions completely. Not only does a third-party evaluation bring impartiality, but if there are many third parties involved, it also helps protect against blind spots.

OpenAI’s Singhal says he’s strongly in favor of external evaluation. “We try our best to support the community,” he says. “Part of why we put out HealthBench was actually to give the community and other model developers an example of what a very good evaluation looks like.” 

Given how expensive it is to produce a high-quality evaluation, he says, he’s skeptical that any individual academic laboratory would be able to produce what he calls “the one evaluation to rule them all.” But he does speak highly of efforts that academic groups have made to bring preexisting and novel evaluations together into comprehensive evaluations suites—such as Stanford’s MedHELM framework, which tests models on a wide variety of medical tasks. Currently, OpenAI’s GPT-5 holds the highest MedHELM score.

Nigam Shah, a professor of medicine at Stanford University who led the MedHELM project, says it has limitations. In particular, it only evaluates individual chatbot responses, but someone who’s seeking medical advice from a chatbot tool might engage it in a multi-turn, back-and-forth conversation. He says that he and some collaborators are gearing up to build an evaluation that can score those complex conversations, but that it will take time, and money. “You and I have zero ability to stop these companies from releasing [health-oriented products], so they’re going to do whatever they damn please,” he says. “The only thing people like us can do is find a way to fund the benchmark.”

No one interviewed for this article argued that health LLMs need to perform perfectly on third-party evaluations in order to be released. Doctors themselves make mistakes—and for someone who has only occasional access to a doctor, a consistently accessible LLM that sometimes messes up could still be a huge improvement over the status quo, as long as its errors aren’t too grave. 

With the current state of the evidence, however, it’s impossible to know for sure whether the currently available tools do in fact constitute an improvement, or whether their risks outweigh their benefits.