AI Cracks a Millennium Prize Problem: Why Is the Math World Anxious?

At the Heidelberg Laureate Forum in Germany, mathematicians in previous years focused on which famous scholars were attending and what interesting problems they were recently working on. But this time, in the hallways, at dinner tables, and even in fragments of casual conversation, everyone was talking about the same thing: OpenAI, Anthropic, and Google are storming into mathematics with overwhelming force.

Ailsa Robertson, a young researcher at the University of Amsterdam, put it bluntly: "AI and large language models set the math world on fire this summer."

Why Are Tech Giants Targeting the Millennium Prize Problems?

Mathematics has become the perfect testing ground for AI because it involves step-by-step logical reasoning, and answers can be verified automatically and objectively. This gives tech giants the incentive to push AI's mathematical capabilities forward at unprecedented speed.

From initially struggling with everyday research-level problems, to solving numerous problems posed by Hungarian mathematician Paul Erdős in batches, to verifying the proof of Fermat's Last Theorem, and now to OpenAI announcing it has solved the Navier-Stokes existence and smoothness problem. Of the seven Millennium Prize Problems proposed by the Clay Mathematics Institute in 2000, humanity had previously solved only one — the Poincaré conjecture. If OpenAI's claim is verified, it will be a milestone moment for automated reasoning.

Jacob Tsimerman, a Fields Medalist at the University of Toronto, said at a forum press conference: "We're seeing rapid growth in capabilities, even faster than people like me expected. Is AI doing new things? I don't know the details, but... solving Navier-Stokes feels fairly decisive."

After the news broke, speculation about which Millennium Prize Problem would be cracked next ran rampant. The Riemann Hypothesis is one of the hot candidates — Anthropic quietly used an unreleased version of Claude in August to attempt this problem, making important progress on questions related to the main goal. And OpenAI is reportedly focusing on the Hodge conjecture.

The Millennium Prize Problems were established by the Clay Mathematics Institute in 2000 to commemorate the centennial of Hilbert's 23 problems, listing seven of the most challenging unsolved problems across mathematical fields, including the Poincaré conjecture, the Riemann Hypothesis, the P vs NP problem, Yang-Mills existence and mass gap, Navier-Stokes existence and smoothness, the Hodge conjecture, and the Birch and Swinnerton-Dyer conjecture. Each solver receives a $1 million prize. To date, only the Poincaré conjecture has been solved, by Russian mathematician Perelman in 2003 (who declined the prize). These problems are not only core mathematical challenges — their solutions often drive breakthroughs across entire fields and even in physics. Therefore, if AI can genuinely solve one of them, it truly marks a new height for automated reasoning.

The Navier-Stokes equations are the core partial differential equations describing fluid motion, widely applied in weather forecasting, aerodynamics, blood flow, and more. The Millennium Prize Problem specifically refers to: in three-dimensional space, given arbitrary smooth initial conditions, does the equation always have a smooth global solution? Or will the solution develop singularities (such as infinite velocity gradients) in finite time? This problem concerns the predictability of the physical world and is a deep challenge at the intersection of mathematics and physics. OpenAI's claim to have solved it means its AI system may have constructed a proof or counterexample, but the math community demands rigorous formal verification, because such proofs are extremely long and prone to hidden errors.

"Just a PR Stunt": The Navier-Stokes Controversy

Not everyone was cheering. Peter Scholze, a Fields Medalist at the University of Bonn, said bluntly during a panel discussion on AI mathematical research: "They solve these difficult mathematical problems really just as benchmarks, some kind of PR stunt."

This dissatisfaction came to a head over OpenAI's Navier-Stokes announcement. Geordie Williamson of the University of Sydney said during the discussion: "I think OpenAI's behavior has been appalling, and we should acknowledge that in the community."

Michael Harris of Columbia University witnessed the core of the controversy up close. Tristan Buckmaster of New York University was making important progress on the Navier-Stokes problem with Anthropic's Levent Alpöge at the time, and reportedly received communications from OpenAI that appeared coercive, censorious, and even threatening. Harris said: "I believed Tristan's description of this interaction... On social media and in traditional media, most coverage confirmed my judgment — they portrayed OpenAI as a bully and a destroyer of disciplinary norms."

As of press time, OpenAI did not respond to a request for comment.

Williamson's concerns go beyond sportsmanship. He pointed out: "As a mathematical community, what we pursue is understanding, but we measure that understanding by unsolved problems, and the problem is that these two measures are becoming irrelevant to each other very quickly." Answers given by AI often come without understandable or reusable new methodologies. "So now we have to reevaluate how we assess people, who gets positions, how we educate students, and so on. This will be a huge challenge."

Levent Alpöge is a mathematician at Anthropic, previously a Benjamin Peirce Fellow at Harvard University, working on number theory and algebraic geometry. Tristan Buckmaster is a professor at NYU's Courant Institute of Mathematical Sciences, specializing in partial differential equations, especially the Navier-Stokes and Euler equations. The two collaborated on progress on the Navier-Stokes problem, indicating that top experts in the field are working deeply with AI labs. OpenAI is alleged to have sent coercive communications to Buckmaster, possibly involving demands that he stop competing research or join the OpenAI team. If true, such behavior would seriously violate academic competition norms, raising mathematicians' concerns about tech giants monopolizing the research agenda.

The Plight of Young Mathematicians: An Academic Ecosystem Hijacked by AI

When tech giants tear up the rulebook in their battle for supremacy, it's ordinary human mathematicians who bear the consequences.

Mita Ramabulana, a young mathematician at the University of Cape Town, is a microcosm of this. He noted that two of the ten mathematical advances OpenAI announced in August overlapped with his own work, which left him disappointed: "Because you spend time thinking about these problems, and now you don't know whether someone can just throw the problem you care about into some large language model and solve it." He worries that some researchers are using large language models to scoop results or gain career advantages.

For Robertson, the problem is even more acute. She sees all her mathematics colleagues using large language models intensively in their research, many maxing out their Pro subscriptions, some even spending thousands of euros on extra tokens — "and these are PhD students who don't even have thousands of euros."

Robertson mentioned that some colleagues feel coerced by tech giants. In July, OpenAI announced it would provide 100,000 frontier model licenses free to academic researchers. Some colleagues feel they have no choice: "If you don't work at the speed that large language models can achieve, you'll fall behind peers applying for the same positions."

This is also why Robertson's PhD research has significantly reduced its mathematical component, shifting toward the social impact of quantum-safe ecosystem transitions: "Because I don't want to pursue a career that's just verifying large language model outputs."

Structural Challenges Facing the Mathematical Community

The core issues raised by this transformation go far beyond the technical level. When AI can generate answers but cannot provide human-understandable methodologies, the evaluation system on which the math community operates — whose work has value, who should get faculty positions, how to train the next generation of researchers — will face fundamental reconstruction.

Tech giants use Millennium Prize Problems as benchmarks to validate model capabilities, while demonstrating technical prowess to investors and potential users. There is an essential tension between this motivation and the "understanding" pursued by the academic community. When problem-solving ability becomes decoupled from depth of understanding, the very definition of mathematics as a discipline may need to be reexamined.

As Harris observed, most coverage on social media and in traditional media confirmed one judgment: OpenAI's behavior is widely seen as a destruction of disciplinary norms. And Williamson's warning points to a deeper crisis — when the standards the math community uses to measure progress drift further and further from the understanding it truly seeks, the very foundation of the entire academic ecosystem is shaken.

One-line Summary

AI cracking a Millennium Prize Problem sparks controversy, as the math world worries its evaluation system is being shaken.

Paragraph Summary

The article reports on AI's rapid progress in mathematics, especially OpenAI's claim to have solved the Navier-Stokes existence and smoothness problem, which sent shockwaves through the math community. On one hand, AI has shown powerful capabilities in Erdős problems and verifying Fermat's Last Theorem; on the other, Fields Medalist Scholze criticized it as a "PR stunt," Williamson called OpenAI's behavior "appalling," and there were allegations of coercive communications toward competitors. More fundamentally, AI can generate answers but cannot provide understandable methodologies, causing the understanding standards on which the math community operates to become decoupled from problem-solving ability, impacting faculty allocation and talent cultivation. Young mathematicians face the dilemma of being hijacked by AI — some pay for tokens out of pocket, others change their research direction. Tech giants use Millennium Prize Problems as benchmarks, and the math community is facing structural challenges.