"Did AI Solve a 90-Year-Old Math Problem?" The Plot Twist and the Real Pitfall Warned by Professor June Huh

There is a problem that mathematicians have been unable to solve for more than 90 years: the world-renowned Navier-Stokes existence and smoothness problem. On September 8, OpenAI announced that artificial intelligence had found a solution to this problem in just 88 hours. At first glance, this seemed like a complete defeat of human mathematicians by AI. But three days later, on September 11, world-leading mathematicians issued a collective warning.

[June Huh / Professor of Mathematics, Princeton University: "There was concern that this could become entrenched as a kind of pursuit that loses its original purpose, proceeding in some sense like a game..."]

Why did mathematicians begin to worry after AI solved a longstanding challenge? And did AI truly solve a 90-year-old puzzle in just 88 hours?

1. What kind of problem was it?
When you stir water in a cup, a vortex forms. But if this vortex is concentrated into an increasingly smaller space, could the water inside keep accelerating so that its velocity grows infinitely? Put simply, the Navier-Stokes equations apply the principle of "force equals mass times acceleration" taught in school to the flow of water and air. They are widely used to calculate real-world fluids, such as airflow around an airplane or weather forecasts. Yet a longstanding mystery remained: does a fluid that starts smoothly continue to flow smoothly over time? Or could its motion at some point concentrate in a tiny area, causing the velocity to surge to infinity? In mathematics, such a situation is called a "singularity." In 2000, the Clay Mathematics Institute, a nonprofit mathematical research institute in the United States, designated this problem as one of the seven "Millennium Prize Problems," offering a $1 million prize for its solution.

2. What did OpenAI discover?
The paper published by OpenAI on September 8 spans 166 pages. The core finding is as follows: an external force is applied to a fluid that was initially at rest. That force is not an unrealistic force that spikes infinitely out of nowhere, but rather changes smoothly over time and space. Even so, the motion of the fluid concentrates into an increasingly narrow space, ultimately creating a situation where the velocity in that spot grows infinitely. This is astonishing because fluids like water possess viscosity. When flow patterns change abruptly, viscosity transfers the motion of faster-moving parts to surrounding areas, reducing differences in speed and smoothing out the flow. Yet despite such an effect, the velocity in one location could still grow infinitely. Of course, this does not mean that real water moves at infinite speed. Real water cannot do that. Instead, it means that if the velocity calculated by the equations shoots up to infinity at a certain point, from then on, the equations alone cannot properly describe actual fluids. Proving whether such a scenario is mathematically possible was the crux of this problem. The Clay Mathematics Institute allowed the problem to be solved either by proving that "fluids are always smooth," or conversely, by finding an example where a singularity forms in a fluid that started smoothly under a smoothly applied external force. OpenAI claims to have proven the latter case.

3. The reality behind the 88 hours
What, then, did the AI do during those 88 hours? Starting September 1, OpenAI had numerous AI systems simultaneously test different methods. Some AI models attempted to prove that the fluid remains smooth indefinitely, while others searched for cases where singularities occur. When clues emerged from a related, slightly simpler problem, resources from other areas were redirected to focus on Navier-Stokes. In the end, approximately 10,000 AI agents tested various methods concurrently, and on September 5, after about 88 hours, OpenAI announced they had reached a proof. Thus, the 88 hours was not the contemplation time of a single genius AI, but closer to the compressed operating time of a massive research laboratory where thousands of researchers work simultaneously.

4. The first twist: Did it really take just 88 hours for a 90-year problem?
Here lies the first plot twist. Hearing up to this point, it sounds as if AI suddenly produced the correct answer out of nowhere where no one had found a path for 90 years. In reality, that was not the case.

[Moon-Jin Kang / Professor at KAIST: "You cannot simply say that AI solved it in 88 hours without any background knowledge. Many mathematicians had actually made substantial progress, and recently, they were genuinely almost there."]

Mathematicians such as Diego Córdoba and Luis Martínez-Zoroa had already spent years developing methods to create singularities in fluids using external forces. However, those forces were not as smooth as required by this specific prize problem. Other mathematicians were also using AI to narrow that final gap. If OpenAI truly bridged that gap, it is undoubtedly a tremendous achievement. However, viewing it as "AI solving a 90-year-old problem in 88 hours with no background" is inaccurate. At the starting point was research built up over a long period by human mathematicians.

5. Is the problem truly settled?
Is the Navier-Stokes problem now settled? Not yet. Along with the 166-page paper, OpenAI released verification materials converted into a machine-checkable format. However, a computer only checks whether the logic of the entered content holds. It must still be verified whether the original mathematical content was accurately translated into a computer-readable form, and the 166-page paper itself must be independently reviewed by other mathematicians. Therefore, for now, stating that "OpenAI has proposed a solution" is the most accurate description.

6. The second twist: Why were mathematicians worried?
An even more interesting twist followed. On September 11, three days after OpenAI's announcement, 25 recipients of the Fields Medal—often called the Nobel Prize of mathematics—including Professor June Huh and Terence Tao, issued a joint statement. The title itself was striking: "A Severe Misalignment of AI in Mathematics." What they took issue with was not that AI is bad at mathematics. Rather, new problems arose because it began performing too well. The core of their joint declaration is this: solving problems is a means to understanding mathematics, not the ultimate goal in itself. What does this mean? We asked Princeton University Professor June Huh, who was awarded the Fields Medal in 2022 and participated in the joint statement.

[June Huh / Professor of Mathematics, Princeton University: "When we were diligently solving math workbooks as students... if the goal while wrestling with difficult problems was simply to finish every problem in the workbook, you could just look at the answer key and complete all of them."]

With an answer key, you can fill in every answer box. But can that truly be called understanding mathematics?

[June Huh / Professor of Mathematics, Princeton University: "Obtaining the answer is not the entirety of research. In fact, one could say it is only a very small part. In particular, one of the greatest uses of what we call open problems in mathematics is that they show us what parts we currently do not know; that role is the most important."]

Open problems are not important solely for the final line of the answer. By pondering why a problem remains unsolved, mathematicians discover gaps in existing mathematics, formulate new methods and concepts, and in the process, the next questions emerge. But if AI uses massive resources to leap too quickly to the answer, mathematicians worry that while humans obtain the answer, they may fail to sufficiently digest why that answer came about, what was newly learned, and what questions should be asked next.

7. Questions remaining for human mathematicians
What Professor Huh was particularly concerned about was the next generation.

[June Huh / Professor of Mathematics, Princeton University: "It makes people succumb to skepticism, wondering, 'Is it meaningful for me to begin this research now and hope for results 5, 6, 7, or 10 years later?'"]

There is also the issue of research opportunities. For a long time, mathematics has been a discipline anyone could enter with paper, pencil, and a good idea. However, if only entities possessing the most powerful AI and massive computing resources can solve problems at the forefront, the starting line for research will shift. That does not mean Professor Huh opposes AI. He noted that he uses AI in his research every day, and said that this is actually
the most exciting era to live as a mathematician.

The issue is not the speed of AI, but what humans might miss while trying to keep up with that pace. OpenAI stated on September 8 that the reason for disclosing this result was that it is important to inform the world about how rapidly AI is developing and what can be expected from future models. If that is true, this event could signal a transformation far larger than the solution to a single math problem. In an era where AI reads vast amounts of knowledge, tests thousands of possibilities at once, and produces new proofs in a matter of days—what role remains for humans?

[June Huh / Professor of Mathematics, Princeton University: "Persistently having questions, continually maintaining intellectual curiosity, and being called to build new horizons—for now, I believe that is the most important role of human mathematicians."]

An era has begun where AI delivers a solution in just 88 hours to a challenge that remained unsolved for more than 90 years. Perhaps the more vital human capability now is not producing the correct answer the fastest, but understanding that answer and seeking the next question that no one has asked yet.

Reported by Choi Seung-hun | Written by Shin Hee-sook | Camera by VJ Lee Ji-hwan | Video by Hong Jin-young | Graphics by Yang Hye-min | Source: -3d-retro | Produced by SBS Digital News
※ Please note: This article was translated by AI and may contain errors.