00:00 Intro
00:46 What kind of problem was it?
01:42 What did OpenAI find?
03:07 The true reality of the 88 hours
03:59 The first twist: really 90 years in 88 hours?
05:01 Is the problem really settled?
05:39 The second twist: why were mathematicians worried?
07:30 Questions remaining for human mathematicians
There is a problem that mathematicians have been unable to solve for more than 90 years: the Navier-Stokes problem, one of the world's greatest mathematical challenges. Yet on September 8, OpenAI announced that artificial intelligence had found a solution to this problem in just 88 hours. On the surface, this seemed like a complete defeat for human mathematicians at the hands of AI. But three days later, on September 11, the world's leading mathematicians issued a collective warning instead.
[June Huh / Professor of Mathematics at Princeton University: "There were concerns that... this could become entrenched as a kind of game that has lost its original purpose."]
If AI solved an unsolved challenge, why did mathematicians start worrying? And did AI truly solve a 90-year-old problem in just 88 hours?
1. What kind of problem was it?
When you stir water in a cup, a vortex forms like this. But what if this vortex becomes concentrated in an increasingly tiny space? Could the water inside keep accelerating, reaching an infinite speed? Simply put, the Navier-Stokes equations apply the schoolbook principle that "force equals mass times acceleration" to the motion of fluids like water and air. They are widely used to calculate real-world fluids, such as airflow around an aircraft or weather forecasts. But there has long been an unresolved puzzle: Does a fluid that starts flowing smoothly continue to flow smoothly over time? Or could its motion suddenly concentrate in a minuscule area, causing its velocity to surge infinitely? In mathematics, such an occurrence is called a "singularity." In 2000, the Clay Mathematics Institute, a U.S. nonprofit mathematical research institute, selected this problem as one of the seven "Millennium Prize Problems," each offering a $1 million reward.
2. What did OpenAI find?
The paper released 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. Rather than an unrealistic force that abruptly spikes to infinity, this force changes smoothly across time and space. Yet even under such conditions, the fluid's motion concentrates into an increasingly confined area, ultimately creating a scenario where its velocity at that point grows without bound. What makes this astonishing is that fluids like water possess viscosity. When a flow suddenly changes, viscosity transfers momentum from faster areas to the surrounding fluid, reducing velocity differences and smoothing out the flow. Despite that action, velocity can still surge to infinity in a single spot. Of course, this does not mean that actual water moves at infinite speed; in reality, water cannot do that. Instead, if calculations from the equations indicate that velocity blows up to infinity at a certain point, it signifies that beyond that point, these equations alone can no longer properly explain real fluid behavior. Proving whether such a scenario is mathematically possible was the crux of this grand challenge. The Clay Mathematics Institute allowed the problem to be considered solved either by proving that "fluids remain smooth at all times" or, conversely, by demonstrating an example where a singularity forms even when a fluid starts smoothly and the external force is applied smoothly. OpenAI claims to have proven the latter case.
3. The true reality of the 88 hours
What, then, did the AI do during those 88 hours? Crucially, it was not a single AI pondering the problem for three days. Beginning on September 1, OpenAI had numerous AI agents test different approaches simultaneously. Some AI agents attempted to prove that the fluid remains smooth indefinitely, while others searched for cases where singularities occur. Once clues emerged from a simpler, related problem, resources were redirected from elsewhere to concentrate on Navier-Stokes. In the end, approximately 10,000 AI agents tested various methods concurrently, and OpenAI stated that they reached a proof on September 5, roughly 88 hours later. Rather than the thinking time of one genius AI, those 88 hours were closer to running a massive research lab staffed by thousands of researchers, operating in an extraordinarily compressed timeframe.
4. The first twist: really 90 years in 88 hours?
Yet here lies the first twist. Up to this point, it sounds as if AI suddenly produced the answer where no one had found a path for 90 years. In reality, that is not the case.
[Moon-Jin Kang / Professor at KAIST: "You cannot say that an AI just solved it in 88 hours without any background knowledge. In fact, many mathematicians had already made immense progress, and recently they were truly almost there."]
Mathematicians such as Córdoba and Martínez-Zoroa had already spent years developing methods to generate singularities in fluids using external forces. However, the force they applied was not quite as smooth as required by this problem. Other mathematicians were also using AI to narrow that final gap. If OpenAI truly bridged that gap, it is undoubtedly a remarkable achievement. Nevertheless, framing it as "AI solved a 90-year-old challenge in 88 hours from scratch" is not accurate either. At the starting point lay extensive research built up over many years by human mathematicians.
5. Is the problem really settled?
Is the Navier-Stokes problem settled now, then? Not quite yet. Alongside the 166-page paper, OpenAI released verification materials converted into a machine-checkable format. However, what a computer checks is whether the internal logic of the entered statements holds up. Whether the original mathematical reasoning was faithfully translated into a machine-readable form must still be confirmed, and the 166-page paper itself must undergo independent review by other mathematicians. Therefore, for now, the most accurate phrasing is that "OpenAI has proposed a solution."
6. The second twist: why were mathematicians worried?
An even more intriguing twist came next. 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, released a joint statement. Even its title was striking: "A Severe Misalignment of AI in Mathematics." Their concern was not that AI is incapable of mathematics. Rather, new concerns arose precisely because AI began performing too well. The core argument of their declaration is that solving problems is a means of understanding mathematics, not the ultimate goal itself. What does this mean? We asked Princeton University Professor June Huh, who won the Fields Medal in 2022 and co-signed the statement.
[June Huh / Professor of Mathematics at Princeton University: "When we were diligently working through math problem books during our school days... and wrestling with a difficult problem, if our only goal had been to solve every problem in the book, we could have simply looked at the answer sheet and finished all of them."]
With an answer key, you can fill in every answer blank. But could that truly be called understanding mathematics?
[June Huh / Professor of Mathematics at Princeton University: "Finding the answer is not all that research is about. In fact, you could say it is only a very small part. One of the greatest functions of what we call grand challenges in mathematics is showing us which areas we do not currently understand—that is their most important purpose."]
Challenging problems are important not merely for that final line containing the answer. By pondering why a problem remains unsolved, mathematicians uncover gaps in existing mathematics, formulate new methods and concepts, and generate the next questions in the process. However, if AI relies on immense computational resources to leapfrog directly to the answer too quickly, mathematicians worry that humans may receive the solution without fully digesting why it came about, what was newly learned, and what question needs to be asked next.
7. Questions remaining for human mathematicians
What Professor June Huh was particularly concerned about was the next generation.
[June Huh / Professor of Mathematics at Princeton University: "It leads people to succumb to skepticism, wondering, 'Does it make sense for me to start this research now and hope for results five, six, seven, or ten years down the road?'"]
There is also the question of research opportunity. For a long time, mathematics was a field that anyone with paper, a pencil, and a good idea could enter. But if only those possessing the most powerful AI and massive computing power can tackle frontier problems, the starting line for research could change as well. That does not mean Professor Huh opposes AI. He uses AI in his own research every day and remarked that this is actually the most exciting era in which to live as a mathematician.
The issue is not AI's speed, but what humans might lose while trying to match that speed. On September 8, OpenAI explained that it made the findings public because it felt it was important to communicate how rapidly AI is advancing and what can be expected from future models. If so, this milestone could represent a transformation far broader than the answer to a single math problem. In an era where AI digests vast bodies of knowledge, tests thousands of possibilities in parallel, and delivers new proofs within days, what role remains for humans?
[June Huh / Professor of Mathematics at Princeton University: "Persistently maintaining wonder, sustaining intellectual curiosity, and being called upon to create new horizons—for now, I believe that is the most crucial role of human beings and mathematicians."]
An era has begun in which AI delivers an answer in just 88 hours to a challenge that remained unsolved for over 90 years. Perhaps the capability that matters more for humans now is not producing the correct answer fastest, but understanding that answer and uncovering the next question that no one has asked yet.
Reported by Choi Seung-hun | Story by Shin Hee-sook | Filmed by VJ Lee Ji-hwan | Video by Hong Jin-young | Graphics by Yang Hye-min | Source: 3d-retro | Produced by SBS Digital News
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