Last week, OpenAI shared a proposed solution to the “Navier-Stokes equation” — one of the seven renowned Millenium Prize Problems chosen by the Clay Mathematics Institute that have stumped mathematicians for many years.
Each of these problems offers a $1 million reward. If OpenAI’s solution is confirmed, this would make it only the second Millennium Prize Problem ever to be solved.
Good. I hope the Riemann hypothesis is the next problem conquered by AI.
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A new ‘golden age’ of mathematics may be dawning — thanks to AI and human ingenuity
I do not mean to convey that these famous open problems are silly or useless — in fact, the Millennium Prize Problems were chosen because of their mathematical importance. The Navier-Stokes equation describes how fluids such as water and air flow.
However, their cultural status has allowed them to grow far beyond their mathematical importance. They have become the monuments of our discipline. They were built for good reasons, are genuinely impressive, but are now obscuring the breadth of modern mathematics.
Math is about recognizing patterns, inventing definitions, building models, connecting ideas and collaborating. As a mathematician, my work focuses on uncovering hidden structure in data and the conditions that lead to the emergence and persistence of localized patterns in non-linear equations.
The modern mathematical landscape is so much broader than identifying an old problem and spending your life trying to solve it.
Math, mystery, intrigue and fame
The status of the Millenium Prize Problems as monuments arises from a feedback loop. A problem is first identified within a sub-discipline. Great mathematicians attempt to solve it and fail, repeatedly. Books, conferences, prizes, historical reviews and widely publicized failed attempts build this monument to legendary proportions.
Students learn the name of the problem and the people who worked on it. Over time, its reputation is solidified, gathering more attention and talent. The accumulated history — starring decades of brilliant protagonists, valiant but failed attempts, mystery, intrigue and fame — itself becomes evidence of importance. The feedback loop has continued within our new attention economy.
These problems promise to make one a hero: the next Isaac Newton. Young mathematicians aspire to intellectual immortality by trying to solve them. Amateurs develop fantasies of discovering one ingenious trick that generations of professionals have missed.
The accessible and elusive Collatz conjecture — which asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1 — has become a comic extreme. It has its own subreddit of fans, attracting enthusiastic amateurs and world-leading experts alike.
The modern math landscape
Mathematicians today are interested in examining structure, abstraction, classification, connections and explanation. An important feature of modern math is that a single question can generate whole research programs — with no trophy at the end.
An example from my own work is the question of how and why patterns form in nonlinear systems — a research area that dates back to the work of pioneering British mathematician Alan Turing.
(Wikimedia Commons)
Stripes, spots, hexagons and other self-organizing patterns feature heavily in fluids, optics, biology, materials science and more. Mathematical discovery has focused on which models produce which patterns, under what conditions and why.
The work brings together many fields of mathematics, including analysis, computation, geometry and computer-assisted methods. There is no “pattern formation conjecture” that lies at the end — no simple yes or no that would put a bow on it.
The explosion of data has opened further opportunities for mathematical exploration and advancement. Major questions revolve around identifying hidden structure in the data. My own work seeks to identify the structural organization and statistical properties of chaotic datasets without relying on knowledge of the equations that generate them.
These are just two tiny examples of the broader mathematical research mosaic. I find myself inspired hearing about colleagues’ work in geometry, probability, optimization, computation and areas I barely knew existed.
What connects much of this work is not a dream of solving the great open problems of mathematics, but the development of new abstract structures and algorithms, and the discovery of new questions.
AI is raiding the trophy cabinet
Of course, great problems can produce great mathematics. Russian mathematician Grigori Perelman, for example, added crucial new ideas to Richard Hamilton’s theory of Ricci flow while solving the Poincaré conjecture — the only Millennium Prize Problem solved by humans.
But if the value of these problems lies in the new theories, methods, and connections produced while trying to solve them, perhaps the solutions and the trophies have received too much cultural emphasis.
Meanwhile, AI companies have taken notice of our trophy cabinet and are raiding it. OpenAI claims to have reached their Navier-Stokes result in about 88 hours (with an additional 17 more for formalization and verification).
Tristan Buckmaster, professor of mathematics at New York University, claimed to have been close to a proof for the Navier-Stokes, with colleague Levent Alpöge, a mathematician from OpenAI’s chief rival, Anthropic. Then OpenAI heard about it and threw 10,000 AI agents (supervised by a small team of humans) and an estimated US$15 million at the problem.
Last week, Anthropic shared “the first complete computer-checked proof of Fermat’s Last Theorem,” which Claude completed in 11 days. Other mathematicians had been working on this for years.
Silicon Valley, therefore, may end mathematical trophy hunting by making sport of it.
Math is more than its monuments
So what is left for the human mathematician? From my perspective, if answers become abundant, then judgment about which questions deserve attention becomes the scarce intellectual resource.
AI may be able to generate conjectures and propose problems, but which mathematics ought to matter is a value judgement for the community.
I still hope that AI solves the Riemann hypothesis. I hope it determines whether or not P is equal to NP — another Millennium Prize Problem. I would be more than delighted to see Collatz put out of its misery. This is not because I have contempt for these problems. It is because I love mathematics and I think it is so much more than its monuments.
The post “OpenAI may have solved the Navier-Stokes equation — but mathematics is more than $1 million trophy hunts” by Jason Bramburger, Associate Professor of Mathematics and Statistics, Concordia University was published on 09/17/2026 by theconversation.com