My short story, The Fate of the Riemann Hypothesis, recently got a lot of attention on social media. Many people liked the story and many people did not. The story precisely expresses my feelings about AI-driven mathematics but my scientific views about it are more nuanced. In this blog post I want to discuss a few of the ways my scientific views depart from what I said in the story.
Let me first talk briefly about something I don’t want to talk about at length. Many people objected to my exaggerated and cartoonish depiction of environmental degradation in the year 2035 and the damage caused by data centers. I presented these details not for their strict accuracy but in order to evoke a certain feeling.
What I really want to talk about is the idea that artificial intelligence could somehow wrap up mathematics by around 2032. I presented the story as if the Riemann Hypothesis were the end of the line. The Riemann Hypothesis is, of course, part of a vast web of results, conjectures, and ideas. The idea that the proof of the Riemann Hypothesis would in itself be the final word is kind of preposterous.
In human mathematics, a proof of the Riemann Hypothesis would most likely spur on more activity in the area. People would start trying to pick off parts of the Generalized Riemann Hypothesis, for instance. Or they would explore the connections to number theory, algebra, complex analysis, mathematical physics, and so on. In his recent Clay Math lecture on the Riemann Hypothesis, Peter Sarnak gives an excellent account of how the Riemann Hypothesis and its generalizations have profound implications for other areas of mathematics.
Full disclosure: In the above discussion, I don’t want to pretend to be an expert on the Riemann Hypothesis. I am really a geometer and computer programmer and not a number-theorist. However, any satire like mine really must, for literary purposes, be about the uber-famous Riemann Hypothesis! A story called The Fate of the Square Peg Conjecture or The Fate of the Collatz Conjecture etc. does not have the same zip. In fact, I wrote the first draft of my story before news of the 2/3-of-the-zeros result broke on August 10. It was a coincidence, I swear. Indeed, I sent the story to a number of mathematician friends and colleagues on August 7.
More fundamentally, this property of being “impossible to wrap up” seems to be the nature of mathematics. Without wading deeply into the philosophy of mathematics, a truly thorny subject, let me say that mathematics appears to be an immense structure that goes way beyond human terms much in the way the Milky Way Galaxy goes beyond a flea sitting on a dog’s tail. It might be the case that the whole thing is like a Hollywood set, and it just vanishes a few miles beyond our ken, but this does not feel right. I discuss this sense of mathematical immensity in my Feb 15 Math-life balance interview with Mura Yakerson.
A more nuanced worry is that, even in the event that the AIs do not evolve into thinkers that can do everything we can and much more, they could hollow out the field of mathematics and destroy it. If the AIs solve big math problems, one after another and with superhuman speed, especially with forbiddingly complicated proofs that need computers to certify them, there will not be much opportunity or incentive for humans to jump in and develop it further. In his recent blog post on this site, Hugo Duminil-Copin makes this point in a very eloquent way. He describes these AI advances as something like nuclear blasts hitting the mathematical terrain, blasts that petrify rather than inspire human mathematicians.
So, even if they do not develop the brains to solve the Riemann Hypothesis, all the AI involvement in mathematics might fatally shrink the field. Machines might end up doing much of the mathematics that does not require extremely original new ideas, leaving only the problems that are accessible to spectacularly talented mathematicians. The problem is that mathematics requires a critical mass of people, having many different abilities, interests, and viewpoints. The mathematicians who could push the frontiers even in such a vastly changed landscape do not just rise up out of the blue. They need teachers, mentors, mathematical friends, colleagues, time and resources to think. William Thurston discusses this point in great detail in his essay, On Proof and Progress.
I don’t think that the subject would survive if only people with nearly supernatural abilities could compete. Who would pay them? Whom would they teach? Rather than wipe out all the conjectures of interest to mathematicians, it seems possible that AI-driven mathematics will change the mathematical landscape and profession in such a way that there really won’t be any (human) mathematicians left to work on the problems like the Riemann Hypothesis.
Received 4 September 2026.
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