There is nothing new under the sun.
Yes, we are living through a technological revolution of dramatic consequences. We who have lived through the birth of personal computers, the rise of the internet, the invention of smartphones, the disruptive eruption of social media, the promise of mass open online learning, we have seen some incredible techno-social turns of events, but this time it is different. This is going to change everything.
However, for perspective, we might like to recall the words of Kohelet, son of David, king in Jerusalem: “There is nothing new under the sun”.
What’s not new? I feel that the concerns we have in light of the AI-industrial revolution are ones I’ve been dealing with for all my career. My point is not that everyone should have gotten depressed much earlier, but rather that the issues are not entirely new. The bad news is that it is harder to ignore these issues, the good news is that we may already have the tools and experience needed to cope.
Existential crises
When I hear that the rise of AI is pushing some mathematicians to an existential crisis, I feel like saying jokingly: “Are you kidding me? You’ve waited until now for your existential crisis? I had mine decades ago!”.
In my eyes, one needs to be kind of philosophically sleepwalking to have not had an existential crisis until some robot came and pulled the keyboard from underneath their fingers. Never mind the horrifying fact that you are mortal; surely you’ve noticed already that nobody cares about a typical pure mathematician’s work. Even some of the most profound and celebrated results in pure mathematics are of absolutely no consequence to anything or anyone except for a handful of other mathematicians, and it might even be the case that contradicting papers exist for over a decade with nobody knowing who is right and there are no consequences even for the mathematicians involved! And if that doesn’t crush you, well think of this: you do realize that there are only finitely many proofs that any human being can discover in a lifetime, and these can be enumerated by a computer, long before AI. So you are only searching in a finite proof space, how deep is that?
Beaten by someone else
When I hear someone saying that an LLM could replace me, I smile: so could a human.
It’s even worse. Euler, Gauss, Poincare, Hilbert, Godel, Groethendick, Bourgain, Terry Tao Who am I, what am I? Am I even working in the same profession? Well, I can still come up with some interesting questions of my own, solve an interesting problem, maybe come up with a very clever or original proof that nobody else thought of. But, honestly, maybe someone else could have, too. Probably so. Should that depress me?
I’ve seen a few cases of a young mathematician being scooped by someone else who published a result the young mathematician already established but has not yet published because they were working towards a bigger goal. It doesn’t take LLMs to get scooped. It can also happen in reverse: more than once I had the sour experience of proving a result I really liked, only to find out that someone else had done obtained the result already, using basically the same ideas. Does that make our efforts a waste of time?
There is some kind of irony here: if the problem is interesting, many will work on it, and the chances you’ll get scooped are high. If you are working without the risk of being scooped then maybe what you’re working on is simply not interesting enough? Now there are LLMs waiting to scoop you – is that a sign that what you are doing is important? Or not?
Math overflow
When I was hired as a faculty member for my first tenure track job, my new office was handed down to me from a retired operator theorist. “I have a surprise for you” he said proudly and lovingly. Was he planning to leave me the contents of his secret whiskey cabinet?
Nope! When I came into the office, I saw that he left four huge, ugly metal filing cabinets, filled with papers, I mean paper papers (printed on paper), filed away in neat folders conveniently sorted and labeled. “I am leaving all this to you!“
Not wanting to disappoint a retiring colleague, I said thanks and counted a few weeks until I was sure he’s not coming back and decided to get rid of all the crap. But surely, there may be some interesting papers in there. So I started working through a couple of tons of papers in operator theory, systems theory, operator algebras Wow, there was almost nothing that I was interested in, or could use. All that math, all those years.
That was years ago. Now look around you. So many papers, so little time to read! I can’t read all the papers coming out in my own specialised subfield, I can’t keep track. Perhaps the community is digesting them, as a community? That doesn’t seem to be the case. Maybe we are missing out on important stuff?
(wait a minute, who’s reading my papers?)
Standing on thin air
Sometimes I would be working on a problem in my field, and slowly realize that I need some kind of lemma in an adjacent field, say complex geometry, which depends on a certain kind of structure having a desirable property. And I would plow through textbooks in other fields until I found, 200 pages into the book, the result that I could use to prove what I needed. Dilemma: should I use it – taking it on faith, or should I first read those first 200 pages of the book to understand the lemma?
Or say I am collaborating, and my colleague completes an argument by applying some fancy theorem that I didn’t know from algebraic geometry or some other alien voodoo. Can I be a coauthor if I don’t understand why that fancy theorem is true? Even in my own field, can I freely use theorems from textbooks, or must I always have some understanding of how they are proved down to the bone? (or at least, maybe if at some point in the past I had an understanding down to the bone, maybe that’s good enough?).
I used to think I should do research with an understanding of everything down to the foundations of mathematics. With time I started to accumulate debts: I would use some theorem in several complex variables, but would promise myself to teach a course on the subject so that I fill that gap (I kept the promise). Or I used a result in von Neumann algebras, because I used a result from a paper that used some deep von Neumann algebra thing – the unique predual – so then I taught a course on von Neumann algebras to cover that base (I didn’t make it to uniqueness of the predual).
This point of view soon becomes unsustainable and at some point one settles for working at a higher level, taking on faith established results from the literature and using them when needed, just as a scientist might use the results of someone else’s experiments. But today, AI can connect all kinds of areas and can overwhelm you with a proof that uses several things outside your area, stuff that none of your collaborators would pull out of their sleeve. What should one do? Can you use it? These are the kinds of dilemmas we always had but are going to have more often.
The tension between wanting to know and wanting solve it
Before I started doing research, all the problems I solved were exercises whose solutions were known to the people who gave them to me. I didn’t care that the problems I solved as student weren’t new, I loved solving them! But more than anything I loved studying new mathematics. Just give me more structures, more theories, more theorems and tell me the beautiful proofs. Of course, I could and would anticipate some of the steps in the proofs. But I knew I wasn’t being original, that was just a way of actively learning new math. When I started doing research, things changed.
One day I showed a book to my masters thesis advisor. “Maybe we can use some of the results” I said, but he waved it away and told me that he is not interested in problems whose solutions appear in books. I was puzzled: don’t you want to know the answers? But later I felt something similar. I once worked on a conjecture, and one day when a solution by someone else appeared on the arxiv I felt .. disappointed. Shouldn’t I be happy? You’d think I’d be at least curious to know how it came out and what’s the proof! But I read the paper with the intension of tearing it apart until I find a mistake (and I did). If I am working to solve a problem and disappointed to hear that it’s solved, doesn’t that show that it is not really an important problem? Doesn’t it show that I am driven by a ridiculous sense of competition?
What about people being disappointed that OpenAI solved the sofic group problem? If they are not happy to hear that the existence of a non-sofic group has been established, doesn’t that mean that the problem itself was not important? Is there really nothing at stake except some egos? Could it be that the problem itself is important, but only as an open problem, while the result is not?
I have an even stranger story. I once wrote an expository essay “Dilation theory in finite dimensions – the possible, the impossible and the unknown“. It had some minor new results, but its contribution was mainly in the overview of the field and the narrative. It also had some open problems – “the unknown”. One of the open problems was a question that I planned to work on, but after finishing the essay I took a couple of months break. I wanted to know the answer, but honestly, I didn’t want to know it just yet. I later had a very nice collaboration on this problem and we solved it, beautifully. Maybe I could have solved it earlier, but that would have spoiled the story, and it would have definitely spoiled the title of the essay! And I used the open problem to get a new collaborator hooked.
Maybe my story is crazy, maybe I was being unreasonable. But I think everyone wants to savor their little wins, to relish in them a bit before moving on. But imagine that now we might be able to doomscroll results on our phone, just swipe up and there they fly up, result after result. Where’s the fun? Well, remember that we always had to pace ourselves.
Teaching
People are very concerned about AI going to change everything about homework. There’s no point in giving students homework, people say, because now they’ll just give it to their chatbot.
Hello? Do you have any idea what’s been going on for decades? In the good old days (thirty years ago) students would physically circulate someone’s handwritten solutions among the class and submit hand copied versions. With time, we started having shared drives so people could download and read someone’s solution, or even cut and paste it. And if nobody in the course was going to do the hard work for everyone, there were Stack Overflow and Wolfram Alpha. Standard math homework seems to me to be the case where the impact of AI will actually be the least dramatic – many students (most of them) have not been writing their own solutions to homework for a very long time.
The best students, however, have been pulling their own weight. I mean the serious students, the student who study for the love study, the curious ones. This category of students will continue to work, but they will need to be disciplined and determined to keep their brains busy. I see them coping.
What changes now is the amount of friction. Now, there is absolutely no friction. You don’t have to ask for favors, you don’t even need to cut and paste. Your agent can read the exercise pdf and prepare a solution pdf, and submit it for you. But, really, who are we kidding if we tell ourselves that things have been going much better?
The future
The future was always beyond a veil of mist. The future was always scary. So now it is scary, too. Today’s future is a new future, but the new-ness of the future is not new. Don’t let the scary mystery crush you. Imagine immigrants sailing for a new land. Imagine nomads, migrating to a new continent. Their whole worlds would change. And changed again. We’ve done this and we’ll do it again.
See you in campus.
Crossposted from my blog.
Received 22 August 2026.
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