Jacob Tsimerman, who’ll likely win the Fields Medal this year, thinks that AI “is boosting his productivity by a factor of two,” mostly by speeding up the boring parts.
Q: How does AI change math, the process or the feel of it?
A: Mostly it speeds up the boring parts. There’s the act of doing math, the professional endeavor, and the act of doing math as a fun endeavor. And I think AI helps the professional endeavor, and it gets you to the fun quicker.
… one of the primary ways that I use AI is to ask sort of dumb questions, or basic questions in fields in which I am not an expert. For example, I do a lot of research on Hodge theory. In a sense, I am an expert in Hodge theory because I’ve spent years thinking about it now. But there are still so many basics that I have to look up every single time, because I forget how the technical details work. In this way, I spend a lot of time during my research asking dumb questions, getting oriented.
Another example: I know how algebra works decently well. I’m used to working with rings. I’m used to working with schemes. I have some intuition there. Say my research needs me to work, as it did in the past, with -$p$adic rigid varieties or some analogous category, with continuous functions and their spectra, or whatever it is. Math has a lot of things that are kind of similar. And then I have intuition about how I’d hope different things might work in similar ways. Before Google, I’d have to go find experts, and they’d have to make time for me — I’d ask them my questions, and then go back and forth with them. With Google this was streamlined; I could look up books, search through them, get the basic theorems, try to put things together, learn the subject.
And now with LLMs, I just ask: “Hey, there’s this theorem in algebra. Does it basically work the same way in this other setting?”
Or: “Hey, if I have a group, and it’s this size, and it has such and such a property, does it also have this other property?”
You can plug that sort of thing into ChatGPT or Claude and it’s reasonably likely to give you something useful. And it can tell me the answer, and it can explain the answer. It can be wrong sometimes. There is a skill, a skill tree, in using it and figuring out when it’s bullshitting and when it’s wrong. But it’s immensely useful.
Q: With dumb questions as the starting point, where do you go next?
A: To break down the process, I would say there are a few different aspects of my math research workflow where AI comes in.
First, there’s the finding your bearing stage, getting oriented, where you’re figuring out what’s going on in your problem, or in your theory, whatever you’re grappling with. One part of that is determining what’s hard, what’s easy, what’s known, what’s not known. So, I’ll literally prompt the AI with: “Hey, I want to solve this kind of question. Give me an overview of what’s known and what’s hard.” And it will do that really well, consistently well.
And then I ask it more targeted questions, such as: “I was thinking of these special cases, or these kinds of analogs, which of these are known, and give me references.”
So that already is a huge time saver, partly because I can do it at scale. It’s much faster than asking a person, an expert; that would take, an email, waiting for a reply, or a meeting. Now I can try it a few different times immediately with the AI.
Second, there’s searching out a strategy, trying various types of arguments to see if they’re even in the realm of making sense. I can spell out my technique and ask if that’s been done before. I can ask, “What are the types of techniques people use?”
A third way it comes in handy is in looking up relevant material, and getting references, providing links — it’s gotten much better at providing links, but sometimes it will link to a website that doesn’t work anymore. I’ll prompt it with: “I want a result like this — is anything like this known? Please point me to references.”
And then fourth, there’s what most people call doing research. The fun parts of it, the real parts. You’ve spent months getting ready, you’re uploaded, you know what’s going on. There’s nothing left to look up. Now you have to think, and you have to come up with the right math. This is where flashes of brilliance happen, or just regular math work, whatever you want to call it. But all the fun parts of math are done here, where you’re just engaged with the problem. When I say my productivity doubles, it’s with everything leading up to this fun step.
Also:
Q: Do you think there will still be a human role in terms of ideas and creativity?
A: I think there will be a point where AI will be strictly better than humans at all aspects of math: learning, proving, coming up with the problems, aesthetics. It will just be better at everything. And this will come pretty soon,
Q: How soon is pretty soon?
A: Five years? I think in two years it might already be better than us at proving stuff. We’ll be able to say to it: “Here is a statement, go prove it.” But I have wide bars of uncertainty around this stuff. It’s hard to predict the future.
He also seems to be a bit of a doomer. :O Might be worth some ppl reaching out to.
Q: Have you discussed the intersection of AI and math much with other mathematicians?
A: Yeah, I have a lot of conversations. I’m pretty worried about AI in general — in math, and otherwise.
Q: Worried how?
A: I think there’s a good chance AI will lead to human extinction. I also think, separately from that, that AI will be better than mathematicians at math very soon.
Some people are advocating for a total pause in AI. I don’t think that’s wrong, I’d support that. But I doubt it will happen. So given that AI is moving forward, it’s important that we stay abreast of what it can do and how to integrate it into our lives. If pushing back against it leads to not learning how to integrate with this new… you can call it a species — call it whatever you want — on the planet, then I think there’s a bigger chance we might be left behind. That’s why I think it’s important to stay connected.
I think there’s a lot of “cope” going on among mathematicians, and a lot of overconfidence about the limitations of AI. It seems like most people are looking at the fact that LLMs are not currently as good as mathematicians at math and concluding for various reasons that it can’t be and never will be as good. Or they’re assuming that it will only be like an assistant, where it proves the simple lemmas, but that it won’t prove the major stuff. And I basically think that that’s all incorrect.
I think it’s going to make being a mathematician not a profession anymore. I don’t think mathematics is unique in that. I do think it might come sooner in math than in other places. Because math is much fewer soft skills; it’s much easier to train yourself. Once you have Lean and the LLMs integrated you can just go — go experiment, learn, prove stuff.
And oh, beyond that, in the first paragraph of the piece:
It also causes him worry. A sixth, nonmathematical, submission he made to the arXiv last year is titled “A Taxonomy of Omnicidal Futures Involving Artificial Intelligence.” This paper is coauthored with a longtime friend from math camp, the mathematician Andrew Critch, CEO and cofounder of EnculturedAI, which is geared toward finding a happy union between artificial intelligence and humanity. The paper’s abstract gives a bracing overview: “This report presents a taxonomy and examples of potential omnicidal events resulting from AI: scenarios where all or almost all humans are killed. These events are not presented as inevitable, but as possibilities that we can work to avoid.”
I plan to reach out, though I have no particular credentials. (I was a math undergrad and published a few papers.) If anybody has an actual connection, please do reach out to him. I’m also unsure what my ask will be. Sign a statement? I can try to put him in touch with the ControlAI folks, who I know are doing good work in Canada?
“is boosting his productivity by a factor of two,” mostly by speeding up the boring parts.
Speeding up the boring parts is what makes working with AI more fun.
I am just a humble coder, but I enjoy developing with AI not because it does awesome things way beyond my reach, but because it gets the boring parts out of my way.
Jacob Tsimerman, who’ll likely win the Fields Medal this year, thinks that AI “is boosting his productivity by a factor of two,” mostly by speeding up the boring parts.
Also:
He also seems to be a bit of a doomer. :O Might be worth some ppl reaching out to.
And oh, beyond that, in the first paragraph of the piece:
It also causes him worry. A sixth, nonmathematical, submission he made to the arXiv last year is titled “A Taxonomy of Omnicidal Futures Involving Artificial Intelligence.” This paper is coauthored with a longtime friend from math camp, the mathematician Andrew Critch, CEO and cofounder of EnculturedAI, which is geared toward finding a happy union between artificial intelligence and humanity. The paper’s abstract gives a bracing overview: “This report presents a taxonomy and examples of potential omnicidal events resulting from AI: scenarios where all or almost all humans are killed. These events are not presented as inevitable, but as possibilities that we can work to avoid.”
I plan to reach out, though I have no particular credentials. (I was a math undergrad and published a few papers.) If anybody has an actual connection, please do reach out to him. I’m also unsure what my ask will be. Sign a statement? I can try to put him in touch with the ControlAI folks, who I know are doing good work in Canada?
Speeding up the boring parts is what makes working with AI more fun.
I am just a humble coder, but I enjoy developing with AI not because it does awesome things way beyond my reach, but because it gets the boring parts out of my way.