What’s the future for pure math research in the age of AI?
We’ll talk later about the general character and value of pure mathematics. But before that, let’s address the issue of the moment: the role of modern AI.
And the first thing to say is that it’s unquestionably useful, sometimes very useful. For me, its greatest use in mathematical pursuits has been its ability in effect to thematically mine the knowledgebase of human mathematics. Starting back in the 1970s, being able to do keyword searches of the scientific literature was a crucial enabler of quite a bit of the research that I did. And now, with modern AI, one can do so much more. Because somewhere inside those LLMs—in a way that we don’t yet scientifically understand—there’s what amounts to a representation of raw ideas gleaned from all those millions of papers and books about mathematics.
And, at its best, it’s not just about retrieving things. It’s also about making connections. Of being able to see that this result here can be put together with that result there to come up with a surprising and useful conclusion. Humans routinely do that too. But they tend to have only read hundreds of papers; AIs have effectively read millions, and it’s cheap for them in effect to try out lots and lots of possible combinations.
