some scattered thoughts on ai for math

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There's a lot of talk about how math community needs to move away from theorem-proving ability as the measure of a mathematician's value, now that theorem-proving ability is cheap (and only getting cheaper). Predictably, there have been some identity crises caused by this change, as mathematicians try to grapple with the fact that the measure that has stood for centuries has been smashed to the ground in a matter of months.

Lucky for me, I never cared too much about theorem-proving. What I liked about math — contrary to literally every other mathematician I know, lol — was writing things up. I used to say that my ideal career would consist of partnering up with a mathematician who likes to solve problems but hates writing them up, so that I could spend my time converting their whiteboard scribbles into papers.

I suppose this means I should slot right into our brave new mathematical future, where an AI models hands the humans a proof and the humans try to explain the proof to ourselves. The role of the human is no longer to prove things, but to understand and canonicalize, and to ensure that a result has some kind of meaning. To digest, as Terence Tao says. This "digester" role is, in some sense, what I wanted to do when I was a budding baby mathematician — to be handed math soup that is reasonably correct, and turn it into a coherent story that someone else can understand.

At the same time, it does feel a little dystopian to be reduced to the mouth of the machine.

This isn't to say that AI for math isn't exciting — it is indeed cool that age-old problems are being felled by the week. We are seeing mathematical progress like we have never seen before, and I think that's a good thing.

But I do feel something analogous to what artists must have felt during the initial releases of DALL-E and Midjourney — a sort of betrayal, maybe? Math, especially the coming-up-with-a-proof flavor of math, used to be magic — magic that took me years of tome-studying and rune-carving to learn how to use — and now it is more like a cheap charlatan's trick, coming closer to machine-work that forgets process in favor of product.

I carry some kind of grief for all the future humans who may never feel that same spark I felt in my Intro to Proofs class all those years ago. Will we begin to think that consumption of proof is all there is to mathematics? Worse, will we end up relegating ourselves to the consumption of proof, letting "proof generation" happen in a black box?

I'll hold off on freaking out too much over the slippery slope. I have been known to be extremely partial to the familiar; maybe I am just adjusting to the new normal. I would not be surprised if all of my opinions change after actually completing a math research project that uses AI.

I do know something for sure, though: AI for math has already changed my life. It has materially changed my career path, turning a gap year into an indefinite break from academia, because I wasn't sure that there would be viable careers in its wake. And yet it has opened up an avenue for me to do research mathematics during that gap, outside of the long-established structures of academia, which would have been unthinkable before.

I guess it's always the same with any technological advancement — it displaces the traditional way of doing things, and at the same time, it displaces the traditional way of doing things.