How research in math will change (from my email)

I am a mathematician…and some of your recent comments on MR about the role of AI in Econ research as well as the (disappearing?) role of academic papers inspired this response. (It is partially but not exclusively about academia, so I hope it is ok that I’m sending it to your GMU address. Also, I’m hoping it doesn’t get flagged as spam because of the ai in the title…)

In no particular order:

-In the course of a math career, one accumulates lots of computational guesses, now one can test those with minimal effort.

-One also accumulates lots of incomplete and half formed drafts, proofs of special cases, etc, etc. Running those past claude and chatgpt can (does!) pay off. A lot of math is cleverly applying linear algebra and while I’m very good at linear algebra, I’m not as good at it as the AI’s are.

-The lower hanging fruit here are slightly off the beaten track, but not esoteric subjects. If you have a good overview of such, you can pretty quickly prod ai’s into making progress on them. (Before, you needed to have a school of grad students for that). Basic techniques (graph theory, algebra, calculus..) that ai’s are already good at can push these forward already. Making progress on truly hot topics is harder.

-There are some quite smart people trying to measure just how good autonomous ai’s are at math (e.g. the first batch project). That’s a fun game, but for practical purposes right now, what is relevant is how good an ai is when guided by a motivated human. I suspect we’ll see some remarkable things on that front in the next few years once math people really grok the good routines.

-For instance, getting claude and chatgpt to referee each other’s arguments is fun, and they genuinely have different insights on parts of the same problem.

-The kids will be all right. Right now, they are making pocket change doing ai training developed a better “feel” for the different ai’s that I probably ever will. And they learn things by asking the ai to explain an argument to them instead of trying to decipher a math book or paper.

-Which brings me to your papers point. I notice that a project informed with the right context is much more informative to me than the physical pdf of a math paper, and much easier to extract information out of by just asking the thing.

-Refereeing will look very different very soon. All the referee reports that have been collected by the journals should be valuable, hard to get data. And running all the accepted and published math papers through ai’s as the `control’ will end with quite a few people having egg on their face. It’s like self-driving cars, but there is no refereeing union.

-The last really big math revolution was all the stuff in the wake of Witten and 4-manifold stuff predicted by string theory in the early 90’s. This is going to be so much bigger than that. Buckle up.