AI is about to make mathematicians more essential than ever

The author argues for evaluating Ph.D. candidates based more on the oral thesis defense than on the actual thesis.

By essentially the same reasoning, I’ve been arguing for prioritizing in-person design/code reviews over code-only async PR comments.

The important thing is to verify that the human has a coherent design in mind and can demonstrate that it got implemented, regardless of who or what was at the keyboard. “I dunno, I guess Claude thought this was a good idea” is not a coherent design.

As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.

Excellent optimistic post in a sea of negativity, and with actual suggestions, too.

After reading, my mental image is this: think of Olympiads in Ancient Greece.

* A weightlifter was only awarded a laureate if he were able to lift a heavy stone (have no idea what they were lifting, for illustrative purposes only :-)

* Along comes Archimedes who invents what we would call an exoskeleton. Now any regular guy can lift twice as much as last year’s athlete.

* What to do? You can cancel the Olympiads, but they are actually useful as training, motivation, etc So now you have to give the prize on other factors, eg how well he can lift, has he opened a gym in the city, etc

BTW, physics and bio are not exempt, so those researchers better read and try to stay ahead.

I admit I just don't understand this attitude.

People had the same complaints that the code produced by early coding models was messy, lazy, poorly commented, had terrible architecture and so forth. The central complaint was that it was just too difficult for humans to review. The answer is just to improve the models and move on.

Similarly now we're getting AI doing math. The proofs compile but are a mess. So just make the models better at writing clean proofs and explaining what they're doing to humans. That's the end of it.

Rather than just go on and on about how it's the end of the world if we don't do this, why don't we just do it?

> We already interview faculty hires; we must now do the same for graduate admissions

They hire PhD students without hearing them give a talk and then doing interviews? In Germany, the applicant gives a talk (30-40 min) to the research group they want to join, usually presenting their master's thesis, engage in discussion, often share lunch with the group, then do 1 on 1s with individual members of the group and a longer one with the PI. Obviously this can vary within Germany too, but I couldn't imagine hiring someone without something like this.

I’m not a mathematician, but if I were I would imagine the main attraction would be the act of thinking hard and solving problems. Maths felt like the ultimate profession for someone who loved puzzle solving. If you delegate the thinking, any percent of it to an LLM, I don’t think it’s maths anymore. Might as well join any other job and earn better money now. A completely ludicrous proposition, that maths will no longer involve mathematical problem solving.

I love how this is (without slighting the problems entailed) coming at it from a perspective of infinitude and abundance (we will always have more problems to solve) - which is the correct framing, particularly when dealing with ideas, or fields in the which ideas are the driver/product/output/material, and ideas themselves, the field itself, are infinite.-

PS. The validation problem, being one.-