What specific direct advice would you give then if you could talk to someone who is currently studying math?

Do you know where “the ball” is going? Do these math students? Do the professors? It’s easy to say a vague nothing platitude like “target where the ball is going to” but such empty vague platitudes do not help anyone and just waste time.

I was recently trying to work out what advice I should be giving my 15 year old son, I asked various AI for their recommendations given "possible" AI time frame and it seemed pretty much study whatever you want but always add " and business". Investing in things that AI will just make better. However, in the case of AI improves robotics to the point it's better than humans... who knows. But all that may not pan out as reality. For me, AI is still making a lot of the same mistakes it was making last year, it's very marginally improved in some aspects (not quite sure how to categorize what its failing at, but its like an over eager worker who really doesn't understand what they are working on but super keen to do stuff). It's gotten a lot better at doing more from single prompts. But it feels like, for LLMs at least, they are bumping into limits. But it can be hard to see because at the same time they are actually doing more. More and more I feel like what I'm doing is getting more ambitious in what I'm asking and then a big cycle of correcting.

I would probably tell them to not study math.

I think that's a really unfair characterization of GP's post. They didn't talk about "target where the ball is going" as am empty platitude - they specifically pointed out that they need to plan for a career that will last ~40 years, and on the contrary a lot of these posts by math luminaries seem to be filled with a lot of "hopium" and platitudes that won't help pay the bills if it turns out the world needs a ton fewer mathematicians.

> What specific direct advice would you give then if you could talk to someone who is currently studying math?

Do it for personal satisfaction, but find another way to pay the bills.

FWIW, I did like that the article at least acknowledged that the fundamental question is whether LLM-based approaches will eventually "max out", i.e. will they be limited to the "convex hull of ideas outlined in literature" as the article out it.

If LLMs do eventually hit a wall, then great, humans will still have a role to play. If not, though, we're all completely fucked - none of this nonsense about "humans managing agents" or providing "unique human insight" and what not, as agents will be more than capable of managing themselves and providing superior insight.

Chess has always been "just a game". Sure, it teaches valuable life lessons, and it is fun to defeat your opponents through superior training and strategy, but it is "just a game".

Mathematics was historically "just a hobby". Much theoretical work is still "just a hobby". But, for the past few hundred years, humans that better understood the theory could find very profitable applications.

That is no longer true. Computers have solved mathematics, like they did chess two decades ago. A human will never find a better application than a computer, just like they will never find a better chess move. Yet people still play chess, and people still make money tutoring chess.

That is the future of humans in mathematics. Mathematics will become mathematics competitions. It will be just another intellectual sport. Sure, a sport that teaches valuable life lessons, but still "just a game". If you are going into mathematics today, your future career is as a competition mathematics coach.