3blue1brown: There's Never Been a Better Time to Go Into Math

I think math will go the way of biology. Biologists enjoy untangling the infinitely complex mechanisms of life, including the brain, and win Nobel Prizes for discoveries like "how water enters a cell," rather than "constructing the first-ever cell capable of absorbing water."

No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch."

I think two things are being conflated: whether math will continue to offer exciting opportunities, and whether it will remain fulfilling for those who love doing it today.

Grant is right about the former. But that doesn't address the latter. A field can have a bright future while losing what drew people to it.

I could be fully wrong here as I am not from the field. But how is this different from let's say a ramanujan-like genius dumping a bunch of solved problems with not yet understandable ways of getting there?

It seemed riveting enough for some mayor mathematicians to "decode" his solutions into readable proofs?

The only difference I spot now is that it was not an Indian man, but a machine. If that bothers you still, it seems less about the art of the craft being taken as it seems to be about who has taken it?

I actually remember that in an old interview (that I can't find sorry) Grant Sanderson said he moved in to YouTube because he thought it was a more promising career than being mathematician, it's interesting to see his opinion change.

A couple of thoughts in agreement..

First, "cognitive labor" is a form of labor - it's different vs. creative work, even though both use your mind. If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work. Cognitive labor is a form of labor. Let's talk about physical labor and leverage to understand how removing labor translates to time. On your farm you buy a tractor to replace your backhoe. If it is a hobby farm you get in the tractor and you're done super fast. Or, you can take that tractor, buy a bigger farm, and spend the same amount of time you'd have spent backhoeing, but in a far more leveraged way. You can trade removed labor for time in a way that suits you.

Second; the joyful moments we get from finding generalizable abstractions and nice solutions are an adaptation. Humans can climb infinitely high conceptual hierarchies - we'll never stop climbing, using the previous ones as tools to find the next. As we do, we gain joy with each discovery because. We get so much done with brains that run on 20 watts - are we tuned to receive a neurochemical reward for finding cognitive efficiency? If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!

Third; everyone else is doing it, it's a baseline skill. Knowing how to work without AI is like knowing how to ride a horse. Useful an […]

Going into math at this point is like buying a used crossword puzzle book.

by the way it feels to me that teaching is one of the most satisfying jobs on earth, you could (and should) be passionate for hours long in front of your students, that's amazing. as a programmer it seems you'd only feel passionate for like 5% of your work, even before AI it wasn't all that joyful, you had to attend boring meetings, debug legacy code bases, trying to make sense of the bad decisions other made (including yourself), it's fine, it brings food to the table.

I think the myth of "passion" has affected way too many youngesters though. You can find meaning in many things in life, and there are already way too many people who kept chasing their "passion" yet at the end realized it didn't bring them real happiness.

Maybe this AI thing is good for us after all, maybe we should take a pause and answer the harder question.

Edit: and yeah, even teachers probably have lots of chores and boring parts of the job.

personally as a math phd student, LLM centric math feels soulless and ultimately is not what I entered the field to do which is to personally make mathematical discoveries with my own brain and cognition, and not direct a discovery machine.

Yes, cue the: cope seethe, selfish mathematicians, care only about personal glory, more theorems = cancer proven, more knowledge>less knowledge, e/acc etc. etc.

I've heard all these tired arguments many times. Whatever - I concede - you're right and I'm morally wrong and bad. Just don't expect people to study this subject which is basically being turned into biology (spend hours sitting in a lab babysitting equipment all day while watching a movie - it's what most bio phd students i'm around seem to do, no offense meant to bio phd students, i'm certain their studies are orders of magnitude more impactful to the society than mine).

it was fun while it lasted.

In the essay Hackers and Painters it was mentioned that there is a project approach to learning and an academic one. The idea of pet projects is killed by language models, because what you did on weekends, a language model now does in half an hour. So you can try the other approach: maybe you should have more general knowledge right away, best practices, so more of an academic approach. In the academic approach you learn from the best reference examples, develop taste, and only then recognize what is good or bad and build your own. But here too you can see that LLMs iterate much faster, while you have to collect patterns for years, and you will also always be in the role of the one who is behind.