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Reports of our demise are greatly exaggerated.
Someone close to me is about to embark on a maths PhD. I'm curious about what advice people here would have for people in that position.
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I wouldn't particularly worry. Big picture: don't base your future on the fears of the present. AI is a tool for humans, so be curious about it and use it if it can help you. Otherwise, ignore the noise.
Here's a research mathematician replying to pretty much exactly this question, and I think it's worth reading: https://davidbessis.substack.com/p/letter-to-a-phd-student

It's also relevant for non-AI reasons. The upshot is: Do it if you want to. You're at an age where you're supposed to be mostly learning, but over time, start transitioning into whyever you did this (which doesn't have to mean staying in academia, and in fact can mean teaching or popularisation or consulting or...).

It remains to be seen if LLMs would do any good in the "theory-building" heavy fields of math. They have certainly proven themselves in branches of math where the progress is verifiable, but fields like AG commonly have papers that do not concretely solve a problem but provide a new perspective/framework. This is iterated upon if other mathematicians find the construction rich and interesting enough, which eventually leads to breakthroughs.

LLMs have yet to show that they can meaningfully make such helpful abstractions. Not saying that it can't be done, but I wouldn't write such doomer posts just as yet.

This crystallised a take.

Unsolved Erdosh problems were touted as a cheap way to generate new perspectives. outcome has been slightly disappointing. overlooked frameworks were all that has been needed so far. not new ones. Could change as LLMs are pointed at other kinds of inexplicables

Soon we will all just be human cattle owner by billionaires who own all the technology used to keep us poor and indoors.

Oh, no - that's actually now.

bwaaaaaa! ha ha ha bwaaaaa! wheeeeeeuew! is the title what happens from too much ketamine? or is the hype machine being tasked with streeeetching things out for one more quarter? bills, elections, push back,lack of relevance, that sort of stuff.
> I feel like at this point, both the prophets of AI utopia like Ray Kurzweil, and of AI doom like Eliezer Yudkowsky, could be forgiven for asking: dude, will you listen to us YET?

What did Kurzweil or Yudkowsky predict that actually came to pass?

I assign this Scott no points for bringing up Penrose as a straw man. That’s a very old canard.

He's embedded in a social and professional world that has every incentive to believe the current state of AI progress is real and important and should be hyped to the stars. I am unsurprised to read such frothing soothsaying as a result.
Luckily, humans will always remain relevant to humans.
Aaronson has worked for OpenAI and probably has stock options. Gowers is funded by the "AI for math" fund by XTX markets.

The students who have been alarmed outside his office should take a course in marketing and journalistic ethics to assess the situation more rationally and figure out that the problem might sit in the office.

It is interesting by the way that Google does use Lean in a loop to refine proofs. This was called heresy by AI boosters earlier who said that Lean was never used in proofs.