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No country for mediocre mathematicians

garvvee.substack.com

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Re: No country for mediocre mathematicians

#21

Post by bananaflag »

ventana wrote: post #2

It's interesting that this piece stands well enough if you replace mathematics with probably any other intellectual profession, including software development or pretty much anything else. And, I lie to anyone who asks me why I’m a mathematician. It is much easier to claim “I love learning the laws of life,” while literally handwaving, than it is for me to flashback to the twenty or so pivotal moments that lead to me…

> And, I lie to anyone who asks me why I’m a mathematician.

I prefer to say "I liked a girl" (because it's the truth)

Re: No country for mediocre mathematicians

#22

Post by MostlyStable »

paulpauper wrote: post #14
bhouston wrote: post #11

I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications…

Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite…

honestly curious question: do you expect this to remain true? If so, for how long? I can think of two potential reasons why it might not stay true.

1. The very best humans remain able to understand/check the proofs, but we go for so long with every proof checking out that society more broadly just decides to trust. We are already doing that with human mathematicians. I can't verify what Terence Tao tells me is correct, I just trust that it is because he (and other human mathematicians) tell me it is. How many proofs/years of them checking out before we reach this point? I don't know, but history suggests that eventually, humans might keep checking, but they will do so only as a hobby. For any purpose that actually matters, we will just start to trust and use it.

2. The proofs that AI comes up with become too difficult/complex for even the very best human mathematicians to understand, and our options become to either trust or to not use at all.

Obviously it's possible that neither of these happens if AI capabilities stall out not too far beyond where we are now, but if they keep progressing at the current rates for another few years, I expect at least one, and maybe both, to eventually come to pass.

Re: No country for mediocre mathematicians

#23

Post by jplusequalt »

paulpauper wrote: post #18
hyperhello wrote: post #3

Hobbies aren’t as fun when you have an overbearing friend who constantly shows off how much more they know and how quickly they can switch to talking about anything you want but in greater depth than you.

mathematicians or physicists fall into this category of knowing a lot about many thing . Sabine videos for example . she knows everything it seems

Sabine is a crank who likes to wax poetically about fields she has no creds in.

Re: No country for mediocre mathematicians

#24

Post by pdm55 »

derangedHorse wrote: post #6

> My physicist friend once asked me what the point of doing research was if someone like Terence Tao could have figured out everything in my dissertation in a tenth of the time. I answered by pointing out that Terence Tao didn’t. Terence Tao did not find a small open problem posited by my advisor and publish a bite sized result making incremental progress. He has only so much time and so many other fish to fry. This…

I have just started reading this Gates Notes about reserving some jobs for humans:

https://www.gatesnotes.com/a-turbulent-ai-era-and-critical-c...

Re: No country for mediocre mathematicians

#25

Post by bananaflag »

paulpauper wrote: post #12
ventana wrote: post #2

It's interesting that this piece stands well enough if you replace mathematics with probably any other intellectual profession, including software development or pretty much anything else. And, I lie to anyone who asks me why I’m a mathematician. It is much easier to claim “I love learning the laws of life,” while literally handwaving, than it is for me to flashback to the twenty or so pivotal moments that lead to me…

A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned. The equivalent for a software engineer is probably a leading AI engineer, with a strong publication count. I think a lot of people who are not mediocre are unaware of what mediocrity actually is. Yeah if you're only in the top .1% and comparing yourself to the literal best in the w…

> A PhD in Arithmetic Geometry and a publication in a top tier journal is hardly mediocre in and of itself, as far the author is concerned.

It kinda is (sadly) because unlike engineering there aren't thousands of postdoc jobs in arithmetic geometry.

And ofc in a year because of AI all math PhDs will be mediocre by definition.

Re: No country for mediocre mathematicians

#27

Post by lo_zamoyski »

derangedHorse wrote: post #6

> My physicist friend once asked me what the point of doing research was if someone like Terence Tao could have figured out everything in my dissertation in a tenth of the time. I answered by pointing out that Terence Tao didn’t. Terence Tao did not find a small open problem posited by my advisor and publish a bite sized result making incremental progress. He has only so much time and so many other fish to fry. This…

> what the point of doing research was if someone like Terence Tao could have figured out everything

A similar question is now being asked: what is the point of doing research, etc. if something like AI can figure out everything?

The question betrays the parochial way in which many people think about knowledge. For them, knowledge is merely an instrument or an effect. It does not occur to them that knowing is a valuable thing in itself, that understanding is valuable and desirable. Yes, some knowledge has merely practical value, but theoretical knowledge is primarily sought for its own sake, because we desire to know reality.

So, even if Terrence Tao, an AI agent, or who or whatever arrives at some bit of new knowledge, it doesn't benefit you as a knowing subject unless you understand it yourself and make it your own.

Re: No country for mediocre mathematicians

#28

Post by GPerson »

paulpauper wrote: post #14
bhouston wrote: post #11

I have some bad news for the non-mediocre mathematics. Given it another year or two or so and there won't be much need for non-mediocre mathematics either. Instead everyone will have on call a near magic mathematician who can push the state of the art for their needs. Math is actually a perfect fit for AI because it is possible to express everything in terms of written language and you can write formal verifications…

Whenever there is a breaking AI-generated proof, it's the job of actual leading mathematicians to formalize/check it . Laypeople are not checking or writing these AI-assisted proofs. Even when Lean is used, it's mathematicians writing these proofs and checking if the formalization was done right. Terrance Tao's career trajectory has reached new highs due to AI. He's more relevant than ever. This is the exact opposite…

I’m not sure about this. Anthropic’s AI constructed complex structures on S^6 and wrote a 108 page paper about it, and a few days later there was already a 250k line lean program claiming to verify it.

Re: No country for mediocre mathematicians

#29

Post by inanutshellus »

axus wrote: post #16
binary0010 wrote: post #10

Earlier quoted context omitted.

Yeah seems like most programmers just do it for the money. I imagine only like 20% of us do it just because we enjoy it.

I feel like the number is higher for software work where I'm at, and lower for every other profession. Scary when you think that your doctor is in it for the money

hopefully the MD that passes all the tests is still worth his salt even if he only chose the profession for the paycheck.

but as one of the nearby professors is famous for saying: "C students gotta go somewhere."

( and since this is HN - he didn't mean the programming language :D )

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