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No country for mediocre mathematicians

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Re: No country for mediocre mathematicians

#31

Post by sheafification »

MostlyStable wrote: post #22
paulpauper wrote: post #14

Earlier quoted context omitted.

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 correc…

> do you expect this to remain true? If so, for how long?

For the foreseeable future. Left to their own devices current LLMs kinda wander off into outsider art territory. They aren’t grounded in the real world and they need that feedback loop to stay within the category of relevant ideas. I haven’t seen anyone working on fixing that.

Regarding 1, the same is true of every other scientific field. Verifying some tidbit of knowledge for yourself as an individual isn’t optimally useful in all circumstances.

Regarding 2, if the proof isn’t understandable then it probably isn’t useful. Many people today work in the hypothetical world where the Riemann Hypothesis is true, and many work in the hypothetical world where it is false. If it takes decades to validate that some horrifically complex AI proof of either fork is true, people will probably continue working on the other fork just in case.

Re: No country for mediocre mathematicians

#32

Post by doctorpangloss »

marcosdumay wrote: post #4
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…

> “what do you like about your job?” For software development, normal people will just assume it's money and probably not even ask...

For mathematicians in the US, it's because their parents like money.

Re: No country for mediocre mathematicians

#33

Post by randusername »

> We're all frustration addicts. We just want to bang our heads against problems we don't yet know how to solve.

I've been tapering off AI lately. I think I've realized that conquering the struggle is the fun part, and accomplishments just don't hit the same if AI is smoothing over every friction and cordoning off all the pitfalls and rabbit-holes.

Re: No country for mediocre mathematicians

#34

Post by sheafification »

GPerson wrote: post #28
paulpauper wrote: post #14

Earlier quoted context omitted.

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.

It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.

I guess it could be AI turtles checking and summarizing all the way down, but is that any more credible than a single AI checking it? I doubt it.

Re: No country for mediocre mathematicians

#35

Post by ventana »

SoftTalker wrote: post #20
axus wrote: post #16

Earlier quoted context omitted.

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

You can be a software developer without any formal training and without any licensure. Not so for an MD. It's going to attract more people who have the mentality of artists or musicians, i.e. people who do it for the love of the craft and as a creative outlet.

> You can be a software developer without ... any licensure.

Don't jinx it. We are extremely lucky in this regard, and it actually looks like a rare exception.

Re: No country for mediocre mathematicians

#36

Post by sheafification »

bananaflag wrote: post #21
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)

My go-to is “It’s the only thing I was good at in school, I was hopeless at everything else,” which is only a slight exaggeration.

Re: No country for mediocre mathematicians

#37

Post by bhouston »

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…

> Terrance Tao's career trajectory has reached new highs due to AI.

Given he is uniquely brilliant, he is likely one of the very last mathematicians to be rendered obsolete for his skills. But AI is pretty unstoppable here, so I would give him maybe another year compared to pretty much all the just really good / great mathematicians.

Re: No country for mediocre mathematicians

#38

Post by BoredomIsFun »

binary0010 wrote: post #10
pwdisswordfishq wrote: post #5

Earlier quoted context omitted.

They would not even be wrong.

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.

True. I like math and CS theory, but despise coding (pays well though). AI is finally taking over this soul-sucking occupation and all I can say - good riddance.

Re: No country for mediocre mathematicians

#39

Post by nkrisc »

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

There are plenty of easier ways to make money than becoming a doctor.

Re: No country for mediocre mathematicians

#40

Post by BoredomIsFun »

jplusequalt wrote: post #23
paulpauper wrote: post #18

Earlier quoted context omitted.

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.

She is a grifter, not crank.
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