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No country for mediocre mathematicians

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Re: No country for mediocre mathematicians

#51

Post by bananamogul »

emil-lp wrote: post #42

> Lying is a core part of communicating mathematics. We lie to kindergarteners when explaining fractions. We lie to fourth graders when approaching limits... Hard disagree. Lying is with intention to deceive. Teaching is simplifying with the intention that they understand and get the correct intuition. Math is not about lying, that's just silly.

I don’t remember us getting to fractions in kindergarten, but maybe the curriculum has radically changed since the early 70s.

What exactly is the lie? 1/4 and 3/8 equals 5/8. Is there’s something more to that? Is that fundamentally wrong?

Re: No country for mediocre mathematicians

#52

Post by BoredomIsFun »

binary0010 wrote: post #43
BoredomIsFun wrote: post #38

Earlier quoted context omitted.

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.

It's an awesome profession for those of us who love it. Tbf coding with ai is still super fun though. I am hoping that engs who hate it like you will finally get kicked out as productivity increases from ai and it will finally go back to just us nerds. It's kinda soul-sucking being around all you guys that just hate this work, please get out and go do farming or something lol.

> It's an awesome profession for those of us who love it.

Yes, by definition of "love" and "awesome".

> Tbf coding with ai is still super fun though.

Agree, it could be entertaining.

> I am hoping that engs who hate it like you will finally get kicked out

Ain't gonna happen, as I am pretty good at it.

> please get out and go do farming or something lol.

I thought about, but it is not well paid. I make money mostly from investments though, still do occasional coding stuff - for money.

Re: No country for mediocre mathematicians

#53

Post by [deleted] »

sheafification wrote: post #34
GPerson wrote: post #28

Earlier quoted context omitted.

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.

[deleted]

Re: No country for mediocre mathematicians

#54

Post by bitwize »

sheafification wrote: post #31
MostlyStable wrote: post #22

Earlier quoted context omitted.

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…

> 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.

I have. DataAnnotation and these other AI-training piecework companies are pretty much the backstop now against total navel-gazing model collapse. With the Dead Internet Theory now pretty much reality, it's not like there is, or is going to be, gobs of untainted human-generated data out there ripe for the harvesting so it's going to take active human effort to keep the models grounded. That is, of course, until they start inhabiting robot bodies so they can live and move around in the real world, and thereby achieve their grounding, as in GitS or Ex Machina...

Re: No country for mediocre mathematicians

#55

Post by kodoman »

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.

an obvious question would be if 250k loc is what is required for the proof or if it can be shortened massively, is this essentially going to be AI trying to search for a smaller proof or is it that a human being would be beneficial in that loop.

Re: No country for mediocre mathematicians

#56

Post by azan_ »

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…

> 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.

That's really mean thing to say

Re: No country for mediocre mathematicians

#57

Post by kodoman »

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

She is just arrogant. And asserts a lot of silly opinion as fact, her stuff on philosophy and theology is generally terrible.The sort of atheist that never actually looks into theology but knows the thing that first came to her head is a definitely the most amazing point against classical theology that has never been considered before.

Re: No country for mediocre mathematicians

#58

Post by aleph_minus_one »

bananamogul wrote: post #51
emil-lp wrote: post #42

> Lying is a core part of communicating mathematics. We lie to kindergarteners when explaining fractions. We lie to fourth graders when approaching limits... Hard disagree. Lying is with intention to deceive. Teaching is simplifying with the intention that they understand and get the correct intuition. Math is not about lying, that's just silly.

I don’t remember us getting to fractions in kindergarten, but maybe the curriculum has radically changed since the early 70s. What exactly is the lie? 1/4 and 3/8 equals 5/8. Is there’s something more to that? Is that fundamentally wrong?

> Is there’s something more to that?

Yes: this is about building the quotient field (field of fractions) [1] for some integral domain, or more generally, building the localization ([2], [3]) of a commutative ring with respect to some given set that is closed under multiplication (the special case of the quotient field for a ring R is obtained when one chooses R\{0} as such a set).

--

[1] https://en.wikipedia.org/w/index.php?title=Field_of_fraction...

[2] https://en.wikipedia.org/w/index.php?title=Field_of_fraction...

[3] https://en.wikipedia.org/w/index.php?title=Localization_(com...

Re: No country for mediocre mathematicians

#59

Post by aleph_minus_one »

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

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

Sabine Hossenfelder, for obvious reasons, knows quite a bit about physics, though on some physics topics she has opinions that are outside the mainstream. For other areas, I am rather certain that she has a talent to learn about them up to some shallow level quite fast, which suffices to create some video about the respective topic, and then move on.

Re: No country for mediocre mathematicians

#60

Post by ryeights »

kodoman wrote: post #45
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…

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