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Mathematics in the age of AI

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Re: Mathematics in the age of AI

#241

Post by [deleted] »

chrisjj wrote: post #233
ipdashc wrote: post #204

Earlier quoted context omitted.

Someone just brought up this point to me a few days ago on here, I'm definitely increasingly convinced that it's one of the main reasons (maybe even the main reason?) AI prose is so annoying to read through, and so rarely seems able to convey true understanding. It assigns the same narrative importance and dramatic tone to everything (the load bearing whatever, the crucial insight, the smoking gun) even when it's tri…

What surprises me is anyone is surprised. Obviously a stocastic parrot has no understanding, so any conveyance of true understanding it delivers will be rare and accidental.

[deleted]

Re: Mathematics in the age of AI

#242

Post by chrisjj »

ipdashc wrote: post #240
chrisjj wrote: post #233

Earlier quoted context omitted.

What surprises me is anyone is surprised. Obviously a stocastic parrot has no understanding, so any conveyance of true understanding it delivers will be rare and accidental.

I mean, having said what I said, we are literally in a thread about the future of mathematics being in question because LLMs are solving advanced problems. I feel like the "stochastic parrot" meme is a bit outdated by now. The bots' output may be annoying to read but they're clearly onto something , whether we call it "understanding" or not.

> I feel like the "stochastic parrot" meme is a bit outdated by now.

The stochastic parrot of my reference is not a meme.

https://en.wikipedia.org/wiki/Stochastic_parrot

The term was introduced in a 2021 paper on AI ethics titled "On the Dangers of Stochastic Parrots: Can Language Models Be Too Big? " that was authored by Timnit Gebru, Emily M. Bender, Angelina McMillan-Major, and Margaret Mitchell.[a]

> The bots' output may be annoying to read but they're clearly onto something

Sure. Next-token prediction with huge source set and computation power. Nothing new there.

Re: Mathematics in the age of AI

#243

Post by a2ff6eeb0 »

Scarblac wrote: post #226
a2ff6eeb0 wrote: post #178

Earlier quoted context omitted.

sure, agreed, but once you have a proof, you can probably get AI to reduce other problems to that problem in P.

Well then, just tell the AI that the statement is true and it will find reductions! In reality, it wouldn't depend on the truth value of the statement, but on the AI understanding the proof . If it understands it then it might be able to use it to find reductions. So the point remains, knowing that P=NP isn't what's important, it's the proof that matters.

Sure, we monkeys don't need to care, though.

Re: Mathematics in the age of AI

#244

Post by sigbottle »

Optimizing for the appearance rather than the underlying substance.

Ahh. I know Terrence Tao didn't have the following in mind when he said those words, but oh man, the philosophy neurons are firing in my brain rn.

Re: Mathematics in the age of AI

#245

Post by a2ff6eeb0 »

spacebanana7 wrote: post #213
Jensson wrote: post #180

Earlier quoted context omitted.

But at that point you have full AGI and its not just today's models. Today's models still need humans to understand things since it builds upon human knowledge. When you have full AGI of course you no longer need humans to understand math. > Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it Developing multivariable calculus requires much more than just s…

It's reasonable to say that current or near future AI can find novel mathematical results and develop applications from those. The idea of AI stepping from a graph theory/combinatorics innovation to some new and useful algorithm isn't crazy.

Exactly. Soon, human brains are going to be obsolete.

Re: Mathematics in the age of AI

#246

Post by esafak »

visarga wrote: post #206
esafak wrote: post #75

Earlier quoted context omitted.

The employer's, whose salary affords your subsistence.

If AI is so great it can do your job it is good enough to provide for your needs directly by automation. Just buy a robot and a plot of land and you don't have to worry about jobs.

Robots can't do that yet, and even then you still need to pay for food, healthcare, land (taxes), transportation, etc.

Re: Mathematics in the age of AI

#247

Post by jumpman500 »

jbstack wrote: post #239
sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

I don't agree with this rule of thumb at all. Let's say tomorrow someone comes up with a formally verified proof that a major encryption algorithm underpinning the security of the internet can be trivially broken, but they can't explain it. You're saying it should be kept under wraps and not published? Tao is essentially saying that the only value in a proof is its ability to be understood, but that's wrong. A proof…

I sort of agree, if you can guarantee the AI generated proof isn't a false positive. To be fair though, your example would be easy to explain to someone. You just show how the encryption algorithm can be trivially broken. A program that can break major encryption algorithm would likely be understandable, or at the very least we could show how it can decrypt things.

Re: Mathematics in the age of AI

#248

Post by nixon_why69 »

jbstack wrote: post #239
sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

I don't agree with this rule of thumb at all. Let's say tomorrow someone comes up with a formally verified proof that a major encryption algorithm underpinning the security of the internet can be trivially broken, but they can't explain it. You're saying it should be kept under wraps and not published? Tao is essentially saying that the only value in a proof is its ability to be understood, but that's wrong. A proof…

Tao is talking about academic publishing, based around learning for it's own sake. If no learning happened, do not publish.

From a different angle, what we don't understand can absolutely hurt us and you're right too, but it doesn't contradict Tao's viewpoint.

Edit: if you had a PoC cracking the encryption, I think the result is still publishable due to impact and the fact of the empirical result. That's different from some esoteric proof that nobody is even sure it's right.

Re: Mathematics in the age of AI

#249

Post by cman1444 »

Jensson wrote: post #180
nilkn wrote: post #110

Earlier quoted context omitted.

Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, medicine, etc., would have great value to humanity even if it doesn't help humans understand abstract truth at all. Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, the…

But at that point you have full AGI and its not just today's models. Today's models still need humans to understand things since it builds upon human knowledge. When you have full AGI of course you no longer need humans to understand math. > Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it Developing multivariable calculus requires much more than just s…

So then it sounds like you agree that math has additional utility beyond just human comprehension.

If I understand you correctly, you're just qualifying that that will only be the case when AGI exists. To be clear, I actually disagree with you here because I think it's very plausible to find a use case for human-incomprehensible math proofs before AGI exists. I'm just saying it sounds like you're agreeing with the parent comment that math is not purely about human comprehension.

Re: Mathematics in the age of AI

#250

Post by cman1444 »

chongli wrote: post #134
d4v3 wrote: post #119

Earlier quoted context omitted.

> Without persuading other people of the “truths” that you discover, there is no real mathematics. Why? If I sat around and studied math by myself and discovered something true yet not yet known but didn't share it, it's still true. Are you saying I didn't "do math" because I didn't share the result? Math exists on another plane and it has 'truths' that we haven't discovered, yet are still 'true', no?

No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make. The area of a triangle doesn't have 1 unique formula, it has many, depending on the system you use. A triangle in plane geometry has a different area than a triangle in spherical geometry, and different again in hyperbolic geometry. When you get to studying the geometr…

This is a needless qualifier for the argument at hand.

A proof can just be "assuming these axioms.....the area of a triangle is X"

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