Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mathematics in the age of AI

arxiv.org

Post reply on HN
Print view View original

221–230 of 292 posts

Re: Mathematics in the age of AI

#221

Post by mahdi7d1 »

czgov wrote: post #186
HWR_14 wrote: post #177

Earlier quoted context omitted.

I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?

If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?

Re: Mathematics in the age of AI

#222

Post by saithound »

czgov wrote: post #186
HWR_14 wrote: post #177

Earlier quoted context omitted.

I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?

If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

> If it is known that A is provably true then one can study the consequences of A being true

But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that.

Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.

Re: Mathematics in the age of AI

#223

Post by wavewrangler »

HWR_14 wrote: post #164
noosphr wrote: post #127

Earlier quoted context omitted.

Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.

If a magic oracle tells you p=np, that's useless. How would that change anything?

I thought the point of publishing was a matter of dissemination, to make available for people to then try to understand it? This is like saying, I don’t like music, so I’m going to tear down the venue. Then, all music genres suffer as a result, and all of society does, too. This idea is no good.

Somebody, eventually, somewhere would understand it, or at least aspire to understand it. And even if he doesn’t, what have they learned in the process? About themselves, about their environment? About failure? I would bet a lot. How useful then, can we say that it is, not because we can understand it, but because we can try? That is useful. This is about the journey. Sometimes the journey is the point.

This is like if math was fascist, this is what would happen. When you start controlling the flow of knowledge like this, it will be bad news all around. And who is to say whether or not something can be understood?Aside from the math nazis.

If we are going to dictate what gets published like this, why bother publishing anything? This feels like a gatekeeping…that’s exactly what it is. Ya’ll getting nervous?

Re: Mathematics in the age of AI

#224

Post by frozenseven »

amoss wrote: post #205
qsera wrote: post #144

Earlier quoted context omitted.

> The "large" is now up to five orders of magnitude larger and "language model" has gone far beyond any simple notion of modeling a singular natural language. Does not matter. It is still an LLM. And I am not the one who is playing word games. You and your idols are, for sake of marketing.

If you place an LLM into a harness, alongside evaluation, feedback and problem decomposition / solution integration - it is still an LLM? There is an LLM acting as a component in a larger system. But that larger system is not an LLM. Calling it an "AI" is indeed an act of marketing as there is no learning / adjustment as we would expect from an intelligence, but calling it an LLM seems to be inaccurate. So what is it…

>Calling it an "AI" is indeed an act of marketing

Again, this is literally the name of the field (and the tech). It's been around longer than you and probably your parents.

Dartmouth workshop (1956):

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

Random dusty undergrad textbook from the early 70s:

https://m.media-amazon.com/images/I/816fxHVJkHL._SL1500_.jpg

>there is no learning...

If human-like continual learning is suddenly the standard, you can just as easily say that terms like machine learning and deep learning are an "act of marketing".

Re: Mathematics in the age of AI

#225

Post by DiscourseFan »

HWR_14 wrote: post #164
noosphr wrote: post #127

Earlier quoted context omitted.

Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.

If a magic oracle tells you p=np, that's useless. How would that change anything?

I would hope the magic oracle would continue to tell me ways in which I can use this knowledge practically.

Re: Mathematics in the age of AI

#226

Post by Scarblac »

a2ff6eeb0 wrote: post #178
Jensson wrote: post #174

Earlier quoted context omitted.

p = np doesn't produce any value though, the stuff you learn solving it might but the fact that they are the same wouldn't be valuable at all.

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.

Re: Mathematics in the age of AI

#227

Post by Scarblac »

Jensson wrote: post #183
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.

Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.

Why would it not be able to find reductions now, but be able to find them just by being told that P=NP is definitely true?

Re: Mathematics in the age of AI

#228

Post by [deleted] »

a2ff6eeb0 wrote: post #193
Jensson wrote: post #183

Earlier quoted context omitted.

Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.

From my understanding, the two are equivalent; if you can reduce an NP problem to a P problem, you've proven P=NP. The rest is application.

[deleted]

Re: Mathematics in the age of AI

#229

Post by shakow »

chongli wrote: post #133
noosphr wrote: post #127

Earlier quoted context omitted.

Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.

A proof by contradiction that p = np is of no use to anyone, given that it wouldn't help you find any polynomial time algorithms for np-hard problems.

I don't think a proof that P = or ≠ NP would give you any polynomial-time algos for arbitrary problems either.

Re: Mathematics in the age of AI

#230

Post by chrisjj »

raincole wrote: post #117
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.

The problem is that there will be far more formally verified proofs than that human mathematicians around the world can read, much less explain. What then? Would the role of mathematicians just become explainers of AI generated proofs?

Then with no way to prove the explanations, anyone can be a "mathematician".
Post reply on HN