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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#841

Post by ex-aws-dude »

marsten wrote: post #827

Math is likely moving into a big science era, much like experimental particle physics and astronomy did before it. Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences. Mathematics will become more like an observational science, with some mathematicians sp…

That’s something I don’t see much discussion about

They spent millions to solve this problem but it’s not like someone is going to pay that for every problem

Won’t progress still be limited financially?

Re: A misalignment of AI in mathematics

#842

Post by thayne »

eru wrote: post #818
robotpepi wrote: post #447

Earlier quoted context omitted.

It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they…

Well, what you are saying that the situation is even better for math than for chess? Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess. But with math, everyone in the world would gain from computers becoming really, really good at it.

But solving math problems is not the same as increasing understanding of math concepts.

Re: A misalignment of AI in mathematics

#843

Post by robotpepi »

eru wrote: post #820
flatline wrote: post #521

Earlier quoted context omitted.

Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be. Tech companies are as much the topic of this post as AI, I think that's the immediacy.

> Does mathematics still have a practical impact without humans in the loop? There's a single answer to that question: yes, math very much has an impact without humans in the loop. Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.

We can't be sure AI will be able to ask the questions of the future. At least right now, AI is not capable of that.

Re: A misalignment of AI in mathematics

#844

Post by boorang »

SavageNoble wrote: post #448
num42 wrote: post #228

Earlier quoted context omitted.

>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI. Title: Terence Tao - SAIR Competitions and the…

I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have. AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanc…

I am curious if we will reach a point where people who are skilled at context engineering/architecture eventually are hired to do jobs completely out of their fields. I think the best pairing would be domain experts + software architects teaming up on AI work in their respective domains.

Re: A misalignment of AI in mathematics

#845

Post by bulder »

afiodorov wrote: post #752
pks016 wrote: post #665

I never expected this many people (on this thread) arguing semantics and what not. I know that not everyone has morality and ethics, but I didn't realize it was this bad. I'm afraid of the ripple effect of the agenda pushed by AI companies will have. In future and even now, they say AI has significantly progressed math and scientific research in general. There is truth to this, but the narrative has done more damage…

I used to be a PhD student more than a decade ago, and I published a paper containing a solution to an open problem. Yet shortly after my first publication I became increasingly disillusioned, because I started to think that within my lifetime AI would reach and eventually surpass my ability to solve such problems—and that we only had a decade or two left. So I started saying that it only made sense to focus on probl…

I think, with all due respect, that your supervisor would be correct to think of that email as an insult to both them and to theoretical mathematicians as a field.

Re: A misalignment of AI in mathematics

#846

Post by NateEag »

jrowen wrote: post #250

This kinda reminds me of the documentary about the top Go master that got beaten by a computer in dramatic fashion and had an existential crisis. Man confronting his own limitations in the realm he previously ruled unchallenged, what a time to be alive. Nobody is going to care that the math isn't being done in the traditional way. The results speak for themselves, this is now a part of the landscape. No amount of han…

> No amount of hand-wringing is going to put the cat back in the bag. Adapt or perish.

We can and have put some ugly, hissing, spitting cats into bags, some of which weren't even in one to begin with:

* Chattel slavery is illegal, and the vast, vast majority of humans agree it's appalling it ever wasn't.

* Food manufacturers in the US are no longer allowed to put highly-dangerous additives to their products and hide the fact.

* Women are allowed to vote.

* Ten-year-old children are no longer being maimed and dying in American factories.

Claiming it can't be done is either fatalism or propaganda for execrable companies whose evil has rarely been matched in the history of capitalist business.

Do I have a clear solution for how to stop the insanity? No, not yet, but that is not a proof there's no way to do it.

You can of course choose how to spend your time in this world, but I don't see the value of either 1) assuming we're screwed and giving up before trying to fight, or 2) shilling for lying assholes like Sam Altman.

Re: A misalignment of AI in mathematics

#847

Post by robotpepi »

eru wrote: post #821
3ash14 wrote: post #445

Earlier quoted context omitted.

Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish. Stockfish does not steal research or scoop researchers. The concentration of computing resources and capital should be examined by the math community.

The trailing edge of AI is catching up fast. There's plenty of open source (and even more open weight) AI models and they are getting better and better. If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?

The problem with your opinions is that you tend to state certain very quesitonable ideas with 100% confidence. Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. We don't even know how much of creative work they are able to do. We cannot make decisions that could destroy decades of progress just because of hype.

Re: A misalignment of AI in mathematics

#848

Post by afiodorov »

bulder wrote: post #845
afiodorov wrote: post #752

Earlier quoted context omitted.

I used to be a PhD student more than a decade ago, and I published a paper containing a solution to an open problem. Yet shortly after my first publication I became increasingly disillusioned, because I started to think that within my lifetime AI would reach and eventually surpass my ability to solve such problems—and that we only had a decade or two left. So I started saying that it only made sense to focus on probl…

I think, with all due respect, that your supervisor would be correct to think of that email as an insult to both them and to theoretical mathematicians as a field.

She was not offended but thought I could benefit from therapy. She didn’t share my opinion - she said it’d not bother her if AI could eventually solve problems for her.

I later realised that my motivation depended heavily on believing I was making a contribution that would otherwise go unmade. The prospect of AI doing that work undermined my motivation, but it needn’t undermine hers. I was trying to explain why I was struggling to continue, though I can see how calling the work “pointless” came across as dismissive.

Re: A misalignment of AI in mathematics

#849

Post by adastra22 »

loglog wrote: post #353
adastra22 wrote: post #306

Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. Alternatively, some claim that mathematics is about understanding these implications. Under the first definition, AI is already, and forevermore will be faster and better at proving theorems. Just like it is better at checkers, chess, and now go. The author asserts that AI proofs are incomprehe…

> Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. That's like saying that programming is about producing valid programs in various programming languages.

It is though. I am not being edgy. Programming is about making valid programs, yes. I literally have no idea what else you might be gesturing towards.

Re: A misalignment of AI in mathematics

#850

Post by adastra22 »

youoy wrote: post #456
adastra22 wrote: post #306

Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. Alternatively, some claim that mathematics is about understanding these implications. Under the first definition, AI is already, and forevermore will be faster and better at proving theorems. Just like it is better at checkers, chess, and now go. The author asserts that AI proofs are incomprehe…

Dont confuse mathematics with the formal system. If you beleive mathematics = formal system then AI is obviously better at it, and we dont need humans. But then who decides why a statement is mor important than another? In the eyes of a formal systems all statements are born equal.

I didn't know some statements in math are more important than others?!

Some are more useful, and that is something you can quantitatively ask.

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