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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#721

Post by ndriscoll »

SpicyLemonZest wrote: post #686
ndriscoll wrote: post #679

Earlier quoted context omitted.

One of the awesome things about LLMs is they make it quick and easy to make PoCs, so yes. Proving that an approach will work before spending a bunch of deep design effort is absolutely valuable. Your exact scenario is something I've literally done: give a half-completed design to a team member and asked them to vibecode a PoC to prove the approach will work and figure out some of the details, explore scaling and fail…

It's valuable for you , the person who's going to spend a bunch of deep design effort, to make POCs. Is it valuable for someone else to drive by, dump some POCs on your lap, and then leave you to do the deep design effort while they run away to study AI? If that person then runs around telling people that they're the real author of your project, because they generated the original POC, would you consider that an accu…

Your analogy is far enough away from the way that the real world works that I'm not sure that I can really even strain my experiences to fit within it. Sure, I guess that would be annoying?

But mathematicians define their field. They're smart people. They're capable of recognizing when someone just did a vibecoded throwaway PoC and when someone has a well structured proof. Actually even before LLMs they'd publish new, clearer or more elegant proofs of old results. They can say that inscrutable proofs are exactly as valuable as they are, and that the first explanation people can actually understand carries its own prestige.

Re: A misalignment of AI in mathematics

#722

Post by oliculipolicula »

fc417fc802 wrote: post #705
octoberfranklin wrote: post #666

Earlier quoted context omitted.

This story's comments are heavily astroturfed. Just compare with the comments on https://news.ycombinator.com/item?id=49639408

I actually feel like it's the other way around. The online discourse over the past ~day or so has seemed unusually irrational to me for a technical audience. Commenters making emotionally charged claims of wrongdoing that appear inconsistent with the published claims without justification of the discrepancies. Granted you might well doubt openai's version of events but there's a general expectation of clear evidence…

I identify as neither mathematician nor "maker of things people want" (coder, hacker, engineer). But having friends who identify as those kinds of professionals, let me make some observations.

To use a metaanalogy from chess (once again), mathematicians play the opening game, and builders play the end game. AI is sort of a middleman connecting understanding to applications.

I think there's a Technical argument to be made that openAI is a threat to the game itself. For example, could it have produced the navier-stokes counterexample without human inputs? since it used the much gossiped research strategy "C" and "D", you can't say that Son of Astra was magicking an unknown unknown from nothing (sorry to cue Rumsfeld)

Subpar PR engine of the OpenAI leadership might kill the pipeline of inputs that they won't admit they still need in this dreamtime before "recursive self-improvement". You can call that emotional. Personally I would accuse mathematicians of "preferring local models that believe in the usefulness of individual contributors, and the uselessness of generalist managers (ie the prompt writers at oAI)"

Big man tlb likes to say that science might be dead but engineering is just getting started. Navier-Stokes is the hammer of the nail in the science coffin. It kills science by killing the prestige of science. The engineers have to imagine that it's likely they will now get all their design ideas from the hypothetical future datacenters.

Re: A misalignment of AI in mathematics

#724

Post by dakolli »

tmhn2 wrote: post #200

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

Did you even read the blog post?

Re: A misalignment of AI in mathematics

#725

Post by gdsimoes »

ThalesX wrote: post #245
boron1006 wrote: post #217

Earlier quoted context omitted.

> Nothing is stopping these folks from continuing to study the problems My understanding is they are? And literally everything in this world is based around incentives. If you say “well you can continue to work on understanding, but your kids are going to starve” that’s not nothing.

It boggles my mind. Why cure cancer? The cancer researchers will be out of a job and their kids are going to starve!

Why not cure cancer and take care of the researchers’ kids?

Re: A misalignment of AI in mathematics

#726

Post by SavageNoble »

breezybottom wrote: post #717
SavageNoble wrote: post #448

Earlier quoted context omitted.

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…

How could you possibly know if it has potential or not? Sounds like AI psychosis setting in.

Because every test I run with it is telling me so? The great thing about math is it can be externally validated.

Re: A misalignment of AI in mathematics

#727

Post by Timwi »

sweezyjeezy wrote: post #615
fph wrote: post #539

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. I think a better comparison is: mathematics just becomes like mining bitcoins.

I think you might have to explain that comparison a bit more to be honest. How are math proofs like bitcoins? A bitcoin has a pre-defined value, a math conjecture / proof is a bit more complicated.

A Bitcoin does not have any pre-defined value. The value of Bitcoin keeps fluctuating, and historically has risen dramatically from its initial value of 0. If this weren't the case, there would be no investment/speculation in Bitcoin because there would be no potential for any ROI.

In reality, the value of Bitcoin is determined by humans (even if indirectly, not by planning), and I think the OP’s point may have been that maths proofs can be regarded similarly. No intrinsic value, just what humans find in it.

Re: A misalignment of AI in mathematics

#728

Post by nickysielicki »

stymaar wrote: post #69
andriy_koval wrote: post #29

Earlier quoted context omitted.

Its by choice. Mathematicians still can use AI to "achieve the primary goal of conceptual understanding and insight"

At the individual level any mathematicians can, but the social group of “mathematicians” will not unless drastic social changes are made, because that's not how the system works today. Drastic social changes usually take decades, and funerals, to occur, so the reasonable hypothesis is that it's not going to change fast enough.

Mathematics belongs to all of us. If the social group collectively known as mathematicians gets depression, I don’t really give a hoot. Five years of guided computer-aided mathematics could produce advancements in physics that materially improve the life of billions of people and/or solve global warming permanently through cheap clean energy.

This moment in time is a good litmus test within these ai labs of whether someone claims to be an effective altruist because it’s trendy or whether they’ve really thought it through, because this is a pretty clear place where there’s a lot of social pressure to acquiesce and let the mathematicians have their norms for a few more years but the thing that is clearly best for humanity is to push forward violently in mathematics and physical sciences and leave them in the dust. The feelings of people who hold a fields medal are not more important than the wellbeing of the rest of the planet.

Re: A misalignment of AI in mathematics

#729

Post by evenhash »

amelius wrote: post #525
zahlman wrote: post #517

Earlier quoted context omitted.

> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize,…

Not if it's lean-verified.

"Lean-verified" is not some magical incantation that makes a supposed proof irrefutable. Even disregarding potential bugs in the kernel as others have said.

Say that AI gives you a Lean proof and says it proves Theorem X. It could just as easily give you the same proof and say it proves (not X). How would you know the difference?

Nothing can really be considered proven unless a human expert can read the Lean proof and determine that (X as defined in the proof) corresponds to X.

It's possible people will just start taking AI at its word. Maybe AI says "Here is a Lean proof of X" and we all just shrug and go "Okay, X is proven." But that's not how it works right now for human mathematicians, let alone AI.*

Re: A misalignment of AI in mathematics

#730

Post by krackers »

moralestapia wrote: post #591
esafak wrote: post #577

Earlier quoted context omitted.

Which mathematician's take on AI do you like? Do you think mathematics should no longer be an intellectual pursuit?

I haven't heard about his take on AI (sorry about derailing a bit), but generally I like Robert Ghrist's approach to life and math. I'll check out if he has said something about it. Interesting guy.

https://x.com/prof_g/status/2098529243831632036#m
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