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A misalignment of AI in mathematics

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Re: A misalignment of AI in mathematics

#931

Post by jrowen »

NateEag wrote: post #759
jrowen wrote: post #248

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…

Thank you for this response, and I will clarify. I would roughly lump all of those into "social issues," whereas I would put "using AI to advance math" under "technological progress." That's why one article likened it to Socrates's fear of the written word. In broad strokes, I would say that once a technology becomes available, no amount of social pressure will stop it from proliferating.

If there's a distinction being made between "using AI for math" and "the particular methods being employed by OpenAI", I think that's splitting hairs. The core of the issue is that math is being done outside of people's heads by a different thinking system and they're worried about the implications.

If you look at something like the EPA (or the FDA as you mention), it is true that certain uses and side-effects of technology have been identified to be detrimental to society and have been restricted, but this letter doesn't seem to be in that league, it really seems like sour grapes to me. Dumping toxic chemicals into the water table is one thing, saying "we don't think people will learn from these methods in the same way that they traditionally have" doesn't hold as much water to me.

Re: A misalignment of AI in mathematics

#932

Post by YeGoblynQueenne »

grey-area wrote: post #822
YeGoblynQueenne wrote: post #820

Earlier quoted context omitted.

>> I’m no big AI cheerleader, but why don’t you try these models to see what they offer - they might suggest some things you haven’t thought of, or save you some time in your research. One reason not to try is to create an air gap between the OP's ideas and the data that future models can train on. We saw that the mathematicians who trusted OpenAI and Anthropic with their preliminary work found the rug pulled out of…

Unless you’re very weak-willed, I wouldn’t worry about independence. LLMs make mistakes all the time, they are nothing like an all-knowing oracle nor are they going to replace humans despite the absurd fantasies of LLM fans and those with a vested interest. Plagiarism is an interesting point, though honestly I think it would be fairly easy to work out who had published similar research if the LLM gives you an idea -…

Thanks. Regarding plagiarism, I agree that it is possible to check; I don't know how easy it is. But I do note that the mathematicians who complained that their work was plagiarised by AI did not seem to realise that they, themselves, were using a plagiarism machine and were instead quite comfortable admitting that, yeah, we worked our Euler result out together with Sol, Claude and the gang.

To clarify, they do attribute the original ideas to Cordoba and Martinez-Zoroa, but they don't seem to acknowledge that their result which they say was achieved "with a great deal of help from LLMs" is also derivative of others' work.

Independence is about avoiding making errors because of the influence of error-prone models. I guess I didn't explain it well.

Re: A misalignment of AI in mathematics

#933

Post by dsjoerg »

sweezyjeezy wrote: post #597
senfiaj wrote: post #272

Earlier quoted context omitted.

Well, chess is a sport where humans are supposed to compete. But math, programming, science are mostly not, and AI might affect economy, careers, etc.

As a chess fan, 100% this. We have known for the last ~15 years who the best human chess player is, and that he will lose against stockfish on his phone. But chess survives because of the human characters involved, the rivalries and dramas, watching two people trying to overcome each other under insane pressure, and sometimes coming up with something astonishing. In short - it's a sport. There is no equivalent in mat…

Uh I was literally on math team

Re: A misalignment of AI in mathematics

#934

Post by kaffekaka »

erichocean wrote: post #926
cagz wrote: post #911

I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".

They want the AI labs to stop solving "important" math problems so that humans can do it, on the theory that when AI solves "important" math problems, it robs humans of the opportunity to gain new insights into those problems. Total horse shit, but that's the essence of it.

The issue is that now that Navier-Stokes is "solved", the amount of resources put into researching it will be reduced, meaning that the insights and knowledge that would have come out of even failed attempts will never be.

An "unsolved problem" as a beacon to strive towards, gaining understanding along the way. With the beacon dead, noone will strive.

Re: A misalignment of AI in mathematics

#935

Post by brap »

I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but:

Perhaps you are misaligned.

Who decided the goal of math must be human insight?

First off, some mathematical truths might simply be far beyond our biological comprehension.

Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives.

Isn't this why we have math in the first place? To solve our real problems? Over time it morphed into this pursuit of pure theoretical insight, probably out of necessity at the time, but is it still necessary?

Re: A misalignment of AI in mathematics

#937

Post by kaffekaka »

nullbio wrote: post #706
doubtfuluser wrote: post #265

Im surprised about the sentiment in this discussion. I totally see the problem Terence is describing. We are loosing a lot in understanding and focus if it continues like that. The solution found for Navier Stokes doesn’t have much „real value“ - but what almost always happened in the past when people worked on the difficult problems, these sparked new ideas / new theorems that broadened our knowledge. Think back at…

His complaint is a very weak argument. If the complaint is about AI just giving answers and not good understanding around them, or frameworks that lead to more solutions from them, then that means there is a gap that can be filled by human mathematicians. So all the AI has done has actually made mathematicians lives easier and provided them with an opportunity to fill that gap. They should be using it to do that, ins…

You have a point, but I think a concern is that the environment in which to fill this gap is threatened since the unsolved problems have functioned as a guiding lighthouse and measure of progress. Frankly: will someone pay for mathematical research to understand things we already have proofs for?

Re: A misalignment of AI in mathematics

#938

Post by lying4fun »

mdnahas wrote: post #862

As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”. I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader. What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these aut…

different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a product that mathematicians are making?

what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. if someone wants to use it, they are free to do so, or to write a blog article how it can be used by non experts. mathematicians do that themselves sometimes, but it’s not their job. myb there should be more incentives for them to do more of such work

i keep seeing this myth that mathematics has some purpose to do this or that, but somehow its purpose is least known to mathematicians, everyone else seems to know better

Re: A misalignment of AI in mathematics

#939

Post by kaffekaka »

brap wrote: post #935

I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but: Perhaps you are misaligned. Who decided the goal of math must be human insight? First off, some mathematical truths might simply be far beyond our biological comprehension. Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to ac…

> Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives.

This is just the problem with the Navier-Stokes solution. We now (supposedly) know the truthiness of the statement, but we have no more understanding of why or how it applies to our quality of life. This is exactly the issue Tao is pointing at.

Re: A misalignment of AI in mathematics

#940

Post by pred_ »

dgreensp wrote: post #910
GPerson wrote: post #703

Earlier quoted context omitted.

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

The declaration literally opens by writing that AI companies (or really anybody) saying, “Hey, let’s see if this powerful reasoning engine can solve an open problem in mathematics” is “detrimental” to the “science” of mathematics. Full stop. So I don’t think it’s being misrepresented. If it’s a science, why isn’t progress good in itself? You can’t have it both ways. The online comments I’ve read that side with the le…

> The declaration literally opens by writing that AI companies (or really anybody) saying, “Hey, let’s see if this powerful reasoning engine can solve an open problem in mathematics” is “detrimental” to the “science” of mathematics. Full stop.

So let's just quickly agree that the actual quote is “However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community.” And that in this, "as a benchmark" is load-bearing.

We wouldn't see nearly the same amount of contempt from researchers had OpenAI picked a research-friendly approach.

What they did: Hear a rumour about the problem being solved by other researchers, then rush to scoop them (unethical), then, when they actually go talk to them, they try to oust an author (also unethical), and when they finally decide to share their own work, do so in the least useful way possible.

What they could have done: Upon hearing the rumours, connect with the researcher in question and propose that they join efforts instead; set up a joint project to test if the machines are useful in any way, and if that's not appreciated, back down again. And instead of dumping only an undigested paper* and a Lean proof, do the digestion prior to publishing anything (as Buckmaster was in the process of doing). If their own lack of competences was keeping them from digesting it, then again, reach out to the researchers to understand if anyone would be willing to do so.

In the second of those two worlds, we wouldn't be seeing nearly the amount of outrage that we are seeing right now.

*: Here, “digestion” is the process of turning an AI slop paper into something humans can read. LLMs can indeed sometimes (if much more rarely than marketing material from the large LLM companies will suggest) produce correct proofs, but they are often written in bizarre ways – they'll use lingo that doesn't exist, seem overly pretentious, dwell on extremely easy steps while glossing over the hard ones. Currently, a real researcher will take that output and transform it into something that others can understand, use, and build upon. This is not so different from what happens when using it to write software, although as someone who does both, I will say that the amount of digestion needed for proofs tends to be orders of magnitudes larger than for code. This meme is quite accurate: https://mathstodon.xyz/@tao/117068266071803252

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