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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#921

Post by GPerson »

40four wrote: post #883
GPerson wrote: post #709

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…

I don’t see why the two are mutually exclusive to be honest. I’m not a mathematician, but I’m a software engineer and whether I like it or not, AI has changed my field dramatically forever. I understand the distaste for the way AI might be affecting the field of mathematics, but the genie is out of the bottle, and it will never be the same. It just took a little longer for it to hit the math community. Software engin…

Mathematicians are not idiots! They’ve been living on the same planet as you for the last few years and everyone in any thinking profession has been debating and coming to terms with reality over the same period. People who aren’t involved in mathematics might see a big headline and come to the conclusion that mathematicians haven’t seen this coming, but that’s a completely ignorant position.

Re: A misalignment of AI in mathematics

#922

Post by GPerson »

looofooo0 wrote: post #886
40four wrote: post #883

Earlier quoted context omitted.

I don’t see why the two are mutually exclusive to be honest. I’m not a mathematician, but I’m a software engineer and whether I like it or not, AI has changed my field dramatically forever. I understand the distaste for the way AI might be affecting the field of mathematics, but the genie is out of the bottle, and it will never be the same. It just took a little longer for it to hit the math community. Software engin…

Soon AI mathematics will be 10x or 100x or 1000x more productive than humans in the proofing theorems business. Mathematics of old style is dead, they should develop ideas how to deal with that as a math community.

> But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal.

Re: A misalignment of AI in mathematics

#923

Post by dgreensp »

GPerson wrote: post #709
tmhn2 wrote: post #198

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…

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 letter explain that the problem is AI proofs are inscrutable and useless, but the reality is using computers to brute-force things has long been part of proofs in one way or another, and AI proofs range in legibility up to 100% (like pointing out a proof exists in a long-lost paper, or writing something that is basically correct and just needs a human reviewer to fix it up). People are probably defending the declaration inaccurately, but I think that’s because the real argument or arguments are unclear.

Is it that students won’t learn math if there’s ChatGPT? That could be discussed.

To a non-mathematician (MIT physics and CS ‘06), the letter sounds like, “We have a fun job. Sometimes there are no practical applications of the work, so it’s just kind of like a sport, er I mean science. If someone solves a problem that has stumped mathematicians for decades or centuries, we worship them as a great mathematician. It’s a status thing. So we don’t like some guy with a computer coming along and solving our problems. The way things unfold with all the ideas coming from humans, over time, maybe it’s slower, but it’s nice.”

I don’t think anyone can really stop someone from using a computer capable of solving unsolved problems to solve unsolved problems, and there are always going to be mathematicians who DO think it’s fun to try to figure out what a computer is doing (if the computer isn’t already explaining it in English, which it generally can), and make progress that way, and it obviously will lead to mathematical advances in human understanding, from my point of view. So the whole thing is a non-issue that no one can do anything about anyway.

Re: A misalignment of AI in mathematics

#924

Post by jacquesm »

eru wrote: post #753
robotpepi wrote: post #444

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 with math, everyone in the world would gain from computers becoming really, really good at it.

I'm not convinced of that.

It is one possible outcome but there are also other possible outcomes.

Re: A misalignment of AI in mathematics

#925

Post by cagz »

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".

Re: A misalignment of AI in mathematics

#926

Post by lukeplato »

Many comments seem to be misinterpreting this, but all this seems to be suggesting is that the AI companies should not be treating mathematical milestones as benchmark targets but need to release the cumulative findings in a human interpretable and digestible way that enriches and develops the field. See Thurston quote on Tao's banner:

> We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.

Re: A misalignment of AI in mathematics

#928

Post by 8n4vidtmkvmk »

SavageNoble wrote: post #678
breezybottom wrote: post #670

Earlier quoted context omitted.

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.

Yeah, but you're missing a gut intuition if something is off.

I wrote a fancy polygon decomposition algorithm in university (pre-AI) which my professor didn't seem very impressed by because it was missing some sort of mathematical rigor. Yet everything I threw at it worked! Even he couldn't find a counter example.

It took a while for me to find some failing cases but it turned out they did exist.

But hey, maybe all I was missing is an AI-written lean proof.

Re: A misalignment of AI in mathematics

#929

Post by HDThoreaun »

GPerson wrote: post #922
looofooo0 wrote: post #886

Earlier quoted context omitted.

Soon AI mathematics will be 10x or 100x or 1000x more productive than humans in the proofing theorems business. Mathematics of old style is dead, they should develop ideas how to deal with that as a math community.

> But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal.

No one is paying mathematicians to develop a conceptual understanding. If the signal for who is “winning” math in academia disappears mathematicians will have a big problem

Re: A misalignment of AI in mathematics

#930

Post by 8n4vidtmkvmk »

redox99 wrote: post #702
ekidd wrote: post #673

Earlier quoted context omitted.

> Those who think it's me or the machine will fail. > Those who realize how much you can accelerate your research with the help of AI will succeed. This is only true up until a point. If I treat a mid-sized model (say, Qwen3.8 Flash Next) like a pair programmer, then yes, it accelerates my work. But I can already see the next stage with Fable: If I give it a couple of paragraphs of spec and $50, then I can just leave…

Of course you're not going to get rich with the kind of software that LLMs can one shot these days. But that kind of software like to-do lists or basic CRUD have been saturated for over a decade, way before LLMs. People overestimate how much you can one shot, yeah a good prompt can get you 90% there but that 10% remaining often takes months of extra work. Software has always progressed this way, lots of devs back the…

I hope it remains this way then.

I am finding it still takes awhile to get my apps to a happy place with AI. Not because the AI is bad but because i have to sit with it for awhile. Figure out what's working, what isn't, what's missing, what turned out to be kind of useless and in the way.

As a different article said, we still need taste.

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