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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#641

Post by GMoromisato »

david-gpu wrote: post #141

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…

I think there's a difference between "photography will change art--we need to be ready" and "photography will change art, therefore stop photography."

There is no doubt that AI has changed the practice of mathematics, just as it has changed the practice of software engineering (and will soon change almost every intellectual job).

Trying to deal with change by saying, "please stop the change" is foolish, IMHO. Mathematicians need to redesign the discipline with AI in mind. But I get that it's easy for me to say that and hard to actually do.

Re: A misalignment of AI in mathematics

#642

Post by skew-aberration »

I'm not convinced this is an alignment or technology problem.

If my boss vibe coded an app for the customer and then assigned me to get it working, it would be impossible to maintain. If he gave me enough AI tokens to vibe code the MVP myself and to my design, I wouldn't mind.

I think the same issue is at play here in maths. OpenAI owns the model and they can direct it as they please. They chose to spend lots of money getting a quick result, instead of developing mathematical infrastructure for the next generation of problems. The managers are in charge rather than the experts.

Re: A misalignment of AI in mathematics

#643

Post by _superposition_ »

genxy wrote: post #425
alkyon wrote: post #366

Earlier quoted context omitted.

It's still an optimistic scenario. Artificial superintelligence may develop hypermathematics of a kind that never will be accesible to human mind, enhanced or not. One can't teach geometry to ants even if you put them on a Moebius strip. It would be more like Lem's novel where it completely disappears from the human horizon: https://en.wikipedia.org/wiki/Golem_XIV

Which is why if humanity had empathy, it would be working on how to make smarter ants, so that they can learn more advanced geometry.

It's quite possible ants understand a geometry more advanced than our own.

Re: A misalignment of AI in mathematics

#644

Post by cyclopeanutopia »

scottyah wrote: post #129
ambicapter wrote: post #93

Earlier quoted context omitted.

What are the token reset shenanigans?

From what I see, a lot of people were angry at Anthropic's limits with the subscription plan. OpenAI had some issue I can't remember, and they reset people's token usage (for the session or weekly limits). I think they got a lot of good press, now OpenAI seems to just do it at random when they want a PR boost. It makes scheduling your worklife a bit difficult if you are limited by that. There are a lot of us who just…

> There are a lot of us who just use the AI on projects until the session limit hits, and wait for the usage to reset.

Do you mean that you can't continue on your own until the reset?

Re: A misalignment of AI in mathematics

#645

Post by kzz102 »

embedding-shape wrote: post #598
kzz102 wrote: post #590

Earlier quoted context omitted.

The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem.

> closing research directions left and right Why would research be closed in one direction? Even if AI or human says "Tried that, didn't work" or whatever, someone (or something I suppose) might very well retry it in the future, if nothing else to reproduce it didn't work, in theory at least.

AI tends to take nearly finished research directions and push it to the conclusion in one step. If deployed massively, it will pluck all the low hanging fruits causing a drought of near term promising research project. Because people who start promising research directions do not get to see it finish, over the long term fewer people will start new directions, causing the field to slowly whither.

Re: A misalignment of AI in mathematics

#646

Post by seizethecheese »

geraneum wrote: post #592
seizethecheese wrote: post #471

I don’t think they make a coherent argument here? This seems to hinge on some argument that because AI doesn’t properly explain its breakthroughs, therefore the breakthroughs are less fertile for human understanding? This makes no sense. Why wouldn’t these under-explained breakthroughs be extremely fertile soil for explanations? Imagine time traveling back in time and offering Leibniz a packet of proofs from the inte…

> Would he say no? And that’s the issue the article is trying to explain.

My thought experiment was trying to extract the issue from the zeitgeist around AI, so not really

Re: A misalignment of AI in mathematics

#647

Post by _superposition_ »

tmhn2 wrote: post #605
onetimeusename wrote: post #428

Earlier quoted context omitted.

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. I don't like nuance here…

I agree entirely with what you're saying, right up until your final question: > why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? I think you answered this yourself earlier: > I think progress is really measured by what humans are able to do and understand People want to make this progress. Therefore people will "grind Everes…

That grind is emotional. And it's something AI will never have. The desire to solve a problem.

Re: A misalignment of AI in mathematics

#648

Post by seizethecheese »

atomicthumbs wrote: post #602
seizethecheese wrote: post #471

I don’t think they make a coherent argument here? This seems to hinge on some argument that because AI doesn’t properly explain its breakthroughs, therefore the breakthroughs are less fertile for human understanding? This makes no sense. Why wouldn’t these under-explained breakthroughs be extremely fertile soil for explanations? Imagine time traveling back in time and offering Leibniz a packet of proofs from the inte…

Because the fertile soil comes from the process of reaching the breakthrough. This should be fairly obvious.

I don’t think it’s obvious. In my Leibniz example, mathematical understanding surely would have accelerated right?

Re: A misalignment of AI in mathematics

#649

Post by coderenegade »

matco11 wrote: post #401
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…

I get excited at the idea of a world in which advanced mathematical problems (and their solutions) become much more accessible to a much greater number of people. As a result, making mathematics much more loved at a societal level. Imagine a world where these most complex mathematical problems are not accessible to a few hundred people, but a few hundred thousands people. ...Those original few hundred gifted mathemat…

This is the hope, but I suspect the reality is that we see an ever widening gap between the fortunate and the unfortunate. We're looking at the automation and commodification of all knowledge, and the best models will be kept locked behind closed doors so that they can't be stolen. And, of course, "for our own protection".

Re: A misalignment of AI in mathematics

#650

Post by paulhebert »

phoghed wrote: post #634
paulhebert wrote: post #631

Earlier quoted context omitted.

Sorry I’m not entirely sure what you’re trying to say

How good were you at those “A is to B as C is to D” SAT questions?

No need to be rude. I didn’t want to misinterpret when responding.

I can see how what is happening to mathematicians is similar to what is happening to coding.

I’m not sure what your broader point is? Mathematicians shouldn’t be upset? Coders should? Something else?

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