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A misalignment of AI in mathematics

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Re: A misalignment of AI in mathematics

#501

Post by bustermellotron »

BeetleB wrote: post #307
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…

Keep in mind that his critique is very recent, and likely applying to a specific use of AI, as opposed to AI as a whole. If you've been following his Mastodon account, he's been happily using LLMs for math purposes for well over a year.

He posted about using ChatGPT to transcribe PDFs when it first became popular. So he’s been enthusiastic about LLMs for a while.

Re: A misalignment of AI in mathematics

#502

Post by 2snakes »

RGS1811 wrote: post #484
petilon wrote: post #452

> We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are…

It's not about job security. It's about the social and intellectual practice of the discipline. The threat to mathematics isn't that suddenly the profitability of their profession (lol) is going to go away, it's that people are thinking of AI as a replacement for the human social and intellectual practices that constitute the discipline.

Kinda crazy to think that academia functions as a kind of humane reverse centaurism. Theory X (reverse centaur) before Theory Y (centaur) for managing the development of others.

Re: A misalignment of AI in mathematics

#503

Post by taurath »

I find this explanation has a lot of applications for programmers within companies. It’s one thing to get your LLM to give an answer, it’s another to bring a group of people into shared understanding of a domain.

Re: A misalignment of AI in mathematics

#504

Post by avsegal »

againstapples wrote: post #476
avsegal wrote: post #270

Earlier quoted context omitted.

Sure, but who will care? If no one understands it, it may as well have not happened. There's not much incentive to understand or internalize the results generated by AI. A human operator gives it a prompt and it produces some lean proof no one wants to (maybe can) read. Without the community of human mathematicians internalizing the proof, simplifying it, and re-communicating it to others we end up losing the main ou…

Why would we assume AI will learn to solve millennium prize problems but will struggle with the easy part of doing the explaining? I think it’s too easy to predict that models 5 years from now will have the same limitations as the they do now, I would be amazed if this was true, GPT3 was the best model available 5 years ago.

I'm not sure it's just a matter of explaining... If it's just explaining, than sure, that's something they already do well.

The questions I have are:

  * is the structure of the generated proof even compressible/elegant to humans in a way that lends itself to being understood?
  * is it possible to transform the proofs to ones that are elegant without redoing all the work?
  * are there incentives to do any of this at scale?
It's possible that a headline grabbing proof of a Millennium Prize problem generates enough incentive for people to simplify and gain understanding from it, but we run into problems when AI becomes the dominant approach for all of math. Although, maybe this is self-limiting? I guess it's possible we just ignore a bunch of AI generated proofs and only keep the ones people find comprehensible in a useful way.

You can always hypothesize that at some point in the future (maybe 5 years? maybe later?) the models will be indistinguishable from humans and there will not be any functional difference at all. It's possible, but we're not there yet. And, as they say, past performance does not guarantee future results. Many technologies plateau at some hard ceiling of performance. Moore's law has had an unusually long run, but it's not a universal rule.

Re: A misalignment of AI in mathematics

#505

Post by kansface »

doubtfuluser wrote: post #267

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…

Some people are just out there doing automated math proofs for reasons. If you want understanding, value, and edification, that is on you, not them.

Re: A misalignment of AI in mathematics

#506

Post by Animats »

feoren wrote: post #465
Animats wrote: post #358

There's an unpopular branch of mathematics which does not have infinities - finiteism.[1] The constructive version of finitism takes the position that there is no such thing as infinity, just arbitrarily large upper bounds. You can have theorems about arbitrarily large numbers, but you never get 1 + 1/2 + 1/4 + 1/8 ... = 2 The benefit of finitism is that it escapes undecidability. The big objection to finiteism is th…

> 1 + 1/2 + 1/4 + 1/8 ... = 2 It's not necessarily clear that this statement requires infinity, if you're willing to treat "... =" as a shorthand. You might prefer something like "1 + 1/2 + 1/4 + 1/8 ... -> 2" if it's more clear, where "->" means something like "gets as close as you like without ever getting further away than that", but really the "=" sign is already overloaded in all sorts of subtly different ways a…

See this introduction to limits.[1]

If you allow infinite recursion, you soon get to Godel and undecidable problems. Finite deterministic systems are decidable, because you can in principle enumerate all the states. The halting problem is decidable for deterministic systems with finite memory. It may be exponentially hard for some programs, but that's quite different from being undecidable.

(This is too long a subject to discuss here, and I haven't worked on constructive mathematics in many years. It's more practical than it was decades ago. You need power tools, which we now have.)

[1] https://www.mathsisfun.com/calculus/limits.html

Re: A misalignment of AI in mathematics

#507

Post by [deleted] »

datakan wrote: post #65

Everyones outraged all the time. It doesn't mean anything anymore. It's that meme from years ago about the red ants and the black ants living in a box peacefully until someone shakes the box and they start trying to kill each other. They go after each other and not the one shaking the box. OpenAI/Anthropic are shaking the box.

[deleted]

Re: A misalignment of AI in mathematics

#508

Post by VulgarExigency »

Quekid5 wrote: post #442
ArcHound wrote: post #430

Earlier quoted context omitted.

It's not that easy. Playing stockfish is like playing tennis against the wall (for untitled players at least). Even if you don't blunder anything, you'll still find yourself in a worse position without any clue as of what went wrong and why. Whereas when playing humans, they can usually explain their approach and when they noticed errors in your play.

> Playing stockfish is like playing tennis against the wall (for untitled players at least). It's the same for Magnus Carlsen. Even with Queen odds, Stockfish is literally unbeatable for the best players in the world. It's just too strong at evaluating all kinds of random tangent moves (and ensuing positional advantage) which no human player can possibly pay attention due to the time required. Stockfish vs any human…

Well, that's actually not true at all. Stockfish is not a very good odds player and at queen odds is easily beatable even by bad players like me. It will just trade down into more trivial and easier to win positions that it perceives as "less bad", since everything is super-losing anyway when you start down a queen.

Leela odds networks, on the other hand, are an entirely different beast. I cannot beat Leela queen odds, much less rook or minor piece odds, and even GMs struggle against Leela knight odds.

Without odds though, yeah, Stockfish is just incomprehensibly strong by human standards. All top chess engines are, but Stockfish moreso.

Re: A misalignment of AI in mathematics

#509

Post by cindyllm »

jrflo wrote: post #173
tmhn2 wrote: post #130

Earlier quoted context omitted.

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system…

I don't think it really attacks human understanding though. You can still read and understand an AI written proof. If another person comes up with a solution to a problem, you can read their methods and understand it. It doesn't matter if a human came up with that or not. It's really only attacking the "generating new ideas" part.

[dead]

Re: A misalignment of AI in mathematics

#510

Post by 2snakes »

feoren wrote: post #474
jrowen wrote: post #121

Earlier quoted context omitted.

Everyones outraged all the time. It doesn't mean anything anymore. Everything is sensationalized, every super niche happenstance is sold as earth-shattering drama, the outrage arms race is so tiresome.

Yeah, I'm so tired of people moaning about how huge swaths of Earth's ecosystem are being destroyed and rendered uninhabitable to humans, how secret police are murdering Americans in the streets, how the president is a child rapist who openly accepts bribes, how unfettered capitalism is destroying tens of millions of lives, how the United States is rapidly falling into facism, how civil rights are being systematicall…

Hyperpolitics is one term for this. There was an article in NYT about the concept. Attention economy for political info causing burnout possibly same phenomenon as Gen Alpha surrealism and viral adoption, but no institutionalization to preserve the lessons.
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