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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#341

Post by ifethereal »

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!

Maybe an analogy of "why not solve all medical problems at once" is closer.

We absolutely want to, of course. But you extinguish an industry and the systems of training that supply it. It's hard to know if letting it go that way is right.

Re: A misalignment of AI in mathematics

#342

Post by philipwhiuk »

Strilanc wrote: post #236

This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal . So this letter's message will fall on deaf ears. Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10…

The point of mathematics is human understanding though.

Re: A misalignment of AI in mathematics

#343

Post by magicalist »

mna_ wrote: post #299
318274 wrote: post #277

Earlier quoted context omitted.

Chess is kept afloat by a couple of billionaires like Sinquefield, MBS and the guy who sponsors freestyle (Fisher random) chess. Carlsen is bored by studying engine lines. The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content. I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now.

Chess is kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on.

I mean, this is the problem with analogies and trying to use them to prove things, right? People working through problems from an analysis book with their friend (or an LLM) is not the same as research mathematics. People playing in a chess club is not the same as what makes for a good chess tournament. Lumping everything together is just making this branch of the conversation less relevant.

Re: A misalignment of AI in mathematics

#345

Post by debatem1 »

mna_ wrote: post #299
318274 wrote: post #277

Earlier quoted context omitted.

Chess is kept afloat by a couple of billionaires like Sinquefield, MBS and the guy who sponsors freestyle (Fisher random) chess. Carlsen is bored by studying engine lines. The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content. I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now.

Chess is kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on.

Also, you learn to be a better chess player by... playing better players. The widespread availability of chess engines has made flawless opponents available to every player.

If your goals are understanding the game, self improvement, building thinking skills-- this is the best chess has ever been. It's only if your goal is to beat every opponent you can find that chess is in a bad place.

Re: A misalignment of AI in mathematics

#347

Post by ksoped »

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…

People aren't ready to discuss AI assisted imagery as art yet. Most discussions lack the nuance that Baudelaire lacks in that critique, which deals with the nature of art and the importance of human intention and input.

Re: A misalignment of AI in mathematics

#349

Post by LegionMammal978 »

pred_ wrote: post #308
jrflo wrote: post #276

Earlier quoted context omitted.

That doesn't seem to be true. The OpenAI NS paper was 166 pages. Wiles-Taylor proof of Fermat's last theorem is 129 pages. The length is not unprecedented for a difficult unsolved problem. To be honest, I feel like the difficulty of reading AI proofs is due to the fact that we are on the verge of being beyond human comprehension. This is a demonstrable fact as no human has figured this out despite the problem being o…

> To be honest, I feel like the difficulty of reading AI proofs is due to the fact that we are on the verge of being beyond human comprehension. I can see where that's coming from, but I really don't think it's the case. Even with Astra, the proofs you get are just off in a way that doesn't signal superhuman comprehension. As 9question1 says, a common theme is that they dwell on insignificant steps. Another one is th…

Yeah, that mirrors what I've seen throwing some of the leading models at a set-theory problem that's stumped me (https://mathoverflow.net/q/511601): in this case, the problem does not easily yield to the standard tools, but the LLMs do not recognize it as a major open problem they should give up on. So they seriously try it, but typically end up in a loop of inventing certain classes of simple solution or counterexample attempts, defeating them, and trumpeting each one as a major result, each time inventing some new terminology.

It's definitely quite curious that the AI labs are able to push these results through seemingly with pure brute force. Perhaps it's largely a function of how many monkeys you have attempting various constructions on top of the known results and strategies the models have memorized.

Re: A misalignment of AI in mathematics

#350

Post by whatever1 »

At some point we will lose track of all the ai discoveries that are worth remembering.

Academia with the publication system had a way of retrieving old discoveries and build upon them.

If my LLM session found something groundbreaking in between the billion tokens it produced, how would you ever know?

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