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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#441

Post by Bourget »

djierardi wrote: post #393
gwd wrote: post #243

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…

But computers have destroyed chess as a "sport". Nobody will sit to watch two chess programs compete, or analyze their tactics. Kinda like how now, anybody can construct a "game" over the weekend or a new song or a slop video. The value of each of these decreases to 0 as the slop overwhelms.

>Nobody will sit to watch two chess programs compete, or analyze their tactics.

I know nothing about chess yet I dare say that I'd doubt this. Surely chess enthusiasts would be interested in analyzing how a superior chess program came out victorious, no?

Re: A misalignment of AI in mathematics

#442

Post by Quekid5 »

ArcHound wrote: post #430
debatem1 wrote: post #345

Earlier quoted context omitted.

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.

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 is like Carlsen vs other players by about 3-5 orders of magnitude[0]. It's that stark.

[0] A wild pun appears.

EDIT: To avoid having to respond to each responder, fair comments about Queen odds. Maybe I was thinking Rook odds? Also, I kinda lumped Stockfish in with all the other engines, but I realize there are other engines with different properties ofc.

Re: A misalignment of AI in mathematics

#443

Post by cevi »

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…

Mochizuki's claimed proof of the abc conjecture was extremely unusual for the reason that nobody was able to extract a single useful idea from the argument. I was starting grad school when it came out, and my immediate visceral response was "if this is what number theory is going to look like in the future, then I will leave mathematics."

The current wave of AI slop mathematics might end up driving the next generation of mathematicians away from the subject for the same reason that Mochizuki would have convinced me to quit if his proof had been accepted by the community. Luckily, my professors had the taste to immediately recognize that it was garbage.

Re: A misalignment of AI in mathematics

#444

Post by derac »

djierardi wrote: post #393
gwd wrote: post #243

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…

But computers have destroyed chess as a "sport". Nobody will sit to watch two chess programs compete, or analyze their tactics. Kinda like how now, anybody can construct a "game" over the weekend or a new song or a slop video. The value of each of these decreases to 0 as the slop overwhelms.

erm actually, chess tournaments rose in popularity and more people watch now than ever

Re: A misalignment of AI in mathematics

#445

Post by 3ash14 »

Bourget wrote: post #432
robotpepi wrote: post #413

Earlier quoted context omitted.

I really hate this overly condescending takes. First of all, what do you know about the internals of math research that allows you to speak with so much confidence. Second, you're not even addressing the issues raised by the letter! This is not about "oh they made a bunch of problems easier". There are huge economical interest behind: who owns and has access to models? are these companies interested in developing res…

If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment. There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.

Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish.

Stockfish does not steal research or scoop researchers.

The concentration of computing resources and capital should be examined by the math community.

Re: A misalignment of AI in mathematics

#446

Post by visarga »

onetimeusename wrote: post #428
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…

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…

> Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak?

Depends on if I want to go by helicopter myself.

Re: A misalignment of AI in mathematics

#447

Post by robotpepi »

Bourget wrote: post #432
robotpepi wrote: post #413

Earlier quoted context omitted.

I really hate this overly condescending takes. First of all, what do you know about the internals of math research that allows you to speak with so much confidence. Second, you're not even addressing the issues raised by the letter! This is not about "oh they made a bunch of problems easier". There are huge economical interest behind: who owns and has access to models? are these companies interested in developing res…

If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment. There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.

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 don't think on the externalities.

Re: A misalignment of AI in mathematics

#448

Post by SavageNoble »

num42 wrote: post #228
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…

>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI. Title: Terence Tao - SAIR Competitions and the…

I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have.

AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanced math training because my experience so far tells me I will do well.

Re: A misalignment of AI in mathematics

#449

Post by jaccola »

gwd wrote: post #243

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…

> I wouldn't be surprised if there are now more chess books now than there ever have been

Well yeah... how would there be fewer??

But the point itself is silly. Few people are putting effort into Maths for the fun of it (and of those that are many derive fun from being the only one who can produce a solution). Chess differs in that it never had any point but the game its self.

Re: A misalignment of AI in mathematics

#450

Post by lukewarm707 »

i was initially optimistic that ai could be distributed. having this technology in the hands of many would counteract the malign elite who would use ai to oppress the rest of humanity. in the meantime given that intelligence is scaling proportionately with inference time compute, we are concentrating far too much power in the hands of the few who have both their own model and datacenter.

putting this amount of power in the hands of so few would require leaders of immaculate moral integrity. what we have in the US at least is an emergent kleptocracy with obvious dark triad traits: sam altman, dario amodei, elon musk, etc. they are malign and will use this power for their own benefit, at the expense of others. ignore pleas of public benefit. look instead at the evidence: infighting, systemic dishonesty, reckless disregard for safety, political lobbying and manipulation, putting power in the hands of the elite few in the guise of safety, using ai in the military to oppress and inflict violence on others.

really to prevent a bad outcome, we would need to act soon enough to prevent the kleptocracy from corrupting politicians and democracy with them. i would ditch the claude or openai subscription and support open models instead, preferably in countries outside the US to prevent global neocolonialism.

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