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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#631

Post by paulhebert »

phoghed wrote: post #629
paulhebert wrote: post #561

Earlier quoted context omitted.

These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers. OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems. Don’t you see how that’s different?

Yeah bro, same for probably the majority of this site that write software for a living and/or hobby.

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

Re: A misalignment of AI in mathematics

#632

Post by sweezyjeezy »

senfiaj wrote: post #274
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…

Well, chess is a sport where humans are supposed to compete. But math, programming, science are mostly not, and AI might affect economy, careers, etc.

As a chess fan, 100% this. We have known for the last ~15 years who the best human chess player is, and that he will lose against stockfish on his phone. But chess survives because of the human characters involved, the rivalries and dramas, watching two people trying to overcome each other under insane pressure, and sometimes coming up with something astonishing. In short - it's a sport.

There is no equivalent in math.

Re: A misalignment of AI in mathematics

#634

Post by phoghed »

paulhebert wrote: post #631
phoghed wrote: post #629

Earlier quoted context omitted.

Yeah bro, same for probably the majority of this site that write software for a living and/or hobby.

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?

Re: A misalignment of AI in mathematics

#635

Post by AmazingEveryDay »

aerodexis wrote: post #214
viccis wrote: post #31

Earlier quoted context omitted.

>Governments are invested in solving mathematical problems for practical purposes. Very ignorant view of mathematics that also begs the question with an unspoken assumption of what a government is and wants while also ignoring the contingent nature of those things throughout history.

I'm genuinely surprised by this comment. I'm not talking about why a mathematician pursues math - I'm talking about where the stipend comes from. Higher math is exceptionally useful for cryptography, defense, econometrics etc. I have a hard time thinking of other motivations that would hold a candle against such things. Is the idea that government (for my purposes : folks w/ a monopoly on violence) is sincerely inter…

Some of the comments here are very strange. Someone called Terrance Tao a useful idiot. Friday in America, maybe people are hitting the beer a bit early.

Re: A misalignment of AI in mathematics

#636

Post by slopinthebag »

alkyon wrote: post #366
tzumaoli wrote: post #234

Earlier quoted context omitted.

Is this the scenario described in Ted Chiang's short story https://en.wikipedia.org/wiki/The_Evolution_of_Human_Science where scientists are "catching crumbs from the table" trying to decipher the results generated by superhuman intelligence?

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

Why would this be optimistic? This sounds extremely negative to me…

Re: A misalignment of AI in mathematics

#637

Post by YeGoblynQueenne »

ndriscoll wrote: post #612
SpicyLemonZest wrote: post #412

Earlier quoted context omitted.

Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made ir…

But it does produce value. We now have an explicit solution and even a proof. Humans can then work on clarifying why it's true. Unsurprisingly, not all that different from software, where models can generate working code just fine. The details will all be there and all correct, but the architecture is currently not ideal, so a human guiding it can greatly improve the proofs. I actually found this to be the case with…

>> Humans can then work on clarifying why it's true.

Presumably you're a human. Are you going to do that?

Re: A misalignment of AI in mathematics

#638

Post by blw96 »

onethought wrote: post #477
Forgeties79 wrote: post #225

Earlier quoted context omitted.

It’s not a parallel. No one ever claimed photography to be the same as painting or some other medium - it was a new medium that wasn’t respected. AI is being treated and pushed as a replacement for every medium.

It literally was a replacement for portraits.

[dead]

Re: A misalignment of AI in mathematics

#639

Post by _superposition_ »

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 really like this take, and while I hate math I value it. Your position sounds extremely plausible and it fits with the pattern we see in the community here. Regardless if it's ai slop or not we still debate the value and attempt to understand. In the process generating new insights and ideas. Life will go on.

Re: A misalignment of AI in mathematics

#640

Post by 12_throw_away »

kfse wrote: post #522
zozbot234 wrote: post #378

Earlier quoted context omitted.

> AI is now capable of constructions so complex that no human or human team can unpack. How can we possibly know this when we haven't even seriously started on the endeavor of actively reverse engineering these AI-generated proofs? That's a proper job for human mathematicians, because the AIs themselves are demonstrably clueless about what steps in a proof are genuinely interesting and load-bearing from a human POV.…

Not to mention, there are already (pre AI) machine-generated proofs that we've pretty much agreed not to try to explain fully, like the four-color theorem which ends up with brute-force verification of 600+ cases (down from close to 2,000 when first demonstrated)

> there are already (pre AI) machine-generated proofs that we've pretty much agreed not to try to explain fully, like the four-color theorem

Algorithmic verification is a very unsatisfying answer to the problem (e.g., surely it's not just dumb luck that every single case happen to have this exact property), but that's an entirely different issue than saying that no one follows logic of the proof method itself.

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