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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#651

Post by david-gpu »

beepbooptheory wrote: post #610
david-gpu wrote: post #576

Earlier quoted context omitted.

You have expressed a few different ideas, so I will address them separately. > It's not about whether the conjectures themselves are interesting or not, or whether people simply have enough time. Tao seems to think otherwise, if I am reading him correctly: I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these…

Are you trying to argue toward some final verdict with regard to LLMs and mathematics? I thought you were just trying to make a comparison to Baudelaire? I think maybe being clearer on this point would help. Even if you argued sufficiently for the latter (which is going to be tough already), it wouldn't really speak to the former. Or at least: that would have to be a separate argument I think. Also, how, in your word…

My opinion is that the field will adapt. AI will not spell doom for mathematics. On the contrary, it is the beginning of a new era. Math is having its Deep Fritz moment, just as computer science is going through the same.

Some folks are struggling to adapt to this change. Tao actually sounds like he is doing alright compared to most, even if some of his arguments seem a bit weak, as I alluded to in other comments in this thread.

Hopefully it makes some sense. And if it doesn't, at least we had a nice chat.

Re: A misalignment of AI in mathematics

#652

Post by Footnote7341 »

Can't all the prestige-maxed mathematicians still study all these famous problems after ai solves them. And even if they convince open-ai to stop dunking on them, some normal user with gpt 7.1 on the normal chat interface will do it in a year.

Even if they stopped anyone from releasing ai proofs for five whole years it would be meaningless seeing as these problems are decades old already. Humans weren't JUST about to solve them until openai stepped on their toes.

Re: A misalignment of AI in mathematics

#653

Post by fasterik »

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 don't think the analogy works because for the past few years Tao has been one of the most vocal advocates of AI in mathematics and has used it extensively in his own research. You can find several of his talks about this on YouTube. It's completely consistent to believe two things at once, that the tools are useful and that the companies are misbehaving.

Re: A misalignment of AI in mathematics

#654

Post by vatsachak »

fdupress wrote: post #588
vatsachak wrote: post #151

Earlier quoted context omitted.

I actually read through a bunch of LLM slop on the weekends trying to catch white whales I couldn't during my math PhD. The incentive is solving the problem and understanding the solution.

And that homes, feeds and waters you how?

In no way, it's just a hobby.

Re: A misalignment of AI in mathematics

#655

Post by SpicyLemonZest »

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…

> 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.

To me this analogy points in the complete opposite direction. Imagine somebody takes a half-completed project design you're trying to figure out, vibecodes a rough prototype of it, emails your manager to announce that the project just launched in alpha, and then dumps it back on your lap for approvals and testing and productionization. Would you say that they've added value to this process? Or did they just strip away all the hard parts of the problem so they could claim credit for the easy part?

Re: A misalignment of AI in mathematics

#656

Post by remywang »

The root of all these is the culture in mathematics (and science in general) to only reward those who “get there first”. This creates a perverse incentive to compete. When no one can out compete a tireless swarm of AI, no one gets rewarded any more.

But nothing’s stopping anyone to still work out an alternative proof, or a more elegant proof, or just trying to prove for the sake of understanding, just like doing homework without looking at the solution. It’s just that you can’t get paid doing that anymore.

Re: A misalignment of AI in mathematics

#657

Post by zeroonetwothree »

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…

Limits can be defined within finitism as long as the end result is finite. Essentially it’s just a process which lets us get as close to 2 as we want.

A better example would be a limit that equals sqrt(2) which finitists would probably say cannot represent a real object because it is only defined as the end of an infinite process.

Re: A misalignment of AI in mathematics

#658

Post by pickleRick243 »

rurp wrote: post #532
causalmodels wrote: post #269

Earlier quoted context omitted.

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

I'm not a mathematician but it seems to me that if all it took to solve the problem was an enthusiast level understanding of the domain and a few hundred dollars of tokens then the result probably isn't that valuable. Even assuming you are the first person in the world to solve it, these kinds of LLM-friendly problems that are now easy to solve and easy to verify will almost certainly be picked off by one person or a…

sounds a bit like cope. Crouzeix's conjecture was solved exactly under these circumstances and I wouldn't describe it as "not that valuable". In any case, AI capabilities will increase dramatically over the next few years while human math capability will not. That means that there's a fixed target regarding whatever is currently considered a "serious math problem" and its difficulty level. Soon the average problem solved with a few hundred dollars of compute will be at that bar.

Re: A misalignment of AI in mathematics

#659

Post by yuuu »

azan_ wrote: post #219
tossandthrow wrote: post #11

Earlier quoted context omitted.

Yes it seems odd. Out sourcing construction jobs was great for the economy while leaving entire cities in rubbles. But as soon as it hits the privileged class there is a call to "provide a specific replacement mechanism".

Math researchers are privileged class? I can guarantee - construction workers are extremely rich compared with math phds and most of postdocs. Talking about privileged class is absolutely laughable here.

I would bet that the parents of math PhDs are generally more privileged than the parents of construction workers.

Re: A misalignment of AI in mathematics

#660

Post by pickleRick243 »

bubblegumcrisis wrote: post #499
causalmodels wrote: post #269

Earlier quoted context omitted.

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

It is interesting isn't it. You asked for a painting. A robot made the painting. You looked at it and said, "well, I guess it's good. Should I put it online or something? Dunno. Hey Fred, what do you think of this?" Meanwhile, your next door neighbor spends their entire life developing their understanding of life through art. They "understand" (maybe not in a way they can articulate) art. You go next door, you look a…

what about cancer?
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