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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#521

Post by flatline »

robotpepi wrote: post #447
Bourget wrote: post #432

Earlier quoted context omitted.

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…

Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be.

Tech companies are as much the topic of this post as AI, I think that's the immediacy.

Re: A misalignment of AI in mathematics

#522

Post by kfse »

zozbot234 wrote: post #378
deanCommie wrote: post #360

Earlier quoted context omitted.

Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity…

> 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)

Re: A misalignment of AI in mathematics

#523

Post by ralph84 »

omnicognate wrote: post #201
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

> primarily as a marketing exercise

Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine.

Re: A misalignment of AI in mathematics

#524

Post by charcircuit »

well_ackshually wrote: post #246
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…

So it wasted everyone's time, thousands of hours of research trying to disprove something said very loudly. What OpenAI is doing is a DoS of the scientific community: wasting your time trying to check if they're not wrong, and claiming glory in the mean time.

OpenAI avoids this by formally verifying the proof.

https://github.com/openai/NavierStokesAndEuler

Re: A misalignment of AI in mathematics

#525

Post by amelius »

zahlman wrote: post #517
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…

> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize,…

Not if it's lean-verified.

Re: A misalignment of AI in mathematics

#526

Post by robryan »

suddenlybananas wrote: post #334
Art9681 wrote: post #159

This reads like people lamenting a bygone era and making a desperate attempt to bring it back. I'm sorry. Outside of the good ol' boys club, no one cares about some process they've romanticized simply because "that's how its always been done". Absolute nonsense. We are moving forward and if that means no human wins a fields medal because they didnt spend three decades working on a problem that could be solved in thre…

Yeah who gives a shit about knowledge or understanding or insight.

You can still do all that. The only thing going is that in some cases the human isn't going to be able to claim that they made the key insights that first solved the problem.

Re: A misalignment of AI in mathematics

#527

Post by causalmodels »

youoy wrote: post #472
causalmodels wrote: post #429

Earlier quoted context omitted.

Maybe I'll end up doing the write ups pseudonymously. I have taken care to make sure the results can meaningfully contribute to field but I don't want to plant flags or really receive credit of any kind. I just think they are interesting. I like my current life and don't want to get dragged into the current fracas surrounding the use of AI in math.

If you have taken care, then share it with the community. People will be thankful and happy. The problem is with people that may do it without contributing to the community.

If this was limited to just three results, I would agree with you. But those three are just the ones I've managed to verify myself. The list of unverified results is quite a bit larger.

The field I've been investigating is not large. Even if I were to take the time and care to beat the interesting results into something meaningful, I'm afraid the pace at which I'm able to produce these results would not be well received.

Re: A misalignment of AI in mathematics

#528

Post by lll-o-lll »

dhbradshaw wrote: post #493
lll-o-lll wrote: post #486

> We are witnessing a general threat to intellectual work This is the crux of it and goes far beyond Mathematics or Computer Science. To get a bunch of humans to do anything, you have to motivate them. Kleos and Timē; renown and stuff. These AI companies threaten to rip this away from everyone but themselves, and this recent millennium prize is the perfect example. Solving this problem as a human would have led to tr…

These are both big motivations but not the only ones. But there's still play. There's still curiosity. And there's still the drive to understand something for yourself.

> But there's still play. There's still curiosity. And there's still the drive to understand something for yourself.

Yes, but think about what that implies if those are the only motivations left. Gone are the professions. Gone are the ambitious.

There is plenty of space for people to work on intellectual pleasure pursuits (as there is with art and music), but the death of all intellectual based industries is still something to avoid. Or to mourn.

Re: A misalignment of AI in mathematics

#529

Post by uonr »

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…

Both of Baudelaire’s criticisms were reasonable, and the same thing happened again when AI image generation showed up. You think the opponents look ridiculous because you’re viewing the history from the winner’s side. As for “the public,” people had a real demand for photography as a way to record things, which is also why it won. There is no comparable public demand for proving Fermat’s Last Theorem.

Re: A misalignment of AI in mathematics

#530

Post by robotpepi »

sim04ful wrote: post #220
yzydserd wrote: post #6

> solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. This is the effect of AI on most intellectual disciplines, and it’s a real worry.

Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ? Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ? Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, rea…

> Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests.

I'd argue that this extremely extreme scenario is the only one in which it kind of makes sense to not have understanding. But let's be honest: no one knows if we'll be there (and it seems unlikely since everything reaches a plateau eventually). So, what happens if we allow ourselves to forget everything and then we don't reach the ideal scenario?

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