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points by cjohnson318 3 days ago | 0 comments

The question for me is, would OpenAI have been able to solve this without Hong Wang's work?

The question for some is, is whether the original authors would have produced their work without building off from the work of other mathematicians.

(which is somewhat valid). Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.

[–] jazzyjackson 3 days ago

IMO that there is any work at all to build from is the result of a long tradition of taking the next step. Professor to student and so on. The danger of AI here is we get to take a leap, say, 10 steps - but then there is no more tradition to have the fortitude and mentoring necessary to continue the progress.

It all gets derailed while betting on RSI and never having to do math research again (but if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter that we get to call it solved?)

[–] olmo23 2 days ago

> if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter

For any applied mathematics: of course it matters if I can use a better algorithm for $PROBLEM. Yes, even if I do not understand it (I'd like a LEAN certificate tho)! As for pure mathematics, it can be argued that it never mattered in the first place.

[–] soon_to_be_sb 3 days ago

This is why the AI companies are making money off selling tokens and raking in investments for as long as it will work and is not looking to create the value themselves and making money off it...

They know that value creation is a dead end sooner or later..

[–] alfiedotwtf 2 days ago

If we suddenly skipped 10 generations of mathematical lineage because of AI, wouldn’t it also be smart enough that you could just prompt it to connect ideas from graduate level maths all the way to the proof!

[–] RugnirViking 2 days ago

no. That's not a given at all? I think most reasonably people now agree that AI intelligence is spiky, that is to say, there are some areas it is amazingly good, and some areas where it spectacularly fails.

One of these areas it's not good at is sadly it's social ability. It's terrible at explaining things - just try asking ask it to explain code !

[–] olmo23 2 days ago

wdym? ai is great at explaining things; it's one of the primary use-cases outside of programming.

[–] RugnirViking 2 days ago

I find there is quite a difference between something like "what do I do next" for a specific problem, and actually trying to learn something hard from an AI. The first it is quite good at, the second it is not. Surface level is easy, going into the weeds is difficult

[–] zhobbs 2 days ago

It seems like future models could build off the 10 steps to take 10 more. It's not 10 steps of AI slop, it's a discovery to build off of just like how human scientific progress has worked.

[–] bemtevi 3 days ago

I think the question is rather, what will happen to human beings when any possible personal intellectual accomplishment will no longer be seen as interesting or relevant by other human beings when AI can do most of it?

It's all well and good to say that we should just go on these journeys for our own enrichment, but even so they will just be doing it alone...or else not do it at all because they need a shared human effort surrounding them to do it, and therefore end up depressed and immersed in drugs or media all day.

Of course we're awed at what AI can do now, because all of us observing it have had the luxury of having such opportunities before AI. I got my PhD before AI and I found satisfaction in participating in a shared math community, which I wouldn't have done if I were starting my PhD now, because I would find the current academic environment unacceptable and useless.

[–] xp84 3 days ago

Many people still do woodworking for the love of the craft, even though factories exist with machines that can do everything hand tools can but 10x better and faster. If AI gets way out in front of anything humans understand, I expect that mathematicians will probably pick up where their understanding actually is, and carry on.

[–] krige 3 days ago

That analogy is rather poor. Woodworking produces discrete, unique, and physical objects, that can be made, and found use for, as many times as the craftsman wishes. Once you discover a law of physics, you can't discover it again, and it's not yours to do with as you please.

[–] NetMageSCW 2 days ago

Why not? If I discovered a law of physics that explains superconductivity and could use it to make a room temperature superconductor and kept it a trade secret?

[–] krige 1 day ago

That's a whole another discussion though. You're bringing in manufacturing to the hypothetical, where it wasn't there before.

[–] xp84 3 days ago

That would be a very exciting experiment. I doubt you could find enough vintage training data to train a LLM enough to do it without it being contaminated by anachronistic data in the weights, but I would be absolutely amazed if it could reproduce that.

[–] anshumankmr 2 days ago

There are some folks trying the same thing as I mentioned. Can check the past posts on HN that talk about the same thjing

[–] gewetensleegte 2 days ago

Other mathematicians have done the work of writing out and publishing these proofs, OpenAI has published Lean certificates.

The first type of work pushes the field of mathematics further, the second kind strip-mines the sense of discovery and accomplishment and replaces it with math homework for high level mathematicians, because in order for it to be useful, it still needs to be turned into a human readable proof.

It's imho not valid to say OpenAI is "building off" other mathematicians work, in the same way as humans, do.

[–] hollowturtle 2 days ago

> Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.

I don't think so, it was a big leap forward in terms of creativity, imagination, rigor and experimentation. Einstein was able to "run" visual thought experiments inside his mind

[–] joe_the_user 3 days ago

whether the original authors would have produced their work without building off from the work of other mathematicians.

That's rhetorical, right? Of course mathematicians built on what older mathematicians built and OpenAI's machine built on that. The real question whether OpenAI's machine has contributed something others will in turn build on.

[–] pfdietz 2 days ago

> The real question whether OpenAI's machine has contributed something others will in turn build on.

This has already happened.

[–] anshumankmr 3 days ago

Not saying I agree with the view, but something along those lines popped up when the Naive Stokes conjecture was seemingly solved (and way before when Open AI began solving Olympiad level problems and so on with their older class of models). Personally, I do see both sides of the argument. Though the broader impact remains to be seen.

[–] ubersketch 3 days ago

The proof uses completely different methods as what harmonic analysts used for the Kakeya conjecture prior so probably yeah.

[–] Valakas_ 3 days ago

Would Hong Wang would have been able to do his work without previous physicists work? That's the real question!

[–] cjohnson318 1 day ago

That's not the real question. Humans make incremental progress and sometimes have a brilliant inspiration that seems to change all of mathematical thinking after it. The question is: is AI making predictable incremental progress? Or is it discovering fundamentally different ways of thinking about math?

[–] casey2 1 day ago

The idea that mathematicians progress math by discovering fundamentally different ways of thinking about it is closer to a hallucination than a meaningful statement about mathematics.

[–] soVeryTired 3 days ago

*her work

[–] gewetensleegte 2 days ago

Why is that even a question? That's how human mathematics has worked for ages, it's OpenAI breaking that chain, which needs to be severely questioned.

Because the real question is not whether anyone or anything built on other work, but whether any human can build on that work.

And so far, yet again, OpenAI has stopped just shy of that, instead creating math homework for mathematical geniuses while taking away their sense of discovery and accomplishment.

[–] Nomennonhabeo 3 days ago

Yes. The all-dimension result follows a completely different approach from that of Wang and Zahl.

[–] Gabriel54 2 days ago

This question strikes me as strange, because it has always been in the nature of the mathematical community to share results as openly and widely as possible. Hong Wang’s work was in the public domain and was meant to be built upon. This is what human mathematicians have been doing for centuries.

[–] casey2 1 day ago

The answer from me is, yes.