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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#931

Post by thegrimmest »

Schlagbohrer wrote: post #901
Nesco wrote: post #714

Earlier quoted context omitted.

You lost me at “except billionaires”. I don’t see how Jeff Bezos benefits from this one much more than let’s say Terence Tao. Can a tech news stay a tech news, without getting bombardes with leftist subtexts all the time?

"leftist subtexts" such as an understanding of capitalist economics in which the people who own everything benefit from the economic activity being done underneath them.

"leftist subtexts" that treat this as a problem, and not as the single largest driver of growth in human history, to which we owe all of the material comfort we now enjoy.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#932

Post by bananaflag »

toilet wrote: post #795
bananaflag wrote: post #709

Earlier quoted context omitted.

As a mathematician, new, conceptual math is when I'll become interested in reading LLM output. I appreciate very much the work done so far, but this sort of asymptotic/quantitative result didn't interest me much even when it was done by humans. (This is not snobbery, just a personal preference.)

I have no idea about research in mathematics: How will mathematicians judge what constitutes new conceptual math that is actually useful, vs a hallucination that might be novel but doesn't introduce anything actual meaningful?

Same as when humans do it.

Human mathematicians frequently introduce new pointless abstractions just to churn out papers. And they are not accepted in serious journals, but they sometimes find a place in some mediocre or bad journal.

Of course, AI will increase this phenomenon manifold.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#933

Post by lesostep »

rithdmc wrote: post #824
lesostep wrote: post #784

I am cautious about AI "discoveries" after Mythos paper. What was the process of a writing a paper? Was the question asked by a mathematician? Was the paper right from a get-go or was there someone who pointed out mistakes? How much attempts were made before solution was found? I will eat my words if an AI oneshotted that one without any external help, but for know I am left wandering whether it's a new way to attrib…

> I will eat my words if an AI oneshotted that one without any external help like having a colleague peer review your paper, or bouncing ideas off a mentor before you write them down? I agree there's a lot of AI marketing BS at the moment, but revising approaches based on feedback is a good thing.

Yes, and no. As someone who had studied and had taught math, I really like peer review.

But peer review is a powerful tool.

Carefully choosing what lemmas to give for solving and reviewing the result is my favorite way to teach young minds. Yes, they do solve most problems themselves. But, most of them likely wouldn't be able to do that before someone dissects problem beforehand and points at weak spots in their explanations.

And that's why I question who prompted the model, how they prompted it, and how much their own ideas influenced the output.

I admit, I don't know enough to judge how much of the right solution was actually enclosed in a first reply

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#934

Post by barrenko »

dxroshan wrote: post #869
dhosek wrote: post #639

Earlier quoted context omitted.

One of the challenges I had in graduate mathematics was just trying to keep all the concepts in my brain. It doesn’t help that you end up with things like homomorphism and homeomorphism tangling one’s brain thanks to their superficial similarities. Heck, just keeping track of basic theorems and definitions is a challenge.

When I return to a subject after spending some time on other topics, I had the same issue with such definitions.

I was starting to wonder if I ever really knew something, or it's just a feeling of familiarity of some sorts that descends.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#935

Post by marand23 »

NiloCK wrote: post #890
pocksuppet wrote: post #845

Earlier quoted context omitted.

Billionaires are going to benefit from AI at the expense of everyone else. That's not leftist ideology, that's just a fact. That's happened with every technology that's ever been created. It happened with the industrial revolution. Why would it be different this time?

What do you think of things like the changes to infant mortality or life expectancy between the industrial revolution and present day? EG, my own oldest child needed a surgery at birth that would have been logistically impossible even 50 years ago. I'd say that she and I have benefited enormously, despite not being billionaires. edit: I solemnly swear that the sibling comment with the strikingly similar "impossible 5…

I mean, i can assure you that I am not a bot either, but wouldn't a bot say that? :p

But yeah, quite a coincidence that we both chose 50 years :)

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#937

Post by Mikhail_K »

trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

> But, for scientists, I find that these tools address the problem of the > exploding complexity barrier in the frontier.

They do the opposite by locking the results the produce within the slop presentation that needs more AI to comprehend.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#938

Post by Rover222 »

mrdependable wrote: post #439
dmix wrote: post #413

Earlier quoted context omitted.

So you think that OpenAI paid some mathematicians to either solve this conjecture problem, or a bunch of related unpublished math related to it, then fed it into an LLM model so they could announce it as being solved by the model? How is that not a conspiracy theory?

It is just a theory, the conspiracy part is not really applicable. I don't see what is controversial about it. Are you implying the machine taught itself the mathematics to do all this?

It's a classic paranoid conspiracy theory, IMO

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#939

Post by Rover222 »

recitedropper wrote: post #276
Rover222 wrote: post #251

Earlier quoted context omitted.

Seems like a very tin-foil-hat-take to me

I'm not letting the government read my brainwaves. In all seriousness though: My suggestion is that those shepherding the frontier of AI start acting with more transparency, and stop acting in ways that encourage conspiratorial thinking. Especially if the technology is as powerful as they market it as.

Hard to argue with that

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#940

Post by fragmede »

csheehan10 wrote: post #912
qnleigh wrote: post #798

Earlier quoted context omitted.

Can you describe what the reaction to these results has been like in your department? Obviously many people are excited, but what else? How do grad students feel about this? Are any professors getting worried about becoming obsolete?

I am a PhD student in mathematical statistics. The people I have spoken too think this is very exciting and cool. There is also a sense of unease about what this will mean in terms of being a mathematician, and what effects it will have on our future employment. I am also a little worried about what it means for your training as a junior PhD. Often you would try and solve a problem your advisor thinks is doable that…

HN comments for Gowers post. https://news.ycombinator.com/item?id=48071262
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