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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

#941

Post by wombatpm »

biztos wrote: post #731
teiferer wrote: post #727

Earlier quoted context omitted.

> Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. And by opening the door to LLM-generated results, you'll see greater and greater amounts without any hope of ever navigating this field again without machine help. It's a little like a software project which more and more gets extended by a AI agents with less and less review by h…

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

So knowledge becomes meta stable. There was an AIDS drug in the 90’s that we stopped being able to make. IIRC Apparently there were two different crystal/folding structures for the compound and the desired one was not the lowest energy. After years of production, the wrong version was produced and they could no longer make the correct version do to contamination. And every facility that tried to study it, wound up no longer being able to make the correct version. It was like a real life ice-IX situation. Scary that changing weights or model parameters could lead to the same thing happening with knowledge.

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

#942

Post by doctorpangloss »

farialima wrote: post #848
doctorpangloss wrote: post #664

Earlier quoted context omitted.

> I think we’re looking at a wonderful machine that can potentially make meaningful contributions to the sciences and maybe even humanity as a whole. That's true. But. Maybe you've seen the Oppenheimer movie, there is a moment where Oppenheimer shakes Teller's hand, basically after the guy ruins Oppenheimer's life in a completely immature betrayal. That's what people are angry about, the academy community is Oppenhei…

> You cannot name a single politician who is a mathematician. I can: https://en.wikipedia.org/wiki/C%C3%A9dric_Villani ( and of course Wikipedia has a list :) https://en.wikipedia.org/wiki/List_of_mathematician-politici... )

it's a pretty short list. guess how long it would be for "Lawyers"

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

#943

Post by i_love_retros »

i_love_retros wrote: post #558
JacobAsmuth wrote: post #531

Earlier quoted context omitted.

Exactly. Maybe OpenAI paid mathematicians to keep this discovery quiet, then added their proof to the training data, then manipulated a second team into prompting for this question such that the model could regurgitate the solution. This would plausibly explain why the model seems so capable at doing things like refuting fundamental theorems of mathematics while in things like competitive programming, biology, and ph…

You're a bot! Hey everyone, over here! I found a bot!

Down voted by the pro AI bot swarm! Financed by big tech!

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

#944

Post by Nashooo »

yourapostasy wrote: post #871
xbmcuser wrote: post #625

Earlier quoted context omitted.

This is the main thing that I keep harping about that human knowledge is too vast today for a person or even a group of people and llm will change that many discoveries that require serendipity in the past will be more likely than ever

I want to hear James Burke of Connections [1] and his writer team to have a free wheeling discussion for a few hours on what they see will happen with LLM’s making these connections with more conscious intent a lot easier. The awesome compression of knowledge aspect of LLM’s is a far undersold aspect of the technology. [1] https://en.wikipedia.org/wiki/Connections_(British_TV_series...

I don't think you can look at the current AI landscape and say any aspect of it is undersold.

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

#945

Post by fragmede »

darkwater wrote: post #756
tsunamifury wrote: post #748

Earlier quoted context omitted.

“Few-shun drive. Mmmm. Yes.” https://youtu.be/pfNS2kWf5cY?si=SH6_QC0bCspV-ngz There are comments that truly reveal a future horrifying and true. Few of them. But I count yours among them. But I’d argue also that airplanes already achieve this complexity to some degree as well as microprocessors.

> as well as microprocessors I mean, microprocessors have been on the "impossible to bootstrap from scratch in a short period of time" for 20 years already.

More like 50. The Intel 4004 came out in 1971, and there's no way to bootstrap even that level of technology after some sort of doomsday scenario.

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

#946

Post by kevinwang »

kevinwang wrote: post #904

Nitpicky/not important, but they say: Since loglog(n) tends to infinity with n, the additional term in the exponent tends to 0, meaning these constructions achieve growth only slightly faster than linear. Would anyone else describe the previous asymptotic behavior like that? I mean obviously loglogn to O(1) is a quantum leap, but wouldn't you describe loglogn as "grows so slowly it's almost constant", so the construc…

Just reread this comment and it's not easy to understand, but the edit window is passed.

What I meant is that they describe loglogn the same way you could describe O(n) or O(n^2) -- it "tends to infinity with n", even though my mental model for loglogn is to treat it as barely more than constant. See: https://cs.stackexchange.com/questions/148197/who-said-first...

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

#947

Post by switchbak »

bnchrch wrote: post #927
pluc wrote: post #920

Earlier quoted context omitted.

People are marveling at what AI can discover purely out of time and chance. AI will undoubtedly find awesome things because there's very few things we've thrown this much money at. For every awesome thing AI finds, there's a million mistakes, fake leads, hallucinations, etc. Amaze away but let's not forget this is an exception much more than the norm.

I'm sorry. But whats the point of this critique? That a raw LLM hallucinates? That we never see all the mistakes and dead ends a complex system using AI hits? Does it even matter if its accuracy rate across all its experiments is We don't see many of the failed attempts of Human Researchers. Why? Because it doesn't matter. What amazing here is that it shows our society can make discoveries faster in the post LLM worl…

As a human, I have many stupid and wrong ideas all day long - most of those don't bubble up to my conscious awareness. If LLMs hallucinate and come up with crazy things, maybe that's ok given that we can filter out the sensible and novel ones.

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

#948

Post by felixg3 »

RealityVoid wrote: post #805
computerex wrote: post #716

Earlier quoted context omitted.

I feel like that’s already becoming true. I sometimes work on problems/projects where the AI agent is definitely more qualified than me to call the shots. For example, this library here for deep learning is 100% ai generated and far beyond my technical capabilities. https://github.com/computerex/dlgo

I find AI a great scaffolding for improving understanding and mental models. BUT! It's all in how you use it.

LLMs are a mirror of the user‘s input capabilities, like every other computer programme.

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

#949

Post by JohnHammersley »

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…

Yes, I share your optimism overall, although I think it is raising a question of what the future role of the researcher is (much like the current debate on developer roles).

I attended a conference on AI for maths and open science a few weeks ago, and was struck by just how many examples of AI-supported solutions there already are. Virtually every speaker had an example of either their own use of (often the frontier) AI models in solving a problem that was previously too hard (for various definitions of hard).

I wrote up a few notes [1], and most of the speaker videos are available via the conference website [2].

[1] https://scholarlyfutures.substack.com/p/ai-and-the-practical...

[2] https://www.newton.ac.uk/event/ooew11/

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

#950

Post by tim333 »

amelius wrote: post #223
throw-the-towel wrote: post #59

See the longstanding debate on whether new math is "invented" or "discovered". Most mathematicians I knew thought it's discovered.

This is like saying a sculpture always existed, the sculptor just had to remove the superfluous material. Or like a musical octave has only 12 semitones, so all music is just a selection from a finite set that already existed. Sure the insane computation we're throwing at this changes our perspective, but still there is an important distinction.

There's more to it than the sculptor example. You could carve anything but the interesting bits of maths are quite specific.
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