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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

#581

Post by piloto_ciego »

School-Cotton wrote: post #361
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…

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

So, I've seen this mindset a lot lately...

The answer is that we simply need to decouple the "right to exist" from "worth."

You should have the right to exist and explore the world simply because you're human, not because you can use your skills to provide some sort of transactional value to someone else. Deprogramming so many people is going to be hard...

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

#582

Post by vatsachak »

pamcake wrote: post #570
vatsachak wrote: post #198

Earlier quoted context omitted.

Not necessarily. Obviously playing Kasparov on the board requires more planning ability than managing a McDonald's but look at where chess bots are now. There's much more to being human than our "cognitive abilities"

> Obviously playing Kasparov on the board requires more planning ability than managing a McDonald's Not obvious and in fact I think the opposite is way more likely. Chess is well-defined and self-contained in a way that managing a restaurant with fleshy customers never will be.

That's true. I should clarify by saying I meant that a human playing on par with Kasparov obviously has the planning ability to manage a McDonald's

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

#583

Post by piloto_ciego »

cpard wrote: post #322
margorczynski wrote: post #313

Earlier quoted context omitted.

Yep. The thing is people (maybe because of our limited scope) just focus on the depth and not the breadth. Because this is a general purpose model - it also has PhD+ knowledge in Physics, Biology, History, etc. I think we still don't really comprehend how much can be achieved by a single "mind" that has internalized so much knowledge from so many areas.

there's so much opportunity on the breadth of things too! I think that you end up having different people focusing on different things though. Personally I'm a more of a breadth person and I could never compete with peers who where more of the depth type of person at college. But I get satisfaction from connecting things that feel irrelevant on first sight, that's what drives me.

This is me too.

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

#584

Post by xpct »

CamperBob2 wrote: post #377
School-Cotton wrote: post #361

Earlier quoted context omitted.

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

What's happening is the verbal/linguistic equivalent of the invention of calculus. No intellectual field will ever be the same again. Who wouldn't find that exciting, and want to experience it?

I don't think change is inherently exciting.

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

#585

Post by IAmGraydon »

Ar-Curunir wrote: post #394
cpard wrote: post #301

Earlier quoted context omitted.

It's up to us I think. We can use LLMs to generate web pages in candy crash style and end up dumper by outsourcing thinking to the machines or we can use it to expand our cognitive capabilities. What makes me more of an optimist in this case is that people who today decide to go into these sciences are mostly people who are driven by intellectual activity so I feel they are the right ones to figure this out, probably…

Unfortunately, LLMs might lead to the demise of the primary institution that allows for people that are in it for the love of intellectual activity to do that activity, namely research universities. Certainly the people proposing the tech are quite opposed to the modern university.

You’re making some generalizations here, but I do agree that one of the primary dangers of LLMs is destruction of institutions of higher education. If thinking power becomes cheap, who will pay the money that universities demand?

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

#586

Post by fourseventy »

dawnerd wrote: post #299
raincole wrote: post #280

I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)

Yet it still codes like a junior developer that memorized all of stack overflow.

What is the last model you used... lol. Linus Torvalds himself said the newest models are better than him at coding.

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

#587

Post by zmmmmm »

As a side observation, it is striking but also not surprising in retrospect that the big successes in AI are coming from domains where things are fundamentally verifiable. Both software and math are either fully verifiable or low-cost verifiable (breaking a test is not the same cost as building a bridge and watching it fall down to see if it worked).

Other domains are extracting value but I feel like there's an order of magnitude difference. It raises the question, what other domains fit into these categories where the AI itself has pretty much free reign to verify its own results?

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

#588

Post by psb5 »

cpard wrote: post #224

The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…

Check out Ashby's Law of Requisite Variety

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

#589

Post by slashdave »

drdeca wrote: post #504
slashdave wrote: post #473

Earlier quoted context omitted.

You have to define what you mean by "interpolate". The mechanisms that LLM use are not mysterious, and they are not the same as used by humans.

If you interpret “interpolate” in the literal sense, and apply it to the mechanisms behind LLMs, then the claim that they only interpolate, is straightforwardly false. Taking it instead as a metaphorical claim may be more valid, but in that case it doesn’t depend on our understanding of how LLMs work.

LLMs are statistical models by construction, so depending on how liberal you want to be with terminology, "interpolate" is not so bad. Might make a statistician upset.

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

#590

Post by theendisney »

Ar-Curunir wrote: post #394
cpard wrote: post #301

Earlier quoted context omitted.

It's up to us I think. We can use LLMs to generate web pages in candy crash style and end up dumper by outsourcing thinking to the machines or we can use it to expand our cognitive capabilities. What makes me more of an optimist in this case is that people who today decide to go into these sciences are mostly people who are driven by intellectual activity so I feel they are the right ones to figure this out, probably…

Unfortunately, LLMs might lead to the demise of the primary institution that allows for people that are in it for the love of intellectual activity to do that activity, namely research universities. Certainly the people proposing the tech are quite opposed to the modern university.

What little intelect we have can be directed to other parts of the vast endless ocean of unknown things.

I hear some specialists (specially multi-disiplinary ones) write things they know few or no one can read. (Which is the most ironic reason for being rejected by a journal)

I recall a funny moment on irc where a truly helpful guy moaned that no one helped him when he had a (programming) question. He was very good at many programming languages and worked in some mix of high level physics and mathematics. He posted SO questions that rarely got an appologetic response from someone able to understand the code and the physics but couldnt wrap around the math. lol I hope he finally gets some help with his wizardry.

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