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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

#731

Post by biztos »

teiferer wrote: post #727
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…

> 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 requires giant cooling machines running 24/7 and again, nobody knows how it works, but with the added bonus that the planet is cooked if they ever stop working.

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

#732

Post by diordiderot »

virgildotcodes wrote: post #698
diordiderot wrote: post #678

Earlier quoted context omitted.

Not in academia, but the amount of crying over rapid technological and intellectual progress because you're not getting credit validates everything critics say about you. No interest in human advancement, just attribution.

I’m not in academia myself, and I think AI solving all our problems ASAP is ideal, even if it means no humans get attribution. What I’m saying is that the ultimate goal of those in power are not these sorts of altruistic or even scientific pursuits, and that the massive labor disruption and hyper concentration of power in the hands of those who are proving time and again that advancement of science and benefiting the…

Oh good. But I think you're over estimating the 'concentration of power', and under estimating 'benefiting the whole of humanity'

Most homeless people have smartphones, and consistent access to food and clean water.

Your average 'poor person' in America has HVAC. An unimaginable luxury in the EU

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

#733

Post by jorisw »

libraryofbabel wrote: post #524
getnormality wrote: post #468

Earlier quoted context omitted.

Yes, this and every internet forum will still be doing this two years hence. Your life will be better if you take to heart this famous passage from Nietzsche: I do not want to wage war against what is ugly. I do not want to accuse; I do not even want to accuse those who accuse. Looking away shall be my only negation.

> Looking away shall be my only negation. I’ve been thinking of building myself my own frontend to HN that makes it impossible to view comments, for this reason. Yet sometimes there are still really interesting discussions and it’s hard to let go of what for me feels like the last social media I want to be part of.

An added stylesheet should be enough to do that

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

#734

Post by energy123 »

vatsachak wrote: post #11

As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.

The issue with this prediction is the gulf between problem-solving using known tools, versus creating new concepts for problems where existing tools aren't enough.

All AI proofs so far, including this one, are using existing tools in new ways, rather than inventing new tools. This is not surprising if you know how these models are trained. These existing tools are in distribution. New tools are not.

Problems worth of a Fields Medal likely require new tools to be invented. Thus it is not clear whether progress within the confines of the current paradigm is enough.

We could get this weird spiky situation where the AI is insanely superhuman at all problem solving, but completely incapable of coming up with a single new tool. It discovers everything there is to discover, subject to existing axioms and concepts.

Timothy Gowers gives some commentary on this in the attached PDF.

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

#735

Post by ai_fry_ur_brain »

golol wrote: post #705
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 are believing a very unlikely scenario. I think the reason is that you have been convinced of a claim which is unlikely and indeed not true. That is: >the model seems so capable at doing things like refuting fundamental theorems of mathematics That is not true and a complete misrepresentation of recent progress of AI in math. It is therefore not necessary to believe the conspiracy theory you described in order to…

Its almost certainly a scam and you're falling for it.

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

#736

Post by teiferer »

shalmanese wrote: post #658
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. Every day, it grows harder and harder to contain a mental map of recent relevant progress by simple virtue of the amount being produced. AI is going to both help and hinder this process though. At the end of the day, mathematics is mostly a social process at this point. The goal is not raw number of…

> Only a rare few new theorems in mathematics nowadays have direct real world applicability.

Has this ever been different?

Math is abstract, rightfully so. It does not have to have direct applicability. Understanding builds over time and applications eventually follow. Number theory used to be a fringe "pure" theory field without applications for the longest time. If we'd only be interested in (and thus fund) what has direct applicability then society would be much worse off.

Side note: I recall my high school class mates rolling their eyes in every math class with "when will I ever need this in my life?" never asking the same question about PE or history or art classes. Now they struggle with their tax return and are routinely getting screwed over by loan sharks. But make no mistake, they can be proud of their A for hitting the goal 5 out of 5 times during soccer in PE class.

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

#737

Post by SpaceNugget »

Nesco wrote: post #714
make3 wrote: post #632

Earlier quoted context omitted.

To me, AI feels like the morbidity of Star Trek teleportation, where it's actually copying the person at to the other end and zapping the original one out of existence. The original human never benefits from the fast transportation. Similarly, we're creating tools to improve knowledge, but we're progressively zapping the human out of the equation. Knowledge is created for something, but it's unclear if very soon huma…

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?

Beverse they are benefitting from the financial situation of owning the ai companies that are getting pumped massive amounts of money, not from the debated usefulness of the output of the LLMs.

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

#738

Post by mangolie »

woah wrote: post #400
lovecg wrote: post #337

Earlier quoted context omitted.

By making it think for 100+ pages https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d... Regular ChatGPT users don’t have a way to do that, this is something they do internally only. edit: apparently that’s only the _condensed summary_ of the chain of thought.

you can do this easily with the api or with codex

You can't really in this way. They have a parameter they control on the backend that can force how much time it thinks for

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

#739

Post by dmos62 »

CamperBob2 wrote: post #713
dmos62 wrote: post #699

Earlier quoted context omitted.

Are you saying comments are getting shadow banned?

From what I can tell, anything that triggers some sort of AI post filter gets automatically flagged. Several posts in this thread are visible only with showdead enabled. My argument is that this rule should apply only to people who post LLM output under their own user names without acknowledgment, or otherwise post it where it doesn't belong. If the topic of a (sub)thread involves LLM output, it should be OK to cite…

I agree. It sucks to have my good faith comment be shadow filtered, without any notice or indication.

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

#740

Post by melagonster »

necovek wrote: post #646
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.)

PhDs used to mean publishing a novel mathematical result: when has that changed?

So finally they reach a part of PhDs level. Current version rely human to integrate results from they model and writting the papper. If LLMs/AIs can do all thing above, we can exactly get a PhDs level model.
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