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An OpenAI model has disproved a central conjecture in discrete geometry

openai.com

921–930 of 1001 posts

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

#921

Earlier quoted context omitted.

Based on some napkin math, that would be about ~100 watt hours of electricity on an H100 cluster, or, roughly the same amount of energy needed to boil a kettle for a cup of tea.

That's an exceptionally fast output you have there... Mind showing your working out?

Lotr ~1.4k pages 1 page ~1k tok -> ~700k tok 1tok ~0.5J -> 350kJ ~100Wh ~1 cup of tea

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

#922

Earlier quoted context omitted.

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

Much of Europe is close to the ocean, high in latitude, or mountainous, and climates there are more temperate. You don’t need AC there; AC is a luxury.

Southeast or central US has considerably higher wet bulb temperatures than Europe does in summer. Without HVAC, there’s a good chunk of the year where it’s too hot to get much done.

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

#923
post #920

Earlier quoted context omitted.

I'm not sure what your point is - can you expand?

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.

Presumably with automated proofs, hallucinations (aka, creativity or confabulation, if we hadn't botched the naming) is a good thing. It's in the empirical world where trusting an LLM is a stupid thing because there's no automated form of fact checking.

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

#924

How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?

No separate Wikipedia page -> just another Erdős problem.

There is no universally agreed-upon "central" conjecture (like "P vs. NP" in CS), but here are some pillars:

1) https://en.wikipedia.org/wiki/Happy_ending_problem

2) https://en.wikipedia.org/wiki/Hadwiger_conjecture_(combinato...

3) https://en.wikipedia.org/wiki/Hirsch_conjecture

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

#925
post #216

Earlier quoted context omitted.

That has been the question since the beginning of humans. Maybe computers can help understand better because by now it's pretty clear brains aren't just LLMs.

The optimists believe brains are very special and we’re far from replicating what they do in silicon. The pessimists just see a 20W meat computer.

And almost everybody seems to forget the brains are about to be replaced every 10 years for past 50 years.

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

#926

Earlier quoted context omitted.

If ASI does create an abundant future I think many are going to have that familiar listless feeling of enabling cheats on a computer game and all the mystery and fun is gone. Technology in general (smartphones, social media, search) even without AI is creating this feeling, as it shrinks the world and makes it less mysterious. It's worse than boredom it's more like nihilism. Then when you strip purpose and meaning fr…

Aye, but it’s also possible for people to find their own purpose and meaning. Some find it in religion, some in art, some in love or nature. It will be a transition, for sure - there would no longer be meaning in “winning the game” in a capitalistic or scientific sense. Anything you want to produce or learn, the AI could already produce or has already learned. Now you have to do it just for the love of the process. I…

Basically that's Viktor Frankl's insight and it's more important than ever. Combined with the Buddhist precept of non-attachment.

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

#927
post #920

Earlier quoted context omitted.

I'm not sure what your point is - can you expand?

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 world. Thats incredible.

Your "critique" of how it happened. Not so much.

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

#928

Earlier quoted context omitted.

> These all are valid, noble points I also used to brood about while being young and financially supported by my parents. Ah, the proverbial silver spoon. Sadly, I never had that luxury. If you look through my comments, you'll notice I'm more at the get-off-my-lawn point. Also, what happened? Real world wear you down and turn you cynical? It is possible to be hopeful and cynical at the same time. This tech is somethi…

I wish I could share your optimism, but no recent event in the world affairs can help with that for me.

> wish I could share your optimism, but no recent event in the world affairs can help with that for me.

What about Ukraine holding Russia back, and now looks like it might actually win? What about the most recent additions to NATO. Hungary's regime change? Canada's save? EU's pivot to arming itself, and quickly?

Buds of green, yeah?

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

#929

I looked at all linked articles and could not find an example of the points (they show a square grid of points with n~=100 but no other ordering of points to show the more optimal layout(s)). Is there anywhere an image example of a superior layout for example with n>={100,1000,10000}..? I would love to see it. I am imagining it would look somewhat like a sloppy pizza.

One of the authors said in a reddit comment (and I hope I am summarizing accurately) that it's impossible to show a diagram as the smallest instance of the technique gives like 10^1000000 points.

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

#930
post #301

Earlier quoted context omitted.

I’ve always been skeptical about the role of LLMs in mathematics, but this is the first time I’ve seen this argument, and I actually find it very compelling. Maybe LLMs will help us develop more horizontal understanding of the field.

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…

How does an AI finding a proof of a question that someone asked very long ago, is going to improve anyone's cognitive capabilities?

Human cognition improves the more you practice it. Not when you outsource it to machines that do the "cognition" for you.

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