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.
An OpenAI model has disproved a central conjecture in discrete geometry
761–770 of 1001 posts
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#762Earlier quoted context omitted.
This doesn't sound correct. Source?
In recent months, Linus said it specifically about code for a personal side project of his. The quote was in the commit message. (I’m not the grandparent commenter, and I think grandparent commenter’s claims may be too broad or require context.)
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#763Earlier 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…
See comment about "scientific equipment that people hadn’t conceived of but which worked"
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#764Earlier quoted context omitted.
My only complaint is the claims always start spreading 6-12 months before the delivery. A little patience goes a long way in what's possible with AI and we all just have to wait and see what parts actually grow this next cycle or not. Guessing at it based on trend lines only leads to people getting excited when it matches their particular guess and ignoring it when it doesn't.
They said that their specific version of model had has this ability one year ago.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#765Earlier quoted context omitted.
The map is not the territory.
I don't know what you're even trying to argue here. We're not comparing math to reality (though there's a strong argument to be made that reality has a structure that is mathematical in nature - structural realism didn't die a scientific philosophy just because someone came up with a pithy saying), we're talking about if math is discovered or invented. Most mathematicians would argue both - math is a language, we hav…
Math is a mental map which coincides with reality in useful ways. Different maps can also be useful. The models we construct are based on arbitrary axioms which we hold to be true. Different axioms could lead to different theories which are just as useful. So it isn't discovered (i.e. mapping directly to reality and waiting to be discovered), it is created.
To pick one example, adding the concept of zero changed our model/map of reality fundamentally without changing reality.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#766Earlier 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…
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#767Earlier quoted context omitted.
In recent months, Linus said it specifically about code for a personal side project of his. The quote was in the commit message. (I’m not the grandparent commenter, and I think grandparent commenter’s claims may be too broad or require context.)
There are a missing the context: The vibecoded application was written in python while the main code was written manually in C by Torvalds in this side project. He never ever said that AI produces better code than him in the language where he is proficientI.
> The python visualizer tool has been basically written by vibe-coding. I know more about analog filters -- and that's not saying much -- than I do about python. It started out as my typical "google and do the monkey-see-monkey-do" kind of programming, but then I cut out the middle-man -- me -- and just used Google Antigravity to do the audio sample visualizer.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#768Earlier 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…
What your describing is already how a lot of science, technology, and engineering works!
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#769I 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.)
No it is not Leibniz/Euler/Galois. More like writing good papers that contribute to the broader understanding of a theory. I think if one evaluated a mathematicians research output and it consisted of mostly the kinds of problems AI has solved so far, it would give the impression that this person is somehow very good at picking accessible problems to target, but has not made a larger impact on the field.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#770Earlier quoted context omitted.
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 I guess sci-fi movies were right all along. Nobody in Star Wars knows how hyperspace travel works, it just works. The little robots know everything but almost no human bothers to care. People just carry on with their bickering lives while the bots whiz in the background, and these robots are astonished at human inefficiency every single time, but rarely do anything about it. And people are still people.