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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

#911

Post by pluc »

xbmcuser wrote: post #625
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…

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

Even a broken clock is right twice a day.

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

#912

Post by csheehan10 »

qnleigh wrote: post #798
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…

Can you describe what the reaction to these results has been like in your department? Obviously many people are excited, but what else? How do grad students feel about this? Are any professors getting worried about becoming obsolete?

I am a PhD student in mathematical statistics. The people I have spoken too think this is very exciting and cool. There is also a sense of unease about what this will mean in terms of being a mathematician, and what effects it will have on our future employment.

I am also a little worried about what it means for your training as a junior PhD. Often you would try and solve a problem your advisor thinks is doable that they assign to you as a learning exercise. It may be more and more difficult to find problems that a junior PhD can solve but that AI can not. Tim Gowers has written about that here: https://gowers.wordpress.com/2026/05/08/a-recent-experience-...

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

#913

Post by hajile »

aussieguy1234 wrote: post #557

So we've got the proof, what are the practical applications of this?

It proves the limit doesn't exist, but doesn't seem to show how to find one of these more optimized limits. Given that nobody has ever brute-forced a counter-example, it may be that calculating these solutions is P=NP hard which would mean sticking with the status quo unless we find a good algorithm to calculate it on quantum computers and can actually get quantum computers large enough to work on the problem.

It's interesting as a math problem and test of AI, but not much else IMO.

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

#914

Post by jdub »

jeremyjh wrote: post #882
ricardobayes wrote: post #775

Earlier quoted context omitted.

IMO, it's due to some problems being better documented, with more well-documented, previous research available. LLMs don't really create novel mathematics, they mostly "connect the dots". LLMs by design are not coming up with anything new, unless by statistical probability, aka "brute forcing". I don't want to minimize LLMs capabilities, it's pretty cool they are doing this, and it's useful from a research point of v…

> LLMs don't really create novel mathematics, they mostly "connect the dots". That is not what the mathematicians are saying. I don't have the knowledge to evaluate this myself, but a number of mathematicians - for example, in the SP - are saying it goes further than that - they really do introduce novel ideas. Of course everything is based on and inspired by some previous work, but that is true of all human mathemat…

Reinforcement learning perturbs the model such that the token prediction process (inference) tends towards the desired result.

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

#915

Post by anthonyrstevens »

pluc wrote: post #911
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

Even a broken clock is right twice a day.

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

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

#916

Post by Windchaser »

pishpash wrote: post #807
worldsayshi wrote: post #754

Earlier quoted context omitted.

Why can't we (or AI) invent ways to explain information that makes it much more digestible? And the solutions simpler? Why is it necessary to continue to increase complexity when we get better intelligence? Can't we find more simple solutions? Or at least more explainable.

Is particle physics digestible even if it is explainable? Some things are not simple, cannot be not abstract, and will not be understood by most, or all, people.

Or biochemistry. It’s complex, and there’s nothing we can do about it.

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

#917

Post by anthonyrstevens »

fc417fc802 wrote: post #859
lefra wrote: post #790

Earlier quoted context omitted.

> There's no one person that knows everything about (say) modern food production True, but it is possible to assemble a team of people that does, with backup for each person. There's also teachers and written knowledge to educate new team members. That's what makes it resilient. I think that's a very different situation from what's decribed.

Agreed, the food production analogy doesn't really work because the issue is the scale of the problem. On the one end there's the realm where you need a few specialists and a small group could potentially figure the entire thing out from scratch given a bit of time and effort. And then at the opposite extreme there's the realm where everything is built on a giant pyramid of artifacts that currently work, just keeping…

Speaking of pyramid (shapes), this reminds me of an idea in Robert Silverberg's Majipoor series - there's a 30-mile high mountain with populated cities all the way up to the top whose weather and temperature is controlled by 8,000-year-old-tech established by the original colonizers. My memory is that nobody at the time of the series' events knows how to operate the tech - it just works.

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

#918

Post by bbor »

black_knight wrote: post #344
bbor wrote: post #250

Earlier quoted context omitted.

math more like an art than a science. That’s a fun turn of phrase, but hopefully we can all agree that math without scientific rigor is no math at all. we likely need some new kind of math. Imo, it's unlikely that an LLM will somehow invent it. Do you think it’s possible/likely that any AI system could? I encourage us to join Yudkowsky in anticipating the knock-on results of this exponential improvement that we’re li…

Math is not based on science! Maths follows logical (or even mathematical) rigour, not scientific rigour!

You're just using a different definition of "scientific". If Math isn't a science, then it cannot follow logical rigor. Math and philosophy are both sciences, even if they differ qualitatively from the natural and human empirical sciences.

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

#919

Post by Windchaser »

energy123 wrote: post #659
isotypic wrote: post #608

Earlier quoted context omitted.

I mean, my reaction to God coming down and saying they were bored of being God and instead they would just sit around and answer all of the mathematician's questions would largely be the same, so yes, who cares if its God's book or the machines Xeroxed copy? "The Book" is more interesting to me if I am the one coming up with the ideas to fill it in. Maybe this is a bit egotistical, but I'd like to think it is allowed…

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 have a musician friend who likes to say that good artists overwhelmingly make art for their own benefit. Not to advance the world or blow people’s minds, but because something inside of them needs to come out, and art is how they express it. And that part of us isn’t going to go away.

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

#920

Post by pluc »

anthonyrstevens wrote: post #915
pluc wrote: post #911

Earlier quoted context omitted.

Even a broken clock is right twice a day.

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.
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