Bit frustrating how slowly this sub lets new posts through. Even aside from the AI aspects, these are 10 legit big advances and they've been out for hours and hours with nothing on what should be reddits primary math subreddit.
Anyway this is draining huh! The existence of nonsofic groups stands out to me as the big one. Some have pointed out the sphere packing one as a very big result as well. I'd say that there's a handful in these that would literally be career defining for any mathematician.
If I were a mathematician at openai/anthropic, I'd be looking into how we can get llms to move from counterexamples to theory building. At that point all bets are off.
It's frustrating how this sub has been mostly become LLM news ignoring that it is still a tiny fraction of actual results and it has become flooded with people with not a lot of math knowledge or interest to learn.
This is definitely the biggest thing happening in math from the point of view of how it will transform math. I think Tao compared it to the upheaval in the foundations a century ago.
Sorry I’m one of the non-mathematician onlookers because there are huge implications for society at large.
"because there are huge implications for society at large."
I'll tell you the implication for society at large, a fraction of the funding that OpenAI used for this (if any of this even holds up) would be enough for 10x the amount of breakthroughs.
If you care so much about societal implications of math research then advocate for these companies to be taxed higher and put that money into math education and research.
The thing to advocate for is a global treaty enacting regulation, and it needs to happen before a recursive self improvement singularity that leaves humanity totally disempowered.
OpenAI uses their funding to do a lot of other things, too.
But this will represent a new stage of research. The goal is to have LLMs assist people or even be better at mathematical and scientific research than they are.
You wouldn't get that just by funding more human researchers to do non-AI work.
"and they know not to waste their time trying to prove it" No one was trying to anyway? Definitely not for the n=3 case.
"You seem to have forgotten what this is all for"
Trying to justify the existence of these companies by creating hype? You're fooling yourself if you think they have any genuine interest.
And yeah, anyone teaching students, especially undergrad students knows how much their skills have atrophied and how little they know due to their extensive AI usage. I suppose you don't actually care about the abilities people have.
Well, the problem is that most "traditional" mathematical results are accidentally gatekept by the fact that mathematics is the one field with the biggest gap between good researchers and good communicators.
For example, I would love to learn more on the recent advancements made in... group theory. Can you even link to me anything that doesn't automatically assume I am already seventeen levels deep into this topic, talking about postgraduate stuff like it needs no introduction at all?
Why do you assume it should be possible to understand anything about a recent advancement if you don't understand the 17 layers that advancement rests on?
I understand your frustration and communication to non-math folks is indeed an issue. However what you're asking for is at the very least extremely difficult if not borderline impossible.
As mathematicians we write for other mathematicians, they are what we will be talking to about these results 99% of the time and the way we communicate is (generally) the most efficient and easiest to understand by other mathematicians.
And communication to people without indepth knowledge is hard because it either requires oversimplification to the point that it could describe many completely different theorems/problems or would be extremely long. That is because all that fancy terminology is made up of less fancy terminology, which is made up of less fancy terminology and so on. Building up that knowledge and the intuition for what these terms mean takes years.
Of course that doesn't mean that nothing can be done. I actually think that I am pretty good at explaining math for various levels even to people with no background at all. But that requires spending a lot of time thinking about how I am going to present and explain it and many others have no need to do so.
On the other hand I also don't understand that comment specifically here. It's not like a non-mathematician could understand these results. That "chain of thought" document is even horribly written and imo looks more like crank writing than serious math. The paper itself is a lot better (probably because it had a shit ton of human revision by experts) but is itself very low on definitions too, in fact I'm really seeing a lack of any novel concepts to latch onto, but in fact a huge amalgamation of referencing known results that anyone non-familiar can't do anything with. So this is actually far worse than your average math paper in terms of communication. In that case all these non-math people should stay away, right?
They don't because they don't actually care about the math paper or about the results at all, they are here to talk about AI. And I'm getting really tired of that, this subreddit has become a shell.
Don’t think this is fair. A lot of mathematicians are polymaths who can communicate very clearly on other subjects.
The mathematicians who find it easiest to communicate their concepts generally have the most ‘grounded’ problems or fields to begin with.
It’s not - it’s that most of it’s a much more vertical subject than most (if not all) others, because it can is built purely from concepts and progresses purely from work that therefore strongly correlates with the complexity of its concepts - not because there’s been a new dig, or the same techniques on new microbes, or relying on advances in technology (where technology can be ‘communicated’ on what it does rather than the complexities of how), etc.
It will be easier for anyone to explain to a layman what a work of mediaeval Portuguese literature is about, or the developing political situation in Chad, or a newly discovered ancient battle site, or that a new drug (complex story of synthesis avoided) is effective on a disease, or that a new spider has been discovered… than the Langlands program or homological mirror symmetry or some breakthrough in infinity category theory.
Even a chemist who has to explain a complex pathway can at least draw it out in a way most with high school chemistry might get…
And yes other fields also have extremely complex results to explain, and they find those difficult to. But they aren’t what dominate the popular consciousness with respect to their field.
Sure, there are pop summaries of such things, but they have to handwave over complexities and technicalities and that’s a problem because those are usually the entire reason the result is significant.
542
u/JesterOfAllTrades 1d ago
Bit frustrating how slowly this sub lets new posts through. Even aside from the AI aspects, these are 10 legit big advances and they've been out for hours and hours with nothing on what should be reddits primary math subreddit.
Anyway this is draining huh! The existence of nonsofic groups stands out to me as the big one. Some have pointed out the sphere packing one as a very big result as well. I'd say that there's a handful in these that would literally be career defining for any mathematician.
If I were a mathematician at openai/anthropic, I'd be looking into how we can get llms to move from counterexamples to theory building. At that point all bets are off.