Ten advances in mathematics and theoretical computer science
781–790 of 1001 posts
Re: Ten advances in mathematics and theoretical computer science
#782Is there anyone here who can comment if these advances are meaningful, novel and how extraordinary these advances are? (E.g most PHDs, top 10% of professors etc. )
Re: Ten advances in mathematics and theoretical computer science
#783People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…
Sigmoidal, not exponential. It would be insane to assume an exponential curve
I mean, "sure, technically correct is the best kind of correct" - but where we sit on this right now? It certainly feels exponential.
A lot of this sort these sorts of posts are just "appeals to geometry" (aka "cope"). This is coming, it's coming hard. Now you need to decide what you want to do with your life in a world where your smarts aren't as special as they used to be.
This is hard (believe me, I know). But what one ought do is not eschew progress and cling to the delusion that things don't change, what one ought to do is try to see how they can leverage these tools for greater and greater accomplishments.
Re: Ten advances in mathematics and theoretical computer science
#784Earlier quoted context omitted.
This is not at the top as it is actively flagged by people that can't psychologically cope with the advances of AI. Hacker News is no longer a web site of an elite.
It’s never been clear to me why the HN algorithm isn’t public. It’s obviously nowhere near as complex as something like Twitter, and of course isn’t a trade secret. The fact it’s private only furthers speculation like this.
Probably to avoid manipulation, there is tons of stuff on HN that hopes to make it to the limelight through this forum channel
Re: Ten advances in mathematics and theoretical computer science
#785I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…
i think i agree, we are going to have /more/ math and now need /more/ mathematicians (we are seeing https://vibemathed.com/)
these LLMs are great are generating arguments but they don't ask questions, we will need mathematicians to shepherd them into more discoveries
i really want to see open weight models crack some breakthroughs
Re: Ten advances in mathematics and theoretical computer science
#786Earlier quoted context omitted.
It has had significant quality of life increases for me. I use LLMs for everything from: - travel and restaurant recommendations. my last few outings have been entirely LLM-advised and they turned out excellent. LLMs seem to have ingested every single Google review, photo, and menu of every business on Earth and can answer very nuanced questions like "is the garlic chicken at garnished with coriander?" - fitness, nut…
1. Do frontier lab LLMs make your rent cheaper? Groceries? Healthcare? 2. Do LLMs reduce the loneliness epidemic? 3. Do they reduce population aging in almost all counties around the world? 4. Do they reduce political polarization? 5. Do they bolster democracies? 6. Do they decelerate climate change and general environmental destruction? 7. Do they accelerate sustainability and the circular economy (not circular fina…
Actually, you are right. We are working with different definitions of quality of life.
The QoL improvement from LLM is somewhere in the ballpark of going from dumb phones to smart phones for an average person (able-bodied, local to the area etc). It's nowhere near Haber-process or penicillin.
Re: Ten advances in mathematics and theoretical computer science
#787Any computable problem will eventually fall to computers. LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like it’s now exponentially easier. That still doesn’t mean that all math is…
In my opinion, after seein the Jacobian conjecture go, the Riemann hypothesis only has about a year left. I’m not sure if people just aren’t as aware, but the Jacobian conjecture practically was on par with those other great problems.
Whether or not it’s on par famously or difficulty level doesn’t predict whether the others will fall. They’re unique problems and math isn’t linear - the Jacobian it managed to find a counterexample and relied on other proofs that had been developed showing >3 case == 3 dimensional case. However, the Riemann may not fall in the same way because it may actually be true or the surrounding math isn’t quite ready to tackle that problem.
Re: Ten advances in mathematics and theoretical computer science
#788Earlier quoted context omitted.
I want to preface my response by saying that I don't buy most of what the AI labs say. I don't think that LLMs will replace most white collar labor for example. I also find many of the practices of these labs to be abhorrent. However, all of these opinions are orthogonal to the fact that LLMs have gotten extremely good at mathematics. > Who says no one was making progress? Let's look at the Jacobian conjecture, since…
[1] is... a read (sounds like a nightmare student, or research prof, or both). A dumb question but by my reading, that work took place 35 years ago, has there not been anything more relevant since then? Something Claude could have for instance used as a basis for what it did? Does seem like a feat however you cut it though. Thank you for the thoughts and references.
Yeah the Yitang Zhang situation just sounds like a total nightmare all around.
There was definitely at least some progress on the problem. I get the general sense that there were potential counterexamples that were close but not quite enough, and that its possible (or even likely) that Claude built on those in order to construct its solution. I also get the sense that when Zhang was working on the problem it was believed that it would be proved true, but since then there were bounds found on the problem that pointed researchers to believe it was false. I am not a research mathematician in this field though, so I could definitely be wrong.
Also, in fairness to Zhang, I believe the dissertation he ended up writing was focused on the 2D case in particular, which is still unsolved (the counter example is only for 3D and above). I cannot imagine that anyone looking at the 2D problem was not also looking at the general case as well though.
Re: Ten advances in mathematics and theoretical computer science
#789Earlier quoted context omitted.
It sounds like they are making a clear argument: models are getting worse for certain domains even while they are getting better at others. I don't know if I agree with that but it doesn't seem like an irrational claim and does seem credible to me.
I just don’t think it’s true, or is significant enough to matter to the direction of travel of AI even if there were something to it. It’s another cope post being lobbed at the idea of AI going somewhere and I’m sick of them.
"The sooner you can be broken out of your denial about all this the better, and we can start actually taking you seriously."
Re: Ten advances in mathematics and theoretical computer science
#790Earlier quoted context omitted.
This is the Lean proof that a nonsofic group exists (34,440 lines): https://github.com/openai/ten-proofs/blob/main/NonSoficGroup... This is an extraction from that of the actual theorem statement (39 lines): https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d...
It may be for this theorem there's a succinct description, but still needs to be checked carefully. However, there are others that are non-trivial.
In some cases you're right, but I think that's often a symptom of mathematics in Lean being relatively immature (i.e., it will get much easier with time). Even then, verifying the statement in Lean is correct is still much easier than verifying the natural language proof is correct.