Ten advances in mathematics and theoretical computer science

Post by nightsd01 » Tue, Aug 04, 2026, 3:52 AM UTC

hibikir wrote: post #797

mekael wrote: post #654

Earlier quoted context omitted.

But who benefits from that economic growth? If it's only the capital owning class, and the rest of us are left in the dust, then the growth is irrelevant. I ,for one, have read enough history to know that it's never the proles who end up benefiting.

I suspect that you have not read enough them. Ask someone in China (which yes, still has a capita owning class) if the proles were better off 50 years ago or now. The only real probes we have now in the west is that we have failed at housing, precisely because instead of growth, we have made many choices to increase returns for old people, and insufficient taxes for real estate.

Post by aorloff » Tue, Aug 04, 2026, 4:02 AM UTC

gerdesj wrote: post #724

plaidfuji wrote: post #674

Any 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…

"Any computable problem will eventually fall to computers." By definition. Its those pesky NP jobbies that get in the way.

Post by andai » Tue, Aug 04, 2026, 4:24 AM UTC

chatmasta wrote: post #804

sothatsit wrote: post #535

People 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…

I expect we can squeeze a lot more exponential out of LLMs because they’ve basically shown that human “consciousness,” insofar as it’s composed of knowledge and rules for synthesizing that knowledge, can be represented mathematically in a very high dimensional space. Why does this “just work?” Nobody really knows, but it clearly does. However, I also expect this squeeze will come at an increasingly expensive price —…

Post by andai » Tue, Aug 04, 2026, 4:28 AM UTC

MostlyStable wrote: post #644

DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

From a mathematician who was intimately familiar with some of these problems [0] >I don’t understand it yet. Maybe it’ll take me an afternoon to check all the calculations, but what would still be missing is why this was an approach that would’ve made sense in the first place. Is there some broader context or theory within which this would’ve been the obvious thing to do? What other results can be proven using these…

Post by andai » Tue, Aug 04, 2026, 4:37 AM UTC

ultimatefan1 wrote: post #118

one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00…