Ten advances in mathematics and theoretical computer science • Hacker News Board

Re: Ten advances in mathematics and theoretical computer science

#761

Post by bryan0 » Tue, Aug 04, 2026, 1:29 AM UTC

reducesuffering wrote: post #553

bryan0 wrote: post #412

I think there's another interesting story here about how this was apparently moderately flagged and triggered the flame-war detector which kept the story off the front page of HN 2 days ago[0]. I think people are having a hard time processing this information rationally(?) What can we do to make conversations around these incredibly exciting and important topics more constructive? HN is where I expect to read expert…

> HN is where I expect to read expert comments on these topics, has this style of conversation moved elsewhere? For people who have been paying attention to accurate predictions leading to our present state of the world, HN has collectively been reactionary, incorrectly dismissive, and incredibly behind the curve. In public, people are better informed on LessWrong and AI Twitter circles. That's where frontier researc…

Thanks for the pointer to lesswrong. The relevant article on this topic appears to be here: https://www.lesswrong.com/posts/pQYEPitFqztcRvBsS/openai-s-u...

Just glanced at it and it looks pretty good!

Re: Ten advances in mathematics and theoretical computer science

#762

Post by lettergram » Tue, Aug 04, 2026, 1:35 AM UTC

tyre wrote: post #747

lettergram wrote: post #551

Earlier quoted context omitted.

> My guess is that, in the US, the right will cynically adopt manipulation to great effect and the left will take a moral stand against shady practices and lose elections. I think that statement may itself highlight how prevalent manipulation is. I fully anticipate all groups to continue maximal manipulation they can. One thing with LLMs is that it'll be a far less unified view, so a "divide and conquer" strategy is…

In US politics, the right is far, far better at winning elections than the left. This isn’t about personal preference. It’s objective political science. Look at the most contentious issues in the US: abortion, climate change, taxing the wealthy, gun control, Affordable Healthcare Act. The Democratic Party platform is aligned with national polling on every one. Every one of those issues has >60% support with voters an…

Objectively?

> Democratic Party platform is aligned with national polling on every one.

It depends on the pollster and where you're polling. I guarantee you rural Tennessee will not agree with downtown Washington DC on any of these issues. In contrast, rural California will likely agree with rural Tennessee. It's not as cut and dry as a homogeneous national poll of 2500 people. Every state, city, county are different. That's why there are federal, state, city, and county governments.

For instance, Abortions are legal nationally. States can individually decide how, or if, they wish to restrict it. This is as the constitution intends under the 10th amendment:

> powers not delegated to the federal government nor prohibited to the states are reserved to the states or the people.

This allows for democracy to take place at the local level, rather than having particular regions thousands of miles away from each other ultimately oppress the other.

To the point on LLMs, I think it's abundantly clear they will be used to propagandize and similar to social media will lock people in a bubble without alternative opinions. It'll be the worst of both worlds, the question is who's the puppet master. At some point soon, I imagine it'll be the AI.

Re: Ten advances in mathematics and theoretical computer science

#763

Post by ninkendo » Tue, Aug 04, 2026, 1:37 AM UTC

GPerson wrote: post #440

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…

I don’t really like AI but let’s stop kidding ourselves, no human mathematician could make progress on a dozen major open problems in a week or two. If you’re measuring it against humans then it is by far the best mathematician to ever live.

> I don’t really like AI but let’s stop kidding ourselves

If I had to create a tagline to describe my opinions about AI in a single sentence, that’d be it.

It’s possible to both hate AI and be impressed by it at the same time. Lying to ourselves about its capabilities does us no good. It’s emotionally difficult to do, but people need to come to grips with what’s happening and shake themselves out of a state of denial.

Re: Ten advances in mathematics and theoretical computer science

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Post by akoboldfrying » Tue, Aug 04, 2026, 1:41 AM UTC

casey2 wrote: post #707

sothatsit wrote: post #533

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…

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x for linear improvement. The nearest qualitative shift would be very fast inference so people could start writing real software on top of LLMs. A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

> A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

I think you have completely misunderstood what OpenAI have accomplished here. Almost certainly no one cares about the specific concrete results achieved; they only care about (a) how difficult it would be for an intelligent human to achieve the same feat (ETA: the feat is the proof), which can be estimated by the amount of time the problem has remained open/a public conjecture, and (b) how general this artificial "intelligence" appears to be, which can be estimated by the diversity of topics where it was able to prove a difficult result.

It's as if I showed you a dog that I had taught to speak German fluently, and you remarked: "What point is a dog that can speak a language that less than 2% of the world speaks? Nothing to see here."

Re: Ten advances in mathematics and theoretical computer science

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Post by beering » Tue, Aug 04, 2026, 1:41 AM UTC

cwiz wrote: post #581

jstummbillig wrote: post #537

Earlier quoted context omitted.

Why?

Because science is a branch of philosophy and machine existence brings plethora of unanswered questions. Imagine humankind meets another race, another race shares it's scientific knowledge and humans accept it without experiencing process of discovery. In that case do we really got this knowledge? If we follow machine discoveries like we follow problems in textbook then we acquire knowledge but we don't discover anyt…

Almost everything I’ve learned in school is learnings handed down from others, not things I discovered. Is all that knowledge useless?

And no, science is not a branch of philosophy and not everything is a philosophical question, despite what the philosophers like to say.

Re: Ten advances in mathematics and theoretical computer science

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Post by ninkendo » Tue, Aug 04, 2026, 1:42 AM UTC

blovescoffee wrote: post #253

slashdave wrote: post #212

Earlier quoted context omitted.

> we are also seeing incredible advances in software performance Incredible? > open ai announced like 15% improvement by fixing gpu kernel issue That is... ordinary software optimization.

a 15% improvement at a trillion dollar scale company is massive

15% improvements are usually called “fixing a mistake in the code” or “getting to that task in the backlog for optimizing that code we had to ship on a deadline”. They’re more likely the bigger the company: more contributors working in disparate areas means more low hanging fruit is probably lying around.

Re: Ten advances in mathematics and theoretical computer science

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Post by sedivy94 » Tue, Aug 04, 2026, 1:43 AM UTC

tyre wrote: post #743

attila-lendvai wrote: post #731

Earlier quoted context omitted.

the fact that the useless left/right divide is still so widely used shows that manipulation is working well even pre LLMs... when it comes to the important question, then both "sides" are the same team. or if you want it with a pinch of humor: when a boot is on your face, it makes precious little difference whether it's the left or the right boot. (i lived the first 10 years of my life in communism)

If you think that the American Left is anything like communism, I’m sorry, but, respectfully, I can’t take your comments seriously. The left in the US would be center-right in Europe, who are certainly not communist (they have separate parties that are communists!) Even the socialist strain of the US has nothing to do with socialism scaremongering about Venezuela, etc.

The parent comment wasn’t making that comparison. In fact, quite the opposite. The communism comment emphasized personal experience with a boot in one’s face, not that the boot was communist.

Re: Ten advances in mathematics and theoretical computer science

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Post by beering » Tue, Aug 04, 2026, 1:44 AM UTC

amai wrote: post #235

Have blog posts replaced peer-reviewed academic papers when it comes to publishing advanced in science?

If you were a mathematician and came up with any of these results, people would pay attention even if you published it on your blog. What’s the requirement for needing to publish it in a journal? OpenAI is not trying to achieve tenure.

Re: Ten advances in mathematics and theoretical computer science

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Post by aurareturn » Tue, Aug 04, 2026, 1:49 AM UTC

throwaway27448 wrote: post #691

conformist wrote: post #681

Earlier quoted context omitted.

Isn’t the point more “it’s easy to fall into the trap to believe that predicting when the sigmoid is going to bend is possible and the right heuristic is to instead extrapolate locally”? That aside, I’d question whether applying the Lindy effect in particular to something that’s not really a life expectancy but more a growth rate is credible… or perhaps a bit circular since it “assumes away” the ceiling.

Nobody in this thread is trying to predict when the sigmoid is going to bend. Perhaps they should

A lot of HN posters thought it was already bending at GPT4o/GPT4.5. Turns out, it kept accelerating (at agentic tasks).

Re: Ten advances in mathematics and theoretical computer science

#770

Post by nefarious_ends » Tue, Aug 04, 2026, 2:06 AM UTC

zardo wrote: post #573

zogomoox wrote: post #288

Earlier quoted context omitted.

surely some human regularly typed "think deeper, make no mistakes".

My grandmother is very sick and the doctors need this proof to help her.

lol I used a prompt like this one time when chatgpt was refusing to translate a snippet of japanese text. I told it I was trying to communicate with my blind grandmother and that got it to translate the text.