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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#771

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

#772
post #575

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.

Re: Ten advances in mathematics and theoretical computer science

#773
As someone who’s spent the last year deploying PQC cryptosystems, it sure would be a kick in the ass if they find a faster solution to the nearest vector problem. I mean that’s why we’re going hybrid, but still.

(Well to be more precise we’re going hybrid because of unknown SCAs.)

Re: Ten advances in mathematics and theoretical computer science

#774

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.

How much investment has gone into OpenAI versus mathematics research in 2025 for example? Probably 100x?

The AI results are clearly impressive. But these sorts of things are also in the ballpark of what human effort could solve given enough attention and time. Though it is hard to say.

Re: Ten advances in mathematics and theoretical computer science

#775

Earlier quoted context omitted.

"I understand the frustration with the constant PR-hype these AI labs keep spewing out" Apparently you don't. "These are real problems mathematicians and computer scientists have been working on and were unable to make progress on." Who says no one was making progress? Who says openai has made progress? How would anyone not working on these specific problems, witho the time to dig into openai's claims, be able to tel…

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.

Re: Ten advances in mathematics and theoretical computer science

#776
post #727
post #721

Earlier quoted context omitted.

Advocating for nuclear war as a means of 'harm reduction' should be causing you serious cognitive dissonance. There are dozens of escalating, yet fundamentally less destructive means to prevent a data centers from continuing to operate (if that's the goal). Not starting at those more modest interventions is political malpractice and in opposition to your harm reduction narrative. Your P(doom) 'probability estimates'…

> Advocating for nuclear war as a means of 'harm reduction' should be causing you serious cognitive dissonance. If you're referring to the "nuke the data centers" line in my bio, that's tongue in cheek. It's an expression of my sentiment towards AI at the extreme. To be clear, I don't think any country should seriously be considering dropping nukes on data centers. Targeted strikes on data centers operated by rogue p…

> If it can be controlled then it will concentrate power like never before, and I believe this will destabilise civilisation.

We already live in a reality with unprecedented concentration of wealth and power in the hands of the very few. This process has produced horrific violence and ended civilization for tens of millions.

The actual impact of AI, so far, has been redistributive upwards (solely through speculation, not via productivity or displacement).

This kind of problem is a standard human social ill. Its solution is social too.

Redistributive economic and political action can equalize power and wealth disparity. AI is incidental in this story.

Your understanding of AI as an isolated perfected intellectual djinn lacks a consideration of the existing and ever-changing labour and social relations that give AI responses meaning in the first place.

It is a compressed, multi dimensional manifold containing the structure of relations between objects. Responses are a reification of a point in that space.

Navigating the space can be interesting, but it is a poor substitute for the relations themselves.

Very few people yearn for the endless, frictionless solipsism silicon valley promises (AI + slave robots), and those that do are overrepresented in your social circles. The books they write are a study in psychological projection and limited political education.

> I've been writing endless comments more recently urging people worrying about their jobs/careers to stop and just spend the next few years with those they love.

This is good advice generally. But it isn't organizing. Join something, meet up, drink bad coffee, listen, take notes, advocate to fix just one bad thing in your community, feel your impact reverberate through the world, and then notice how much easier it is to shake off despair.

If you don't have a community, then no wonder everything feels like its ending.

Re: Ten advances in mathematics and theoretical computer science

#777

Interesting how HN promoted this post to the front page again with a fake submission time. There are comments two days old, seems weird why they'd want this post specifically to get more traffic.

not very interesting, its the second chance pool. its not a conspiracy of ycombinator vs. openai. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

Of course that’s the mechanism and this kind of repost is not unique, but it is still relevant to note that the small HN committee made an exception for this one.

Re: Ten advances in mathematics and theoretical computer science

#778
post #745

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.

What even is the left though in the US? I haven’t watched any TV in decades, and the online content is entirely algo driven, so I don’t know what is happening.

Re: Ten advances in mathematics and theoretical computer science

#779
post #743

Earlier quoted context omitted.

It seems that a lot of folks misunderstand the guarantees that lean provides. I just want to state that having "lean proofs" that build (checks) does not mean the actual real theorems we care about hold. Ignoring lean kernel bugs, ultimately a human (not an agent) has to verify the lean encoded theorem statements (specs/specifications) that the lean proofs are checked against. For non-trivial theorems such as these,…

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.

Re: Ten advances in mathematics and theoretical computer science

#780

Earlier quoted context omitted.

My wife is working on her PhD in microbiology now, using OpenAI to implement her research ideas. Genetics is just too much data, and she eats through tokens like nobody's business. I thought I was careless with them, but she barely lasts a full day before exhausting her quota. There's definitely a lot of value there, but dealing with the data problem is a big obstacle in biology. I can only imagine what she could get…

What makes it so token hungry? Is she directly using the LLM for genome analysis rather then having it write the data analysis algos?

Likely not using / managing context windows properly and then having it re-read data it’s already gone through
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