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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#731

Post by kypro »

lkey wrote: post #560
cubefox wrote: post #516

Earlier quoted context omitted.

> It is not 'logical' to imagine a hypothetical doomsday scenario that justifies a preemptive nuclear war You hallucinated the "preemptive nuclear war". He didn't say anything about nukes. That's your own invention. > Does it bother you that the people who are publicly cocksure that P(doom) is moments away 20% is not "cocksure". The "moments" is again an exaggeration.

I did not, I read kypro's (the OP I was replying to) bio, to whit: Every problem is a search problem. Nuke the data centers. P(doom) = 98.9% (Aug-2026) P(doom) = 98.2% (July-2026) P(doom) = 98.2% (Jun-2026) P(doom) = 98.5% (May-2026) P(doom) = 98.8% (mid-April-2026) P(doom) = 98.7% (April-2026) P(doom) = 98.7% (March-2026) P(doom) = 98.5% (mid-Feb-2026) P(doom) = 97% (Feb-2026) P(doom) = 94% (Jan-2026) P(doom) = 93%…

I've removed the "nuke the data centers" line now.

It's was an expression of my sentiment, not a policy position I'd support. I wrongly assumed that was obvious, but some people are making bad-faith assumptions about me and my sanity.

Not that it should need to be said on a comment thread where I am express concern about civilisation in a post-ASI world, but I obviously don't want to see a nuclear war.

Re: Ten advances in mathematics and theoretical computer science

#732

Post by [deleted] »

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…

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#733

Post by attila-lendvai »

tyre wrote: post #548
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…

We will get much better at manipulation and better at people “writing” things to justify their own feelings. What’s new about LLMs is that you can scalably manipulate people individually. It used to be that you could either have scale (speeches, tweets, interviews, website, etc.) or individual engagement (replying to mail/tweets/town hall questions.) Now you can pull the history and preferences of an individual, then…

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)

Re: Ten advances in mathematics and theoretical computer science

#734

Post by [deleted] »

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…

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#735

Post by anon373839 »

curt15 wrote: post #688
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…

Another interesting question is why the frontier labs are piling on pure maths, which has little direct economic value compared to something like law or improving the efficiency of their own models? How much OpenAI and Anthropic are paying to serve these models for ordinary users is the elephant in the room. A cynical take is that the frontier labs are trying their best to pump up their pre-IPO valuation through flas…

> Another interesting question is why the frontier labs are piling on pure maths

The reason is that the original scaling axes (parameters, training tokens, test-time compute) have saturated already, but RLVR (reinforcement learning from verifiable rewards) is still scaling well. And math has this nice property where you can synthetically generate arbitrary volumes of rewards to train the model, because math is self-contained and completely objective. Open-ended reasoning and analysis don't have that convenient property, and that is why progress is much slower outside of math and coding.

Re: Ten advances in mathematics and theoretical computer science

#736

Post by namr2000 »

class3shock wrote: post #712
namr2000 wrote: post #659

Earlier quoted context omitted.

I understand the frustration with the constant PR-hype these AI labs keep spewing out, but on other hand I just can't understand this sentiment at all. These are real problems mathematicians and computer scientists have been working on and were unable to make progress on. Now they have been given a new tool and using that tool have solved those problems. And its not just one or two problems, its many very difficult p…

"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 that was the open math problem I was most familiar with prior to its solution. Yitang Zhang, one of the worlds most renown mathematicians (famous for his lower bound on the twin prime conjecture) spent 8 years working on this problem with his advisor (who himself is a renown mathematician) and turned up completely empty handed. His advisor described it as a "waste [of] 7 years of his own life and my time" [1]. Of course, these two were not the only ones working on this problem for the almost 100 years its been open, but they should have sufficient credentials to show that they were not fools or amateurs.

And in a single afternoon an LLM disproved the conjecture. How is that not an extraordinary feat of technology?

> Who? And doing what?

A close friend is studying differential geometry in a PhD program. Sadly I doubt anything I say on his work will convince you, so I will instead offer two anecdotes:

Terrence Tao (widely considered the worlds greatest living mathematician) has said AI is precipitating "a crisis in the foundations of mathematical values and practices" [2].

Timothy Growers (fields medalist & one of the leading researchers in combinatorics) has said that the latest models are now at the point where they are "producing a piece of PhD-level research in an hour or so, with no serious mathematical input from me" [3].

You can find many more fields medalists and mathematics researchers with the same impression. If you look in this thread you can see bluesky/twitter threads from those who were actively researching some of these problems who are in shock at the solutions.

[1] https://www.math.purdue.edu/~ttm/ZhangYt.pdf [2] https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p... [3] https://gowers.wordpress.com/2026/05/08/a-recent-experience-...

Re: Ten advances in mathematics and theoretical computer science

#737

Post by wombatpm »

tyre wrote: post #548
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…

We will get much better at manipulation and better at people “writing” things to justify their own feelings. What’s new about LLMs is that you can scalably manipulate people individually. It used to be that you could either have scale (speeches, tweets, interviews, website, etc.) or individual engagement (replying to mail/tweets/town hall questions.) Now you can pull the history and preferences of an individual, then…

Biology would greatly benefit. We barely understand transcription and protein structure. And the straightforward systems that we know like insulin have complex post translational modifications. So while we have a map of the partial proteonome, we have barely scratched the surface on networks regulation and interactions.

Re: Ten advances in mathematics and theoretical computer science

#738

Post by charlie90 »

5555watch wrote: post #501
evenhash wrote: post #408

Earlier quoted context omitted.

> Whilst current models can't 'intuit' and come up with conjectures People keep saying this. Why? Surely the AI can complete the prompt “Generate new research questions based on these observations”? When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.

I like the illustration that the models are working on a convex hull of known information. Filling gaps with linear combinations of known facts and results. They can't exit the hull until the "intuition" starts spawning points outside the convex hull.

Thats how humans work, as well.

Re: Ten advances in mathematics and theoretical computer science

#739

Post by [deleted] »

rencrisa wrote: post #604
simonw wrote: post #274

The GitHub repo with the Lean formalizations just came out a couple of hours ago: https://github.com/openai/ten-proofs It also links to a paper written by an LLM where the model "reconstructs how the proof came together" based on the unpublished reasoning traces: https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf I wish they'd publish the prompts though!

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,…

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#740

Post by NiloCK »

haldujai wrote: post #726
throwaway27448 wrote: post #693

Earlier quoted context omitted.

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

It hasn’t bent already? 2022-2024 certainly seemed far more exponential than 2024 to present.

I find this astounding. 2024 to present thread is can write a coherent 15 line function to ... what exactly?

No future for research mathematicians othet than as tastemakers / agenda setters?

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