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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

#271

Post by slashdave »

globular-toast wrote: post #265
slashdave wrote: post #216

Earlier quoted context omitted.

Seriously? We already know how to solve all of these issues. What we lack is collective political will.

We only know how to do it by means of considerable sacrifice. That's why nobody wants to do it. Solving the issue would be doing it without sacrifice or somehow getting us to do it regardless.

> We only know how to do it by means of considerable sacrifice

Little sacrifice actually

> Solving the issue would be doing it without sacrifice

So... you are expecting magic?

LLMs cannot create resources out of thin air.

Re: Ten advances in mathematics and theoretical computer science

#272

Post by matt_daemon »

antirez wrote: post #100
robinhouston wrote: post #87

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

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.

Re: Ten advances in mathematics and theoretical computer science

#274

Post by simonw »

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It also links to a paper written by an LLM where the model "reconstructs how the proof came together" based on the unpublished reasoning traces: https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf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!

Re: Ten advances in mathematics and theoretical computer science

#275

Post by Phemist »

black_knight wrote: post #240
c7b wrote: post #211

Earlier quoted context omitted.

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

If the proofs are formally verified by a proof assistant (Agda, Roq, Lean, ⋯), I see no reason we would need to know how these came about. All the information needed is in the proof.

What if the AI has discovered some new function F that allows it to generate (insanely large) proofs for a ton of theorems in a ton of different fields. Wouldn't you like to know more about this `F`? That seems to be the real innovation in this case. How much about it could be gleaned from the individual proofs themselves? What if this `F` is actually simple enough to be digestible by humans?

Re: Ten advances in mathematics and theoretical computer science

#276

Post by root_axis »

antirez wrote: post #100
robinhouston wrote: post #87

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

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.

[flagged]

Re: Ten advances in mathematics and theoretical computer science

#277

Post by c7b »

jsenn wrote: post #252
c7b wrote: post #238

Earlier quoted context omitted.

Because the math isn't solely about the proof being correct. You don't need to take my word for it, here's one of the most famous living mathematicians' take on it: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...

I don’t see Tao suggesting what you have suggested there. Instead he suggests that humans responsibly disclose AI use, and that mathematicians develop a set of norms to deal with an overabundance of AI generated results. For example, he suggests that authors should be able to discuss their results in detail to demonstrate understanding before publication.

I agree with your reading of the presentation and I mostly agree with the presentation - but I believe the recommendations should go a bit further than they do there.

Re: Ten advances in mathematics and theoretical computer science

#278

Post by c7b »

somenameforme wrote: post #250
c7b wrote: post #238

Earlier quoted context omitted.

Because the math isn't solely about the proof being correct. You don't need to take my word for it, here's one of the most famous living mathematicians' take on it: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...

I can't help but wonder about the human motivation there though. For instance as it became increasingly clear that LLMs were capable (and becoming ever more capable) of competently solving meaningfully complex software development tasks, suddenly then there came to be a lot of talk of 'prompt engineering' as a skill. The chronology doesn't make a ton of sense unless you consider that the main motivation may have been…

I think those concerned about ensuring a place for human mathematicians usually go in different directions than my suggestion, at least those I've seen so far. Like this post that was recently featured on HN: https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...

My perspective is more like a FOSS philosophy for math. Even if a closed version has the same immediate effect, it's just better for everyone if everyone can look under the hood and tinker with it.

Re: Ten advances in mathematics and theoretical computer science

#279

Post by simianwords »

mathisfun123 wrote: post #268
simianwords wrote: post #220

Earlier quoted context omitted.

Hmm. But this level of skepticism looks performative and seems to serve as a signalling thing rather than a functional thing. You do you though. If OpenAI solves the millenial problems, my skepticism will only be restricted to the correctness of proof. Not that it was "marketing" haha

> If OpenAI solves the millenial problems, my skepticism will only be restricted to the correctness of proof. Not that it was "marketing" haha Company X does not make money from proving theorems but does make money from selling you a service which supposedly proves theorems. Company X then proves some theorems and explicitly calls out they were very cheap to prove using its service. And you think you're actually clev…

do you think you are clever for being skeptical about LLMs if OpenAI comes up with a correct proof of Reimann's hypothesis? "but you shouldn't trust OpenAI because something something marketing"

i would classify you as a flat-earther if that happens.

Re: Ten advances in mathematics and theoretical computer science

#280

Post by [deleted] »

NitpickLawyer wrote: post #198
danparsonson wrote: post #192

Earlier quoted context omitted.

Never understood all this talk about moving goalposts - you understand that's how science works, right? We improve, we learn, we recalibrate our expectations based on what we've learned. If we never "moved the goalposts", we'd be stuck scoring the same goals over and over.

> We improve, we learn, we recalibrate our expectations based on what we've learned. That's not what people mean when they say "moving the goalposts". It means that people are adamant that something wasn't important/hard/impressive once the "AI" solves it. And then they come up with another thing that needs to be solved in order to prove it is important/hard/impressive. And once that happens, they do it again. And ag…

[deleted]
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