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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#851

As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.

our local AI models are already capable of running McDonalds.

Why aren't they doing so?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#853

The summarized chain of thought for this task (linked in the blogpost) is 125 pages. That's an insane scale of reasoning, quite akin to what Anthropic has been teasing with Mythos.

AFAIK, extremely long CoT is fairly routine for those math-finetuned private models. Also, is Mythos unusually verbose compared to Opus?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#854

Earlier quoted context omitted.

I’m not in academia myself, and I think AI solving all our problems ASAP is ideal, even if it means no humans get attribution. What I’m saying is that the ultimate goal of those in power are not these sorts of altruistic or even scientific pursuits, and that the massive labor disruption and hyper concentration of power in the hands of those who are proving time and again that advancement of science and benefiting the…

Oh good. But I think you're over estimating the 'concentration of power', and under estimating 'benefiting the whole of humanity' Most homeless people have smartphones, and consistent access to food and clean water. Your average 'poor person' in America has HVAC. An unimaginable luxury in the EU

> Your average 'poor person' in America has HVAC. An unimaginable luxury in the EU

Lmao, did HN just glitch out and start showing me Pieter Levels' tweets?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#855
post #224

The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question. The more I read about these achievements the more I get a feeling that a lot of the power of these models comes from having prior knowledge on every possible field and having zero problems transferring to new domains. To me the potential beauty of this is that these tools might help us break thro…

That's the whole point of LLM, connecting all the missing dots no single human could possible keep in working knowledge, even just for a subfield of mathematics alone. The era of polymaths is over for a reason, so we build a new one to tackle that. If LLMs can build on top of that once all remaining ones are found or if this stalls is yet to be proven, but humans stalled out there too.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#856

Earlier quoted context omitted.

These all are valid, noble points I also used to brood about while being young and financially supported by my parents.

> These all are valid, noble points I also used to brood about while being young and financially supported by my parents. Ah, the proverbial silver spoon. Sadly, I never had that luxury. If you look through my comments, you'll notice I'm more at the get-off-my-lawn point. Also, what happened? Real world wear you down and turn you cynical? It is possible to be hopeful and cynical at the same time. This tech is somethi…

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#857

Earlier quoted context omitted.

On the other hand, it is proven that if you need to count things, the only thing you can discover/invent is the natural numbers.

Really?! Care to cite a reference to that proof?

"The Nature and Meaning of Numbers" (1888) by Dedekind. He proved that any set of mathematical objects conforming to the second order Peano axioms is isomorphic to the natural numbers. Peano axioms basically formalize the notion of well-behaved (that is practically useful) counting numbers.

If you were to dig deeper, you'd get to the murky philosophical depths of foundations of mathematics, but I prefer to not go there. Practically, if you want to reliably count something, you end up with the natural numbers (or, maybe, their subset that ultrafinitists are trying to formalize).

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#858

Earlier quoted context omitted.

So, I've seen this mindset a lot lately... The answer is that we simply need to decouple the "right to exist" from "worth." You should have the right to exist and explore the world simply because you're human, not because you can use your skills to provide some sort of transactional value to someone else. Deprogramming so many people is going to be hard...

All sane and noble in theory, but in practice, how do you see that happening? Let's start with the first practical step: how do you dethrone the psychopaths in charge of the world who own about everything on Earth and have all the world's lethal force in their pockets?

Revolution? People used to do that.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#859
post #790

Earlier quoted context omitted.

That's already how civilization works. There's no one person that knows everything about (say) modern food production, from top to bottom. If it ever stopped working (because too much knowledge was lost somehow), most people would die. And yet the system seems fairly resilient. Mostly, only local knowledge ever seems to be necessary to keep the whole thing running. Super-intelligence (or even just super-normal-intell…

> There's no one person that knows everything about (say) modern food production True, but it is possible to assemble a team of people that does, with backup for each person. There's also teachers and written knowledge to educate new team members. That's what makes it resilient. I think that's a very different situation from what's decribed.

Agreed, the food production analogy doesn't really work because the issue is the scale of the problem. On the one end there's the realm where you need a few specialists and a small group could potentially figure the entire thing out from scratch given a bit of time and effort. And then at the opposite extreme there's the realm where everything is built on a giant pyramid of artifacts that currently work, just keeping each individual piece running day to day requires a dedicated expert, and the combined stack took hundreds or thousands of lifetime equivalents to develop.

The idea being that once a toolchain becomes sufficiently complex if you ever have to bootstrap it again for whatever reason you won't be able to speedrun the process the way you might naively expect. I think modern chip production likely already reached this point several decades ago. As evidence I'll point out that China only recently achieved EUV and remains several nodes behind despite directing an obscene amount of resources towards the initiative.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#860
post #714

Earlier quoted context omitted.

You lost me at “except billionaires”. I don’t see how Jeff Bezos benefits from this one much more than let’s say Terence Tao. Can a tech news stay a tech news, without getting bombardes with leftist subtexts all the time?

Billionaires are going to benefit from AI at the expense of everyone else. That's not leftist ideology, that's just a fact. That's happened with every technology that's ever been created. It happened with the industrial revolution. Why would it be different this time?

A few years ago i had laser eye surgery and now i can see well. Something that was not possible 50 years ago. Claiming that EVERY new technology comes at the expense of normal people is an absurd statement.
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