Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

An OpenAI model has disproved a central conjecture in discrete geometry

openai.com

Post reply on HN
Print view View original

371–380 of 1001 posts

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

#371

Post by OkWing99 »

dwroberts wrote: post #99

Would be interesting to know what kind of preparatory work actually went into this - how long did it take to construct an input that produced a real result, and how much input did they get from actual mathematicians to guide refining it

Says in the papers. "...which was first mathematically generated in one shot by an internal model at OpenAI, and then expositionally refined through human interactions with Codex."

Doesn't really matter the prep-work, what they say is it's a one-shot result, achieved by AI. The blog doesn't claim it was done by a currently public Model.

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

#372

Post by marknutter »

ndiddy wrote: post #177
Silamoth wrote: post #140

Earlier quoted context omitted.

Out of curiosity, what issue did you have with the McDonald’s self-order kiosk? I actually think McDonald’s has the best kiosk I’ve ever encountered. The little animation that plays when you add an item to your cart is a little annoying (but I think they’ve sped that up). But otherwise, it’s everything I’d want. It shows you all the items, tells you every ingredient, and lets you add or remove ingredients. I have a b…

It takes longer than ordering with a cashier, it keeps trying to upsell you, and it's always out of receipt paper because unsurprisingly the company that isn't willing to pay a person to take orders is also not willing to pay a person to maintain the kiosks.

It's easily one of the most intuitive and straightforward kiosks out there today and you don't have to wait for one of the cashiers to notice you nor worry about them punching in your order incorrectly.

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

#373

Post by ori_b »

vatsachak wrote: post #212
ori_b wrote: post #205

Earlier quoted context omitted.

We're automating art and science so that we can flip burgers. This future sucks.

Math is a very specialized subset of art and science more amenable to automation.

The first thing we automated passably was art, even before programming. Were you not paying attention?

This future still sucks. The tech industry is making the world a worse place.

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

#374

Post by azakai »

pegasus wrote: post #316
bbor wrote: post #246

Earlier quoted context omitted.

To keep my usual rant short: I think you’re assuming a categorical distinction between those two types of innovations that just doesn’t exist. Calculus certainly required some fundamental paradigm shifts, but there’s a reason that they didn’t have to make up many words wholesale to explain it! Also we shouldn’t be thinking about what LLMs are good at, but rather what any computer ever might be good at. LLMs are alrea…

The fundamental paradigm shift is the categorical distinction. And what would constitute many new words for you? It introduced a bunch of concepts and terms which we take for granted today, including "derivative", "integral", "infinitesimal", "limit" and even "function", the latter two not a new words, but what does it matter? – the associated meanings were new.

There was a lot new in calculus, but it also didn't come out of nowhere.

That Newton and Leibniz came up with similar ideas in parallel, independently, around the same time (what are the odds?), supports that.

https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculu...

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

#375

Post by karmasimida »

anthk wrote: post #343
karmasimida wrote: post #35

Earlier quoted context omitted.

To be strict, Math is not Science. But AI is supercharging Math like there is no tomorrow.

LLM's? I doubt it. Systems with Prolog, Common Lisp and the like with proof solvers? For sure. LLM's are doomed to fail. By design. You can't fix them. It's how do they work.

You can have a word with Terrence Tao, he had different opinions here

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

#376

Post by oh_my_goodness »

m-hodges wrote: post #40

To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…

We know that LLMS "just interpolate" their training data. Maybe there's a mystery about what "just interpolate" means when the data set gets enormous. But we know what LLMs do.

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

#377

Post by CamperBob2 »

School-Cotton wrote: post #361
trostaft wrote: post #232

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

What's happening is the verbal/linguistic equivalent of the invention of calculus. No intellectual field will ever be the same again. Who wouldn't find that exciting, and want to experience it?

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

#378

Post by [deleted] »

davebren wrote: post #365
atleastoptimal wrote: post #206

To all AI skeptics: What is preventing AI from continuing to improve until it is absolutely better than humans at any mental task? If we compare AI now vs 2022 the difference is outstandingly stark. Do you believe this improvement will just stop before it eclipses all humans in everything we care about?

> What is preventing AI from continuing to improve until it is absolutely better than humans at any mental task? No matter how much compute time it's given to combine training samples with each other and run through a validation engine it will still be missing some chunk of the "long tail". To make progress in the long tail it would need to have understanding, and not just a mimicry of understanding. Unless that happ…

[deleted]

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

#379

Post by layer8 »

atleastoptimal wrote: post #206

To all AI skeptics: What is preventing AI from continuing to improve until it is absolutely better than humans at any mental task? If we compare AI now vs 2022 the difference is outstandingly stark. Do you believe this improvement will just stop before it eclipses all humans in everything we care about?

> everything we care about

One qualitative distinction that remains for the time being is that humans care about things while AIs do not. Human drive and motivation is needed to have AI perform tasks.

Of course, this distinction isn’t set in stone.

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

#380

Post by Silamoth »

marknutter wrote: post #372
ndiddy wrote: post #177

Earlier quoted context omitted.

It takes longer than ordering with a cashier, it keeps trying to upsell you, and it's always out of receipt paper because unsurprisingly the company that isn't willing to pay a person to take orders is also not willing to pay a person to maintain the kiosks.

It's easily one of the most intuitive and straightforward kiosks out there today and you don't have to wait for one of the cashiers to notice you nor worry about them punching in your order incorrectly.

Glad someone else feels the same way! Knowing that I enter my order in correctly is the biggest win there for me as a picky eater. The cashier is just entering it into a computer anyways, so it makes sense for me to enter it in myself. I honestly wonder why more restaurants don’t do this. It’s not that hard to wrap a halfway decent UI around the system you already have.
Post reply on HN