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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

#901

Post by Schlagbohrer »

Nesco wrote: post #714
make3 wrote: post #632

Earlier quoted context omitted.

To me, AI feels like the morbidity of Star Trek teleportation, where it's actually copying the person at to the other end and zapping the original one out of existence. The original human never benefits from the fast transportation. Similarly, we're creating tools to improve knowledge, but we're progressively zapping the human out of the equation. Knowledge is created for something, but it's unclear if very soon huma…

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?

"leftist subtexts" such as an understanding of capitalist economics in which the people who own everything benefit from the economic activity being done underneath them.

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

#902

Post by Supermancho »

dclowd9901 wrote: post #687
Supermancho wrote: post #572

Earlier quoted context omitted.

>That's literally my job... Since you’re not in a unique position, I can confidently state that your comparison of LLMs to jr developers seems unfounded. Today, LLMs produce code that is superior to junior developer code by an order of magnitude. Notably, they demonstrate consistent syntax, clear separation of concerns, strong test coverage, organizational rigor, idiomatic API usage, and the ability to generate and m…

I'm not sure what your background is, but as a staff level engineer, I can assure you they do not. They in fact seem to lack any understanding of architectural intent within a sufficiently large code base. This seems obvious since they can't fit the entire code base in their context at once. We have many folks (not engineers) at our company using LLMs to open PRs, and every one of these PRs has profound architectural…

> They in fact seem to lack any understanding of architectural intent within a sufficiently large code base. This seems obvious since they can't fit the entire code base in their context at once.

This is a critique of scale, moving the goalpost.

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

#903

Post by p_j_w »

fc417fc802 wrote: post #872
pocksuppet wrote: post #849

Earlier quoted context omitted.

Recently I tried to order at a Subway (which has decent quality food outside of the USA). They have kiosks. The kiosk only responded to touch about 60% of the time and took two seconds to respond. The employee who could've easily taken my order was just standing there bored. The future is here and it sucks.

> which has decent quality food outside of the USA Is there something wrong with their food in the USA?

Subway is consistently the worst sandwich shop in a given city. I’m sure worse sandwich shops exist, but I’ve never been to one.

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

#904

Post by kevinwang »

Nitpicky/not important, but they say:

Since loglog(n) tends to infinity with n, the additional term in the exponent tends to 0, meaning these constructions achieve growth only slightly faster than linear.

Would anyone else describe the previous asymptotic behavior like that? I mean obviously loglogn to O(1) is a quantum leap, but wouldn't you describe loglogn as "grows so slowly it's almost constant", so the constructions achieve growth "almost n^{1+c}"? But I guess that might be overcorrecting too hard.

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

#905

Post by recitedropper »

justanotherjoe wrote: post #900
recitedropper wrote: post #881

Earlier quoted context omitted.

- https://www.theverge.com/cs/features/831818/ai-mercor-handshake-scale-surge-staffing-companies - https://outlier.ai/math/en-us - https://www.opentrain.ai/ - https://www.pin.com/blog/ai-labs-hiring-train-models/ Much of this is data annotation, reasoning trace evaluation, and problem set curation. But there is no way they haven't atleast paid some mathematicians to work on research grade problems in tandem with thei…

At one point you just have to look at a mirror and ask, what would impress you. Also why pay anyone, when they can keep up with all the papers that not one man can read them all? That seems to me like wasted money. Another point is that that's not how AI training works anyway. It's much easier to put it in context rather than re-train them with every bit of random maths you find out. Things at the tail-end of the pow…

The opening line of my parent comment is: "This is impressive, no question." I am impressed, and the chain you are replying to is questioning how much that impression should be tempered.

They pay people for expert training data they do not share because it gives them an edge over other AI companies. And, as always, deep learning is enormously data-hungry, and we've gotten to the point where publicly available data has been exhausted.

AI companies absolutely retrain models regularly to keep up with the cutting edge. There is a reason why this announcement references an internal, unreleased model, rather than "we just put a lot of new math papers within the GPT5.5 context window and found this."

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

#906

Post by ori_b »

amunozo wrote: post #759
ori_b wrote: post #373

Earlier quoted context omitted.

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.

Calling AI-generated images art is a stretch. Same thing with creative writing. It can make some low-cost illustrations and writing, but it is very far from decent art. Compare those results with their amazing coding or math capabilities.

https://www.astralcodexten.com/p/how-did-you-do-on-the-ai-ar...

Two years old now, and as the cryptographers say, attacks only get better.

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

#907

Post by utopiah »

inciampati wrote: post #623
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…

I am also using these models to accelerate scientific discovery. Yes, they are making all the difference at the frontier. At least, they feel they are. The messy thing is that we still need to communicate with each other and that's not getting dramatically faster or better. As you note the models need to be built so they do more work to participate in our communication economy. Or we will do so much, alone, to get no…

> I am also using these models to accelerate scientific discovery. Yes, they are making all the difference at the frontier.

Can you please expand on how you do so?

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

#908

Post by utopiah »

lesostep wrote: post #784

I am cautious about AI "discoveries" after Mythos paper. What was the process of a writing a paper? Was the question asked by a mathematician? Was the paper right from a get-go or was there someone who pointed out mistakes? How much attempts were made before solution was found? I will eat my words if an AI oneshotted that one without any external help, but for know I am left wandering whether it's a new way to attrib…

No need to be cautious.

If a for-profit (because... you know, OpenAI isn't at all what it initially was) huge corporation (again, not a cute startup trying to help humanity) publish anything it's a piece of marketing. Every single word a corporation say is marketing.

So... that's also that, a piece of marketing to sell more of whatever their potential client can buy. It's not a piece of research. It's an ad. That's it.

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

#909

Post by doright »

pickleRick243 wrote: post #540
JacobAsmuth wrote: post #525

Earlier quoted context omitted.

Exactly. I would rather we let these discoveries stay hidden for a while longer such that human ingenuity may untangle them from the coils of reality. A machine? A mechanical man? Deins to produce something as pure as mathematics without the divine fervor of the ineffable spirit of Man?! It's just not what God wants.

Human ingenuity is untangling perhaps the deepest question of all- what is the essence of Reason and the intellect that so privileges man? I don't know if it's what God wants, but it's certainly getting close to some existentially fundamental questions. While many seem to be anxious or pessimistic about the future of intellectual/artistic pursuits (understandable although I disagree), I do find the utter lack of curi…

One has to be in a secure enough position in life to be able to manifest such curiosity to begin with. On the contrary many people feel threatened.

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

#910

Post by amunozo »

ori_b wrote: post #906
amunozo wrote: post #759

Earlier quoted context omitted.

Calling AI-generated images art is a stretch. Same thing with creative writing. It can make some low-cost illustrations and writing, but it is very far from decent art. Compare those results with their amazing coding or math capabilities.

https://www.astralcodexten.com/p/how-did-you-do-on-the-ai-ar... Two years old now, and as the cryptographers say, attacks only get better.

Those are either copies or bad. I think the difference in quality and originality is huge, even if they can create plausible looking images in already invented styles.
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