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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

#341

Earlier quoted context omitted.

I absolutely believe that AI will supercharge science. I do not believe it will replace humans.

I absolutely believe that AI will supercharge science and replace humans. Why shouldn't it? Humans are poorly optimized for almost anything, and built on a substrate that's barely hanging together

I’d give humans some credit, they’re an adaptable bunch. AI won’t replace humans in the same way humans did not replace cockroaches. It’s a non-sequitur.

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

#342
post #177

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.

Hmm. I’ve never really had those issues. It’s also much faster and easier than ordering with a human. I guess it does try to upsell you, but humans often do, too. And to me, it’s worth it to just click “No” in exchange for the added convenience (mostly in getting my order right).

I have had them run out of receipts, but it’s never mattered for me. If I’m dining in, the plastic number you carry to your table makes sure I get my food. And if I’m taking it to-go, they always find me anyways.

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

#343

AI isn't going to supercharge science but I wouldn't be as dismissive as other posters here.

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.

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

#344
post #250
post #61

Earlier quoted context omitted.

> I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibniz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like an art than a science. For example, many belive that to…

math more like an art than a science. That’s a fun turn of phrase, but hopefully we can all agree that math without scientific rigor is no math at all. we likely need some new kind of math. Imo, it's unlikely that an LLM will somehow invent it. Do you think it’s possible/likely that any AI system could? I encourage us to join Yudkowsky in anticipating the knock-on results of this exponential improvement that we’re li…

Math is not based on science!

Maths follows logical (or even mathematical) rigour, not scientific rigour!

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

#345

See the longstanding debate on whether new math is "invented" or "discovered". Most mathematicians I knew thought it's discovered.

Any design already exists as a possibility, so it could be said to be both invented and discovered, depending on how you look at it.

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.

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

#348
post #133

Timothy Gowers' tweet about this: "If you are a mathematician, then you may want to make sure you are sitting down before reading futher.". woah.

Unfortunately Gowers has taken Tao's lead on this one.

Gowers has one of my favourite video series about how he approaches a problem he is unfamiliar with: https://www.youtube.com/watch?v=byjhpzEoXFs

It is disheartening to see him jump into this GenAI puffery.

I hope these GenAI labs are paying Tao handsomely for legitimizing their slop, but more likely he's feeling pressure from his University to promote and work with these labs.

My guess is Gowers wants in on that action, or his University does.

Either way, it makes me sad. If its self motivated... even sadder.

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

#349
post #284

I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)

I still laugh.

Have you updated your priors after this announcement? If not, why not?

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

#350

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…

I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.

"Predicting the next token" is meaningless. Every process that has any sort of behavior, including a human writing, can be modeled by some function from past behavior to probability distribution of next action. Viewed this way, literally everything is just "predicting" the next action to be taken according to that probability distribution.

The most likely series of next tokens when a competent mathematician has written half of a correct proof is the correct next half of the proof. I've never seen anyone who claims "LLMs just predict the next token" give any definition of what that means that would include LLMs, but exclude the mathematician.

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