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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

#151

Post by kmeisthax »

Terr_ wrote: post #67
vatsachak wrote: post #11

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.

> manage a McDonald's Dystopia vibes from the fictional "Manna" management system [0] used at a hamburger franchise, which involved a lot of "reverse centaur" automation. > At any given moment Manna had a list of things that it needed to do. There were orders coming in from the cash registers, so Manna directed employees to prepare those meals. There were also toilets to be scrubbed on a regular basis, floors to mop,…

Casual reminder that the author's proposed solution to the labor-automation dystopia is to invent a second identity-verification dystopia. Also casual reminder that the author wanted the death penalty to anyone over the age of 65.

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

#152

Post by clarle »

arsan87 wrote: post #119

neato. can we do any thing with this new found knowledge or is this mathematical sports? can we please put these ground breaking AIs to work on actual problems humans have?

People thought neural networks were just an interesting thought exercise a few decades ago and not for practical ML problems, and look what happened since then.

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

#153

Post by c7b »

Lerc wrote: post #46
vatsachak wrote: post #11

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.

I disagree. It will be able to perform work deserving if a fields medal before it is capable of running a McDonalds. I think it will be running a McDonalds well before either of those things happen, and a fields medal long after both have happened.

One could hardly ask for a task better suited for LLMs than producing math in Lean. Running a restaurant is so much fuzzier, from the definition of what it even means to the relation of inputs to outputs and evaluating success.

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

#154

Post by Karrot_Kream »

taimurshasan wrote: post #50

I wonder how much this cost vs a Math Professor or a team of Math Professors.

Sadly math professors aren't very expensive. Academics are paid terrible wages. Until recently, tenure was the carrot at the end of a grueling education. But now that tenure positions are getting rarer (well, tenure positions aren't growing vs the number of aspiring academics is), they continue to be cheap highly educated labor.

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

#156

Post by frozenseven »

voooduuuuu wrote: post #98
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…

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.

Show me on the anatomical prop where the magical "real reasoning" gland is.

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

#157

Post by motoxpro »

voooduuuuu wrote: post #121
peterlk wrote: post #120

Earlier quoted context omitted.

Yes they do…? Who cares if they just predict the next token? The outcome is that they can invent new abstractions. You could claim that the invention of this new idea is a combination of an LLM and a harness, but that combination can solve logic puzzles and invent abstractions. If a really large spinning wheel could invent proofs that were previously unsolved, that would be a wildly amazing spinning wheel. I view LLM…

Ask an LLM to invent a new word and post it here, I will be waiting. You will see that it simply combines words already in the training data.

[flagged]

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

#158

Post by dvt »

lukol wrote: post #139
dvt wrote: post #105

Earlier quoted context omitted.

Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)

This "new math" might be a recombination of things that we already know - or an obvious pattern that emerges if you take a look at things from a far enough distance - or something that can be brute-forced into existence. All things LLMs are perfectly capable of. In the end, creativity has always been a combination of chance and the application of known patterns in new contexts.

> This "new math" might be a recombination of things that we already know

If you know anything about the invention of new math (analytic geometry, Calculus, etc.), you'd know how untrue this is. In fact, Calculus was extremely hand-wavy and without rigorous underpinnings until the mid 1800s. Again: more art than science.

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

#159

Post by logicchains »

pear01 wrote: post #82
throw-the-towel wrote: post #54

Earlier quoted context omitted.

The capability they lack is being able to be sued.

Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them. https://en.wikipedia.org/wiki/Qualified_immunity Assuming you can still sue McDonalds I am not sure if this is a problem in the robotic llm case. I'm also trying to imagine a case where you would want to sue the llm and not the company. Given robots/llm don't have free will…

>Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them.

Police are a monopoly; nobody has a choice about which police company to use. McDonalds are not a monopoly, and many customers would prefer to eat at competitors run by entities that could be sued or jailed if they did anything particularly egregious.

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

#160

Post by logicchains »

aurareturn wrote: post #2

One thing seems for certain is that OpenAI models hold a distinct lead in academics over Anthropic and Google models. For those in academics, is OpenAI the vendor of choice?

OpenAI models seem to have been trained on a lot of auto-generated theorem proving data; GPT 5.5 is really good at writing Lean.
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