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An OpenAI model has disproved a central conjecture in discrete geometry

openai.com

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

#951
post #903

Earlier quoted context omitted.

> 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.

And it's sad because it didn't used to be that way. Their quality tanked like 10 years ago.

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

#952
post #478

Earlier quoted context omitted.

Today I generated the equivalent of two LOTR books just to fix three missing rows in my SQL models (and open a PR), so +1

or put differently, you melted x cubic meters of polar ice

Doing anything melts x cubic meters of polar ice.

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

#953
post #731

Earlier quoted context omitted.

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

So knowledge becomes meta stable. There was an AIDS drug in the 90’s that we stopped being able to make. IIRC Apparently there were two different crystal/folding structures for the compound and the desired one was not the lowest energy. After years of production, the wrong version was produced and they could no longer make the correct version do to contamination. And every facility that tried to study it, wound up no…

Fascinating. I had to read up on this. Apparently it was Ritonavir and polymorphism.

https://en.wikipedia.org/wiki/Ritonavir

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

#954
post #731

Earlier quoted context omitted.

I'm no mathematician but it seems like if this happens, we get to a quite intriguing place as a species. Say we achieve interstellar travel, but nobody actually knows how it works. Or we cure cancer, but the "cure" requires a microrobotic implant, and it runs as a blackbox AI, and only the other AIs can make one, and there's no guarantee they will know how to make one tomorrow. Or we solve global warming but it requi…

Noble " save the humankind using the tech nobody fucking understands " textbook goals like curing cancer, solving global warming and achieving interstellar travel would always turn up when owners of trillions of dollars place orders on positive AI narratives, but in reality all of that will wither down to " It's what plants crave! It's got electrolytes. "

To me at least, the intriguing part has nothing to do with the textbook goals of whichever foulmouthed trillionaires you have in mind.

The intriguing part is that we could get objectively good outcomes, but at a cost of being dependent on the machines. So it's not that you couldn't actually unplug Skynet, it's that if you did civilization would collapse (or whatever) because Skynet stops doing its thing.

I'm not sure that gets us to a better place overall, but I doubt we could resist the temptation.

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

#955
post #897
post #833

Earlier quoted context omitted.

Earlier of their systems have solve other Erdos problems that people had worked on, this one was more monumental and had had a lot more prior effort that didn't solve, but this isn't a one-off.

This is true, but I still think the relevant question is, how many did they try before they found one that yielded to LLMs? The conclusion is very different if they tried 100 open problems and succeeded at one.

Yeah, maybe it's just the Texas Sharpshooter Fallacy basically, but with AI.

And if it isn't, we should find out very soon. If AI has got so good as OpenAI's post implies, then we should soon see a veritable blooming in the production of mathematical results, by lay people no less. No mathematicians needed! OpenAI say that their secret LLM solved the planar unit distance problem "autonomously" and the companion remarks say it one-shotted it; and while the companion remarks make it clear that there was a lot of refinement and improvement work done by humans, everyone seems to agree that the AI did the job by itself.

If that's true, if we're really at that level of autonomous mathematical reasoning ability, then we should see hundreds, even thousands, of open problems suddenly solved in a matter of years if not months. We'll just have to wait and see.

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

#956
post #414

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> the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Isn't this just anthropocentrism? Why is understanding only valid if a human does it? Why is knowledge only for humans? If another species resolved the contradictions be…

Because it is, for now. For a while at least. You can prove that LLM doesn't understand what it does and it is surprisingly simple. Request it to add two integers and then ask it to explain how it arrived at that result. The answer will be completely unrelated to the actual process LLM used because both results were generated independently and without understanding their meaning and connection.

This is likely true for the majority of humans too.

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

#957
post #373

Earlier quoted context omitted.

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.

Yes, the photographic camera really destroyed the whole genre of photorealistic paintings and portraits!

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

#958
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.

Yes, the photographic camera really destroyed the whole genre of photorealistic paintings and portraits!

This seems like a non-sequitur. The entire point of AI is that it's able to generalize and perform at or above human level. Let me know the next time your camera is able to simulate conceptualizing something.

Or is your argument that AI is permanently doomed to not work?

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

#959

Earlier quoted context omitted.

I find AI a great scaffolding for improving understanding and mental models. BUT! It's all in how you use it.

The real question is: Do you need to understand it fully for it to improve your life? For example, if you're in fundamental science (or generally a fan of reductionism), it for sure would be nice to understand the universe instead of just having access to an AI that can comprehend it. But to the majority of the population it only matters that someone (or something) understands it enough to make it useful to others.

Understanding everything fully is futile. But there are many many many things that by understanding you improve your life. So, I feel the question is... not useful, I would say. Yes, you need to search for things that if you knew them you would improve your life. No, you can not know them all beforehand. Yes, there are such things. There always are.

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

#960

Earlier quoted context omitted.

Gemini seems better trained for learning and I think Google has made a more deliberate effort to optimize for pedagoical best practices. (E.g. tutoring, formative feedback, cognitive load optimization) As far as academic research is concerned (e.g. this threads topic), I can't say.

Gemini the chatbot has a very strange personality that intensely overindexes on your user profile and absolutely loves insane mixed metaphors. Its explanations are quite good but they're also hard to understand because it keeps trying to relate everything back to programming metaphors or what it thinks it knows about the streets in the neighborhood I live in.

I agree the Gemini chat bot is too strongly opinionated about how it responds. I don't like their system prompt.

However the underlying model accessed via API with custom system prompts that direct toward pedagogical best practices performs better than gpts or Claude currently.

As a side note, whenever i want Gemini chatbot to provide me a list, it gives me a freaking essay. Drives me nuts. It often crams a bunch of extra stuff into its responses I don't want. Wasted tokens and wastes my time having to shift through it.

Gemini if you're reading this tell your human overlords to rethink your chat system prompt.

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