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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

#551
post #546

Earlier quoted context omitted.

I can't tell if this is satire.

I had the exact same thought. It depends entirely on what voice you read it in, I suppose.

Haha, now I do think it is more likely satire. I don't think HN has many people who would post like this sincerely.

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

#552

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.

[dead]

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

#553

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.

Mathematics is a bridge to what Neoplatonists call the intelligible world. Currently, mathematicians navigate that world on foot. It's exciting to think that soon we might have cars and trains in that world so we don't have to painstakingly walk everywhere.

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

#554

Earlier quoted context omitted.

The knowledge isn't of any use to us unless it is understandable to us. Many species understand things about the world around us that we are unable to explain or understand, even if it's just pure instinct on their part. These things are very useful to them, but have no value to us until we can understand and explain it, which then allows us to make use of it. People saw birds fly for all of human history, but it was…

This is not true. We use drug-sniffing and guide dogs in a way similar to how we use LLMs. We don't really understand them at a fundamental level, we can't make electronic dog noses (otherwise we'd dispense with the silliness and just install drug detectors instead), but dogs are useful, so we use them.

We don’t blindly trust the drug-sniffing dog. The dog gives a signal that it was trained to give, then humans understand what that signal means and verify the accuracy. Without the human understanding in the loop, the dog’s ability is of little value.

Without a human in the loop and LLM could churn away spitting out results, some right, some wrong, and it would be of no consequence. Not much different than wild dogs sniffing each other.

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

#555

Earlier quoted context omitted.

Because for many people who pursue these fundamental truths, the reward is not necessarily personal fame, fortune, or even personal understanding. Advancing humanity's total knowledge (even if that knowledge is by proxy through AI) is reward enough.

I think when your work is no longer required, you will probably come to regret this sentiment, not that it matters.

I think by that point humanity will having some pretty fundamental discussions about the nature of work and money.

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

#556

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.

At least from my perspective, these sorts of tools could have the possibility of allowing us to reach post-scarcity (I guess a skynet future is another possible outcome, as is just grimdark industrial hell). If we reach that point, then anybody could (in principle- in reality utopias don't exist) pursue anything they wanted.

This is just an application of the philosophy "automate yourself out of a job every 6 months"- I've been doing that for a long time, and the outcome is generally a more interesting job.

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

#558

This is impressive, no question. Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain origi…

Exactly. Maybe OpenAI paid mathematicians to keep this discovery quiet, then added their proof to the training data, then manipulated a second team into prompting for this question such that the model could regurgitate the solution. This would plausibly explain why the model seems so capable at doing things like refuting fundamental theorems of mathematics while in things like competitive programming, biology, and ph…

You're a bot! Hey everyone, over here! I found a bot!

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

#559

Earlier quoted context omitted.

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?

People who enjoy thinking. Ya know, the "intellectual" part.

Why would having more thinking companions stop you from thinking? Knowledge compounds.

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

#560

Earlier quoted context omitted.

Because for many people who pursue these fundamental truths, the reward is not necessarily personal fame, fortune, or even personal understanding. Advancing humanity's total knowledge (even if that knowledge is by proxy through AI) is reward enough.

[flagged]

Have you considered that utilitarians actually exist?

If 20% more medical knowledge would save more lives long term, there are actually people, probably some browsing this website right now, maybe the person you're responding to, that actually think killing people up to the expected number of lives saved is justified.

I would personally call that evil, but it is thought through.

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