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Amateur armed with ChatGPT solves an Erdős problem

scientificamerican.com

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Re: Amateur armed with ChatGPT solves an Erdős problem

#211

Question for those who believe LLMs aren't intelligent and are merely statistical word predictors: how do you reconcile such achievements with that point of view? (To be clear: I'm not agreeing or disagreeing. I sometimes feel the same too. I'm just curious how others reconcile these.)

It doesn't matter if you use a car or go there walking. If your goal is cave exploration, the tools are irrelevant.

Re: Amateur armed with ChatGPT solves an Erdős problem

#212
post #200

It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. I feel like LLMs are much better at making these types of connections than humans because they 1) know about many more theories/approaches than a single human can 2) don't need to worry about looking silly in front of their peers.

As a civilization we went the left-brained/sequential/language based way of thinking (with computers and AI being the crown achievement of it). Personally i for example remember like around 3rd grade i switched from the whole-page-at-once reading mode into the word by word line by line mode and that mode stuck with me since then (at some point while at the University i had for some period of time, probably it was the…

If that is your hope you are probably in for a rude awakening. Left brained/right brained is a wooden exaggeration according to more recent research [1].

[1] e.g. https://www.sciencenewstoday.org/left-brain-vs-right-brain-t...

Re: Amateur armed with ChatGPT solves an Erdős problem

#213
post #202

It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. I feel like LLMs are much better at making these types of connections than humans because they 1) know about many more theories/approaches than a single human can 2) don't need to worry about looking silly in front of their peers.

Exactly. Much of the intellectual work is, in fact, intellectual labor . It’s mostly about combining various information in one place — the exact task that LLM far outperforms human. People traditionally misclassified this class of work as “creative”. It’s not really.

What is your idea of "creative"/"creativity" then?

Re: Amateur armed with ChatGPT solves an Erdős problem

#214
post #189

Given by the fact that the problem is 60 year old, isn't there a chance this was indirect solved already and the model just crossed informations to figure out the problem? By looking the website this problem was never discussed by humans. The last comments were about gpt discovering it. I was expecting older comments coming to a 60 year old problem. Am I missing something? Great discovery though, there might be probl…

To some extent, does it matter?

If models are able to pull and join information that already existed in pieces but humankind never discovered by itself, doesn’t this count towards progress anyways?

Re: Amateur armed with ChatGPT solves an Erdős problem

#215
post #189

Given by the fact that the problem is 60 year old, isn't there a chance this was indirect solved already and the model just crossed informations to figure out the problem? By looking the website this problem was never discussed by humans. The last comments were about gpt discovering it. I was expecting older comments coming to a 60 year old problem. Am I missing something? Great discovery though, there might be probl…

Exceedingly unlikely. This was one of the more discussed Erdos problems, and multiple experts have attested to the technique's novelty. If you're referring to the lack of comments on the erdosproblems website, that doesn't really mean much. From its own blog[0], the site was only started in 2023 and only really gained momentum as a place to discuss AI solving attempts, you aren't going to see serious mathematicians discussing the problems there even if there have been significant efforts to solve it.

[0]: https://www.erdosproblems.com/forum/thread/blog:1

Re: Amateur armed with ChatGPT solves an Erdős problem

#216
I asked ChatGPT to draw the outline of an ellipse using Unicode braille. I asked for 30x8 and it absolutely nailed it. A beautiful piece of ascii (er, Unicode) art. But I wanted to mark the origin! So I asked for a 31x7 ellipse instead. It completely flubbed it, and for 31x9 too.

When a model gives a really good answer, does that just mean it’s seen the problem before? When it gives a crappy answer, is that not simply indicating the problem is novel?

Re: Amateur armed with ChatGPT solves an Erdős problem

#217
I will get downvoted for this but I can't help thinking that billions of dollars have gone into chatgpt over a period of years and an LLM can direct all its "attention" (in a metaphorical sense) on one problem. I think if you gave top mathematicians a few million (so a fraction of a percent of chatgpt budget) to solve this problem over four years, they probably would have at least made significant progress. I don't think chatgpt has solved thousands of similar problems (even stretching that across all ham disciplines). Basically my thesis is that universal basic income could have had a similar impact, and also encouraged human flourishing elsewhere.

Re: Amateur armed with ChatGPT solves an Erdős problem

#219

For the uninitiated, Paul Erdős was a pretty famous but very eccentric mathematician who lived for most of the 1900s. He had a habit of seeking out and documenting mathematical problems people were working on. The problems range in difficulty from "easy homework for a current undergrad in math" to "you're getting a Fields Medal if you can figure this out". There's nothing that really connects the problems other than…

> Each time there's a new model release a few more get solved. I'm no expert, but based on the commentary from mathematicians, this Erdős proof is a unique milestone because the problem received previous attention from multiple professional mathematicians, and the proof was surprising, elegant, and revealed some new connections. The previous ChatGPT Erdős proofs have been qualitatively less impressive, more akin to l…

>one wonders if stoking the model to be unconventional is part of the success

I've long suspected that a lot of these model's real capabilities are still locked behind certain prompts, despite the big labs spending tons of effort on making default responses to simple prompts better. Even really dumb shit like "Answer this: ..." vs "Question: ..." vs "... you'll be judged by " that should have zero impact in an ideal world can significantly impact benchmark results. The problem is that you can waste a ton of time finding the right prompt using these "dumb" approaches, while the model actually just required some very specific context that was obvious to you and not to it in many day-to-day situations. My go to method is still to have the model ask me questions as the very first step to any of these problems. They kind of tried that with deep research since the early o-series, but it still needs improvement.

Re: Amateur armed with ChatGPT solves an Erdős problem

#220
post #171

Earlier quoted context omitted.

I don't have any opinion about "real intelligence" or not. I'm not a P(doom)er, I don't think we're on the bring of ascending as a species. But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are.

Just to clarify because I’m not sure I understand: So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?

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