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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

#141

Post by CSMastermind »

LPisGood wrote: post #88

Some Erdős problems are basically trivial using sophisticated techniques that were developed later. I remember one of my professors, a coauthor of Erdős boasted to us after a quiz how proud he was that he was able to assign an Erdős problem that went unsolved for a while as just a quiz problem for his undergrads.

Worth mentioning, though, that people have already tried running all of them through LLMs at this point.

So this is proof of the models actually getting stronger (previous generations of LLMs were unable to solve this one).

Re: Amateur armed with ChatGPT solves an Erdős problem

#142

Post by bojo »

shybear wrote: post #139

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.

This is what I have been doing. I don't think I've made any amazing breakthroughs, but at the same time I can't help but feel like I've come across some white paper-worthy realizations. Being able to correlate across a lot of domains I feel like I intuitively understand but have no depth of knowledge has been a fun exercise in LLM experimentation.

Re: Amateur armed with ChatGPT solves an Erdős problem

#143

Post by emp17344 »

tptacek wrote: post #132
emp17344 wrote: post #129

Earlier quoted context omitted.

But the systems that do that impressive work are no longer just LLMs. Look at the Claude Code leak - it’s a sprawling, redundant maze relying on tools and tests to approximate useful output. The actual LLM is a small portion of the total system. It’s a useful tool, but it’s obviously not truly intelligent - it was hacked together using the near-trillions of dollars AI labs have received for this explicit purpose.

What does this matter? You can build a working coding agent for yourself extremely quickly; it's remarkably straightforward to do (more people should). But look underneath all the "sprawling tools": the LLM itself is a sprawling maze of matrices. It's all sprawling, it's all crazy, and it's insane what they're capable of doing. Again if you want to say they're limited in some way, I'm all ears, I'm sure they are. But…

Well, hang on a second - it sounds like you may actually disagree with the user who created this thread. That user claims that these systems exhibit “real intelligence”, and success on this Erdos problem is proof.

You seem to be making the claim that LLMs are statistical text generators, but statistical text generation is good enough to succeed in certain cases. Those are different arguments. What do you actually believe? Are we even in disagreement?

Re: Amateur armed with ChatGPT solves an Erdős problem

#144

Post by maplethorpe »

hx8 wrote: post #58
mhb wrote: post #39

> He’s 23 years old and has no advanced mathematics training. How is he even posing the question and having even a vague idea of what the proof means or how to understand it?

> “I didn’t know what the problem was—I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with,” he says. “And it came up with what looked like a right solution.” He sent it to his occasional collaborator Kevin Barreto, a second-year undergraduate in mathematics at the University of Cambridge. Seems like standard 23 year old behavior. You're spending $100-$200/mo on…

Couldn't he have just asked ChatGPT if it was correct? Why do we still feel the need to loop in a human?

Re: Amateur armed with ChatGPT solves an Erdős problem

#145

Post by tptacek »

emp17344 wrote: post #143
tptacek wrote: post #132

Earlier quoted context omitted.

What does this matter? You can build a working coding agent for yourself extremely quickly; it's remarkably straightforward to do (more people should). But look underneath all the "sprawling tools": the LLM itself is a sprawling maze of matrices. It's all sprawling, it's all crazy, and it's insane what they're capable of doing. Again if you want to say they're limited in some way, I'm all ears, I'm sure they are. But…

Well, hang on a second - it sounds like you may actually disagree with the user who created this thread. That user claims that these systems exhibit “real intelligence”, and success on this Erdos problem is proof. You seem to be making the claim that LLMs are statistical text generators, but statistical text generation is good enough to succeed in certain cases. Those are different arguments. What do you actually bel…

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#146

Post by freakynit »

shybear wrote: post #139

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.

This is what I personally consider as "reasoning" ... knowledge generalization and application across domains.

Re: Amateur armed with ChatGPT solves an Erdős problem

#147

Post by CSMastermind »

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 the fact that one of the smartest people of the last 100 years didn't immediately know the answer when someone posed it to him.

One of the things people have been doing with LLMs is to see if they can come up with proofs for these problems as a sort of benchmark.

Each time there's a new model release a few more get solved.

Re: Amateur armed with ChatGPT solves an Erdős problem

#148

Post by nadermx »

This just shows that with the right training, in this case a thesis on erdos problems, they where able to prompt and check the output. So still needed the know how to even being to figure it out. "Lichtman proved Erdős right as part of his doctoral thesis in 2022."

Re: Amateur armed with ChatGPT solves an Erdős problem

#149

Post by fwipsy »

nadermx wrote: post #148

This just shows that with the right training, in this case a thesis on erdos problems, they where able to prompt and check the output. So still needed the know how to even being to figure it out. "Lichtman proved Erdős right as part of his doctoral thesis in 2022."

Lichtman is an expert who commented for the story. Liam Price is the one who prompted ChatGPT. "He’s 23 years old and has no advanced mathematics training."

Re: Amateur armed with ChatGPT solves an Erdős problem

#150

Post by pepa65 »

vatsachak wrote: post #120
resident423 wrote: post #8

I wonder if the rationalizations people come up with for why this isn't real intelligence will be as creative as ChatGPTs solution.

Well it still gets easy problems wrong With real general intelligence you'd expect it to solve problems above a certain difficulty with a good clip

That "it" is a huge variety and range of things...
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