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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

#151

Post by nadermx »

fwipsy wrote: post #149
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."

“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."

So basically two undergrads/graduates in math, "advanced" is subjective at that point.

Re: Amateur armed with ChatGPT solves an Erdős problem

#152

Post by pepa65 »

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…

He does say that LLMs are just a part of the models used these days.

Re: Amateur armed with ChatGPT solves an Erdős problem

#153

Post by fwipsy »

nadermx wrote: post #151
fwipsy wrote: post #149

Earlier quoted context omitted.

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."

“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." So basically two undergrads/graduates in math, "advanced" is subjective a…

I don't see where it says Price was an undergraduate/graduate in math.

Re: Amateur armed with ChatGPT solves an Erdős problem

#154

Post by vjerancrnjak »

cryptoegorophy wrote: post #41
adamgordonbell wrote: post #3

Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…

Mine took 20min. Pro. https://chatgpt.com/share/69ed83b1-3704-8322-bcf2-322aa85d7a... But I wish I was math smart to know if it worked or not.

Ask it to formalize it in Lean.

Re: Amateur armed with ChatGPT solves an Erdős problem

#155

Post by smaudet »

yayachiken wrote: post #110
jaggederest wrote: post #24

Earlier quoted context omitted.

> Every Mathematician Has Only a Few Tricks > > A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdös’s work. > You admire Erdös’s contributions to mathematics as much as I do, > and I felt annoyed when the older mathematician flatly and definitively stated > that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. > W…

I think when thinking about progress as a society, people need to internalize better that we all without exception are on this world for the first time. We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death…

> it actually was able to ingest the entirety of human knowledge

Even this, though, is not useful, to us.

It remains true that, a life without struggle, and acheivement, is not really worth living...

So, it is nice that there is something that could possibly ingest the whole of human knowledge, but that is still not useful, to us.

People are still making a hullabaloo about "using AI" in companies, and there was some nonsense about there will be only two types of companies, AI ones and defunct ones, but in truth, there will simply be no companies...

Anyways I'm sure I will get down voted by the sightless lemmings on here...

Re: Amateur armed with ChatGPT solves an Erdős problem

#156

Post by jdub »

freakynit wrote: post #146
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.

Less reasoning than a dimension of brute force unfamiliar to human brains.

Re: Amateur armed with ChatGPT solves an Erdős problem

#157

Post by dalyons »

javawizard wrote: post #122
SR2Z wrote: post #72

Earlier quoted context omitted.

Luckily for us, whole fortunes can be made by filling in the blanks between what we know and what we realize .

That deserves to be on a plaque somewhere. I've been using LLMs for much the same purpose: solving problems within my field of expertise where the limiting factor is not intelligence per se, but the ability to connect the right dots from among a vast corpus of knowledge that I would never realistically be able to imbibe and remember over the course of a lifetime. Once the dots are connected, I can verify the solution…

What’s your field

Re: Amateur armed with ChatGPT solves an Erdős problem

#158

Post by nadermx »

fwipsy wrote: post #153
nadermx wrote: post #151

Earlier quoted context omitted.

“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." So basically two undergrads/graduates in math, "advanced" is subjective a…

I don't see where it says Price was an undergraduate/graduate in math.

I don't see where it doesn't say he is, I feel its implied. Another source, proves me right? https://www.newscientist.com/article/2511954-amateur-mathema...

https://archive.is/oQvO4

Re: Amateur armed with ChatGPT solves an Erdős problem

#159

Post by energy123 »

CSMastermind wrote: post #147

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 literature search or solving easier problems that have been neglected.

Reading the prompt[1], one wonders if stoking the model to be unconventional is part of the success: "this ... may require non-trivial, creative and novel elements"

[1] https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba...

Re: Amateur armed with ChatGPT solves an Erdős problem

#160

Post by lIl-IIIl »

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…

According to the article he was using the free ChatGpt tier at first, I til someone gifted him a Pro subscription to encourage "vibe-mathing'.
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