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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

#3

Post by adamgordonbell »

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-b164-8385-bf2e-8533e9baba...

Re: Amateur armed with ChatGPT solves an Erdős problem

#5

Post by tomlockwood »

My big question with all these announcements is: How many other people were using the AI on problems like this, and, failing? Given the excitement around AI at the moment I think the answer is: a lot.

Then my second question is how much VC money did all those tokens cost.

Re: Amateur armed with ChatGPT solves an Erdős problem

#6

Post by ipaddr »

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…

Tried the same prompt and ended up no where close on the free plan.

Re: Amateur armed with ChatGPT solves an Erdős problem

#7

Post by Eufrat »

Humans and very often the machines we create solve problems additively. Meaning we build on top of existing foundations and we can get stuck in a way of thinking as a result of this because people are loathe to reinvent the wheel. So, I don’t think it’s surprising to take a naïve LLM and find out that because of the way it’s trained that it came up with something that many experts in the field didn’t try.

I think LLMs can help in limited cases like this by just coming up with a different way of approaching a problem. It doesn’t have to be right, it just needs to give someone an alternative and maybe that will shake things up to get a solution.

That said, I have no idea what the practical value of this Erdős problem is. If you asked me if this demonstrates that LLMs are not junk. My general impression is that is like asking me in 1928 if we should spent millions of dollars of research money on number theory. The answer is no and get out of my office.

Re: Amateur armed with ChatGPT solves an Erdős problem

#9

Post by gdhkgdhkvff »

tomlockwood wrote: post #5

My big question with all these announcements is: How many other people were using the AI on problems like this, and, failing? Given the excitement around AI at the moment I think the answer is: a lot. Then my second question is how much VC money did all those tokens cost .

Why do you care about either of those questions?
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