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.

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

Of course LLMs are still absolutely useless at actual maths computation, but I think this is one area where AI can excel --- the ability to combine many sources of knowledge and synthesise, may sometimes yield very useful results.

Also reminds me of the old saying, "a broken clock is right twice a day."

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.

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