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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

#31
post #23

The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question. 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 th…

Also just the sheer value of brute force. 80 hours! 80 hours of just trying shit!

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Re: Amateur armed with ChatGPT solves an Erdős problem

#34
post #23

The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question. 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 th…

Also just the sheer value of brute force. 80 hours! 80 hours of just trying shit!

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#35

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…

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Re: Amateur armed with ChatGPT solves an Erdős problem

#36
post #15

Earlier quoted context omitted.

Neither does the Collatz conjecture, Fermat's last theorem, .... (Of course, those problems are on another plane than this one.)

But that’s exactly my point. These are absolutely worth studying, but being what they are, nobody should be dumping massive amounts of money on them. I would not find it persuasive if researchers used LLMs to solve the Collatz conjecture or finally decode Etruscan. These are extremely valuable, but it is unlikely to be worth it for an LLM just grinding tokens like crazy to do it.

Is it worth it to buy a super-yacht?

Re: Amateur armed with ChatGPT solves an Erdős problem

#37

The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question. 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 th…

Wait, what do you mean "LLMs are still absolutely useless at actual maths computation"? I rely on them constantly for maths (linear algebra, multivariable calc, stat) --- literally thousands of problems run through GPT5 over the last 12 months, and to my recollection zero failures. But maybe you're thinking of something more specific?

Re: Amateur armed with ChatGPT solves an Erdős problem

#38
post #6

Earlier quoted context omitted.

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

Is there a known lag that it takes the Pro plan's abilities to migrate to the free plans?

Do not use the free plan. It is not good.

Re: Amateur armed with ChatGPT solves an Erdős problem

#40
post #37

The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question. 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 th…

Wait, what do you mean "LLMs are still absolutely useless at actual maths computation"? I rely on them constantly for maths (linear algebra, multivariable calc, stat) --- literally thousands of problems run through GPT5 over the last 12 months, and to my recollection zero failures. But maybe you're thinking of something more specific?

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