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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

#11

Post by Eufrat »

gdhkgdhkvff wrote: post #9
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?

I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.

Re: Amateur armed with ChatGPT solves an Erdős problem

#12

Post by anematode »

Eufrat wrote: post #11
gdhkgdhkvff wrote: post #9

Earlier quoted context omitted.

Why do you care about either of those questions?

I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.

Neither does the Collatz conjecture, Fermat's last theorem, ....

(Of course, those problems are on another plane than this one.)

Re: Amateur armed with ChatGPT solves an Erdős problem

#13

Post by userbinator »

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 the old saying, "a broken clock is right twice a day."

Re: Amateur armed with ChatGPT solves an Erdős problem

#14

Post by inerte »

Eufrat wrote: post #11
gdhkgdhkvff wrote: post #9

Earlier quoted context omitted.

Why do you care about either of those questions?

I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.

I would question at $60k. At $100k is a steal.

Re: Amateur armed with ChatGPT solves an Erdős problem

#15

Post by Eufrat »

anematode wrote: post #12
Eufrat wrote: post #11

Earlier quoted context omitted.

I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#16

Post by walrus01 »

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.

For one, everything its 'intelligence' knows about solving the problem is contained within the finite context window memory buffer size for the particular model and session. Unless the memory contents of the context window are being saved to storage and reloaded later, unlike a human, it won't "remember" that it solved the problem and save its work somewhere to be easily referenced later.

Re: Amateur armed with ChatGPT solves an Erdős problem

#17

Post by jasonfarnon »

Eufrat wrote: post #11
gdhkgdhkvff wrote: post #9

Earlier quoted context omitted.

Why do you care about either of those questions?

I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.

Also, it's one thing if the AI age means we all have to adopt to using AI as a tool, another thing entirely if it means the only people who can do useful research are the ones with huge budgets.

Re: Amateur armed with ChatGPT solves an Erdős problem

#19

Post by anematode »

Eufrat wrote: post #15
anematode wrote: post #12

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.

Maybe... but I would love if 1% of the investment in AI were redirected to the mathematics education and professional research that would allow progress on any of these problems...

Re: Amateur armed with ChatGPT solves an Erdős problem

#20

Post by jasonfarnon »

ipaddr wrote: post #6
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.

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