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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

#21

Post by Someone1234 »

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.

Does the free plan even have access to thinking models?

Re: Amateur armed with ChatGPT solves an Erdős problem

#23

Post by karlgkk »

userbinator wrote: post #13

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!

Re: Amateur armed with ChatGPT solves an Erdős problem

#24

Post by jaggederest »

userbinator wrote: post #13

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…

    > 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.
    > What the number theorist did not realize is that other mathematicians, even the very best,
    > also rely on a few tricks which they use over and over.
    > Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory.
    > I have made a point of reading some of these papers with care.
    > It is sad to note that some of Hilbert’s beautiful results have been completely forgotten.
    > But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory,
    > it was surprising to verify that Hilbert’s proofs relied on the same few tricks.
    > Even Hilbert had only a few tricks!
    > 
    > - Gian-Carlo Rota - "Ten Lessons I Wish I Had Been Taught"
https://www.ams.org/notices/199701/comm-rota.pdf

Re: Amateur armed with ChatGPT solves an Erdős problem

#25

Post by FrasiertheLion »

karlgkk wrote: post #23
userbinator wrote: post #13

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!

It's 80 minutes, not 80 hours.

Re: Amateur armed with ChatGPT solves an Erdős problem

#26

Post by [deleted] »

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?

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#27

Post by brianjking »

jasonfarnon wrote: post #20
ipaddr wrote: 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?

GPT 5.5 Pro is not available to any plan outside of ChatGPT Pro ($100 or $200) tier or the API as far as consumer access.

Re: Amateur armed with ChatGPT solves an Erdős problem

#28

Post by resident423 »

walrus01 wrote: post #16
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.

What your describing sounds more like the model is lacking awareness than lacking intelligence? Why does it need to know it solved the problem to be intelligent?

Re: Amateur armed with ChatGPT solves an Erdős problem

#29

Post by jychang »

walrus01 wrote: post #16
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.

There's humans that have memory issues, or full blown Anterograde amnesia.

Re: Amateur armed with ChatGPT solves an Erdős problem

#30

Post by Matticus_Rex »

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.

Was this a surprise?
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