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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

#71

Post by [deleted] »

y0eswddl wrote: post #48
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…

Yeah, they're great at interpolation - they'll just never be worth much at extrapolation.

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#72

Post by SR2Z »

y0eswddl wrote: post #48
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…

Yeah, they're great at interpolation - they'll just never be worth much at extrapolation.

Luckily for us, whole fortunes can be made by filling in the blanks between what we know and what we realize.

Re: Amateur armed with ChatGPT solves an Erdős problem

#73

Post by resident423 »

walrus01 wrote: post #43
resident423 wrote: post #28

Earlier quoted context omitted.

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?

We say African Elephants are intelligent for a number of reasons, one of which is because they remember where sources of water are in very dry conditions, and can successfully navigate back to them across relatively large distances. An intelligent being that can't remember its own past is at a significant disadvantage compared to others that can, which is exactly one of the reasons why alzheimers patients often requi…

There's probably a limit to how intelligent something can be with no long term memory, but solving Erdos problems in 80 minutes is clearly not above it, and I think the true limit is probably much higher than that.

Re: Amateur armed with ChatGPT solves an Erdős problem

#74

Post by hyraki »

jasonfarnon wrote: post #56
brianjking wrote: post #27

Earlier quoted context omitted.

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.

Yes, but don't we expect GPT 5.5 Pro will eventually be a free tier? Maybe I'm missing something because I only use the free tier. But the free tier has gotten way better over the last few years. I'm pretty sure, based on descriptions on this site from paid subscribers, that the free tier now is better than the paid tier of say 2 years ago. That's the lag I'm wondering about.

You should pay for it if you find value in it.

Re: Amateur armed with ChatGPT solves an Erdős problem

#75

Post by thesmtsolver2 »

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.

Remember when people thought multiplying numbers, remembering a large number of facts, and being good at rote calculations was intelligence?

Some people think that multiplying numbers, remembering a large number of facts, and being good at calculations is intelligence.

Most intelligent people do not think that.

Eventually, we will arrive at the same conclusion for what LLMs are doing now.

Re: Amateur armed with ChatGPT solves an Erdős problem

#77

Post by ecshafer »

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 .

I've tried my hand at a few of the Erdos problems and came up short, you didn't hear about them. But if a Mathematician at Harvard solved on, you would probably still hear about it a bit. Just the possibility that a pro subscription for 80 minutes solved an Erdos problem is astounding. Maybe we get some researchers to get a grant and burn a couple data centers worth of tokens for a day/week/month and see what it comes up with?

Re: Amateur armed with ChatGPT solves an Erdős problem

#78

Post by Eufrat »

mhb wrote: post #36
Eufrat wrote: post #15

Earlier quoted context omitted.

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?

No.

Re: Amateur armed with ChatGPT solves an Erdős problem

#79

Post by emp17344 »

jychang wrote: post #29
walrus01 wrote: post #16

Earlier quoted context omitted.

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.

There are humans who can’t read. That doesn’t mean Grammarly is “intelligent”. These things are tools - nothing more, nothing less.

Re: Amateur armed with ChatGPT solves an Erdős problem

#80

Post by nopinsight »

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…

> "a broken clock is right twice a day."

The combinatorial nature of trying things randomly means that it would take millennia or longer for light-speed monkeys typing at a keyboard, or GPUs, to solve such a problem without direction.

By now, people should stop dismissing RL-trained reasoning LLMs as stupid, aimless text predictors or combiners. They wouldn’t say the same thing about high-achieving, but non-creative, college students who can only solve hard conventional problems.

Yes, current LLMs likely still lack some major aspects of intelligence. They probably wouldn’t be able to come up with general relativity on their own with only training data up to 1905.

Neither did the vast majority of physicists back then.

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