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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

#431

Post by ndriscoll »

gverrilla wrote: post #419
ndriscoll wrote: post #355

Earlier quoted context omitted.

Why wouldn't you just use coding agents and ensure you have e.g. Lean and Mathlib in the environment?

the system prompt could be narrower, for instance. there's no reason for such a harness to know about React stuff, for instance.

Does Claude Code's system prompt know about react? Why? That would be dumb even for coding for e.g. server side applications.

Like when I'm programming with Go or Scala or Rust, codex just assumes the relevant stuff is on my PATH. If it needs to reference library definitions, it looks at the standard locations (which the model already knows) for the package cache. etc.

Re: Amateur armed with ChatGPT solves an Erdős problem

#432

Post by philipallstar »

orangebread wrote: post #430
nkrisc wrote: post #412

Earlier quoted context omitted.

Mimicry is how kids learn the expected reactions to particular emotions. A kid mimicking your surprise doesn’t mean they are surprised (as surprise requires an existing expectation of an outcome they may not have the experience for), but when they do feel genuine surprise, they’ll know how to express it.

How do we know that AI isn't feeling genuine surprise then?

Because it's a statistical process generating one part of a word at a time. It probably isn't even generating "surprise". It might be generating "sur", then "prise" then "!"

Re: Amateur armed with ChatGPT solves an Erdős problem

#433

Post by 0xBA5ED »

tptacek wrote: post #145
emp17344 wrote: post #143

Earlier quoted context omitted.

Well, hang on a second - it sounds like you may actually disagree with the user who created this thread. That user claims that these systems exhibit “real intelligence”, and success on this Erdos problem is proof. You seem to be making the claim that LLMs are statistical text generators, but statistical text generation is good enough to succeed in certain cases. Those are different arguments. What do you actually bel…

I don't have any opinion about "real intelligence" or not. I'm not a P(doom)er, I don't think we're on the bring of ascending as a species. But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are.

"But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are."

Umm, why doesn't it capture it? Why can't a statistical text generator do amazing things without _actually_ being intelligent (I'm thinking agency here)? I think it's important to remind ourselves, these things do not reflect or understand what they're outputting. That is 100% evident with the continuing issues with them outputting nonsense along with their apparently insightful output. The article itself said the output was poor but the student noticed something about it that sparked an idea and he followed that lead.

Re: Amateur armed with ChatGPT solves an Erdős problem

#435

Post by 0xBA5ED »

fc417fc802 wrote: post #193
baxtr wrote: post #171

Earlier quoted context omitted.

Just to clarify because I’m not sure I understand: So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?

Not parent but I think you're being rather dense. They are _obviously_ statistical text generators. There's plenty of source code out there, anyone can go and inspect it and see for themselves so disputing that is akin to disputing the details of basic arithmetic. But it is no longer useful to bring that fact up when conversing about their capabilities. Saying "well it's a statistical text generator so ..." is approx…

It is still important to mention that because atoms have limitations and so do statistical generators. Plain and simple. People are walking around thinking organic brains are just statistical generators and they're gonna build AGI with GPUs. It's absurd.

Re: Amateur armed with ChatGPT solves an Erdős problem

#436

Post by Xmd5a »

somewhatgoated wrote: post #332
petra wrote: post #329

Earlier quoted context omitted.

I don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???

It has an “high effort” mode that makes it think really long

Ahhhh... you need ChatGPT pro at 100 bucks/month. Am I correct?

Re: Amateur armed with ChatGPT solves an Erdős problem

#437

Post by steveklabnik »

chvid wrote: post #273
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…

I am curious if there is a “harness” for maths out there (like the system prompt and tool collection in Claude code but for maths instead of coding)? Asking the llm to structure its response in plan and implementation, allowing it to call tools like python, sage, lean etc.

https://aristotle.harmonic.fun/ is the one I've heard of previously in regards to LLMs solving previous Erdős problems.

Re: Amateur armed with ChatGPT solves an Erdős problem

#438

Post by threethirtytwo »

bsza wrote: post #256
simianwords wrote: post #243

Earlier quoted context omitted.

what? the post is literally titled "Amateur armed with ChatGPT solves an Erdős problem". stop spreading FUD about unaffordability

They used ChatGPT Pro to solve it. Over 50% of people in the world couldn't afford ChatGPT Pro ($200/mo) even if they spent more than half of their income on it. [1] What was that about "spreading FUD about unaffordability"? [1] https://ourworldindata.org/grapher/share-living-with-less-th...

This is the most pedantic argument ever.

"All men are created equal" is obviously not literally saying all humans are 100% equal. Just like how "ChatGPT equalizes intelligence" is not saying ChatGPT equalizes the intelligence of all humans to a level of 100%.

I'm not going to spell out what I meant by: "ChatGPT equalizes intelligence". You can likely figure it out for yourself, because the problem doesn't have anything to do with your reading comprehension. The problem is more akin to self delusion, you don't want to face reality so you interpret the statement from the most absurdist angle possible.

The admins at HN actually noticed this tendency among people and encoded it into the rules: "Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith."

Re: Amateur armed with ChatGPT solves an Erdős problem

#439

Post by zitterbewegung »

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…

I'm doing the obvious thing and cut and pasting the other similar problems into chatgpt.

Re: Amateur armed with ChatGPT solves an Erdős problem

#440

Post by bitwize »

dalmo3 wrote: post #287
bonesss wrote: post #249

Earlier quoted context omitted.

> machanistic interpretation Awesome term/info, and (completely orthogonal to whether they’ll take err jerbs ): I’m really excited about the social/civic picture that might be enabled by a defined and verifiable ontological and taxonomical foundation shared across humanity, particularly coupled with potential ‘legislation as code’ or ‘legal system as code’ solutions. I’m thinking on a time horizon a bit past my own l…

Ah, yes, 2001 but on land.

I consider the scene with Dr. Chandra and SAL 9000 to be a fairly realistic predictive description of how experts interact with LLMs. SAL even has a somewhat obsequious personality.
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