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Amateur armed with ChatGPT solves an Erdős problem

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Re: Amateur armed with ChatGPT solves an Erdős problem

#341

Post by jeremyjh »

gorgoiler wrote: post #216

I asked ChatGPT to draw the outline of an ellipse using Unicode braille. I asked for 30x8 and it absolutely nailed it. A beautiful piece of ascii (er, Unicode) art. But I wanted to mark the origin! So I asked for a 31x7 ellipse instead. It completely flubbed it, and for 31x9 too. When a model gives a really good answer, does that just mean it’s seen the problem before? When it gives a crappy answer, is that not simpl…

No, that simply is not the case. The whole point of deep learning - and the reason it has been successful in so many domains over the last 20 years - is that generalization does occur. Leela will kick your ass at chess whether she's seen the position before or not, even if her search depth is set at 1 ply.

In the case of LLMs, the compression ratio alone absolutely requires this.

Re: Amateur armed with ChatGPT solves an Erdős problem

#342

Post by famouswaffles »

latexr wrote: post #233
famouswaffles wrote: post #178

Earlier quoted context omitted.

Intelligence is Intelligence. It's intelligent because it does intelligent things. If someone feels the need to add a 'real' and 'fake' moniker to it so they can exclude the machine and make themselves feel better (or for whatever reason) then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it. It's the equivale…

> It's intelligent because it does intelligent things. Most people would consider someone who can calculate 56863*2446 instantly in their head to be intelligent. Does that mean pocket calculators are intelligent? The result is the same. > then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it. That is the equiv…

>Most people would consider someone who can calculate 56863*2446 instantly in their head to be intelligent. Does that mean pocket calculators are intelligent? The result is the same.

If you wanted to insist a calculator wasn't intelligent and satisfy my conditions then you can. At the very least you can test for the sort of intelligence that is present in humans but absent from calculators and cleanly separate the two. These are very easy conditions if there is some actual real difference.

>That is the equivalent of responding to criticism with “can you do better?”. One does not need to be a chef (or even know how to cook) to know when food tastes foul.

No it's not, and this is a silly argument. Foul food tastes different. Sometimes it even looks different. You can test for it and satisfy my conditions.

You come across a shiny piece of yellow metal that you think is gold. It looks like gold, feels like gold and tests like gold. Suddenly a strange fellow comes about insisting that it's not actually gold. No, apparently there is a 'fake' gold. You are intrigued so you ask him, "Alright, what exactly is fake gold, and how can I test or tell them apart ?". But this fellow is completely unable to answer either question. What would you say about him ? He's nothing more than a mad man rambling about a distinction he made up in his head.

What I'm asking you to do is incredibly easy and basic with a real distinction. I'm not going to tell you to stop believing in your fake gold, but I am going to tell you I and no one else can be expected to take you seriously.

Re: Amateur armed with ChatGPT solves an Erdős problem

#343

Post by cubefox »

urutom wrote: post #265
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…

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

[dead]

Re: Amateur armed with ChatGPT solves an Erdős problem

#344

Post by [deleted] »

teiferer wrote: post #198
Tarq0n wrote: post #174

Earlier quoted context omitted.

Not definitively. LLMs are stochastic with respect to input, temperature and the exact prompt. It's possible that the model was already capable of it but never received the exact right conditions to produce this output.

Every model is able to solve each problem, given the right prompt. (Worst case, the prompt contains the solution.)

[deleted]

Re: Amateur armed with ChatGPT solves an Erdős problem

#345

Post by zeven7 »

petra wrote: post #329
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 don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???

I have Gemini and ChatGPT and keep them on the highest thinking settings. ChatGPT will regularly think 40-60 minutes on the same problem that Gemini will think 10-15 minutes on. The quality of ChatGpt’s response is usually a little higher but not that much higher. My takeaway is Gemini is better at thinking faster, maybe has better more dedicated hardware behind it, and I use Gemini if I want a faster answer but ChatGPT I’d I want to push the quality of the answer a little higher.

Re: Amateur armed with ChatGPT solves an Erdős problem

#346

Post by jackcarter »

bertil wrote: post #336
urutom wrote: post #265

Earlier quoted context omitted.

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…

It’s funny that this is probably due to bias in the training texts, right? Humans are way more likely to publish their “Eureka!” moments than their screwups… if they did, maybe models would’ve exhibit this behavior.

Now that AI labs have all these “Nevermind” texts to train on, maybe it’s getting easier to correct? (Would require some postprocessing to classify the AI outputs as successful or not before training)

Re: Amateur armed with ChatGPT solves an Erdős problem

#347

Post by andrepd »

urutom wrote: post #265
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…

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

The simulacrum of a thing is not the thing! Not only is the "interesting!" unrelated to any "thought process", the whole """thinking""" output is not a representation of a thought process but merely a post-facto confabulation that sounds appropriately human-like.

Re: Amateur armed with ChatGPT solves an Erdős problem

#348

Post by gus_massa »

Anon1096 wrote: post #325
gorgoiler wrote: post #216

I asked ChatGPT to draw the outline of an ellipse using Unicode braille. I asked for 30x8 and it absolutely nailed it. A beautiful piece of ascii (er, Unicode) art. But I wanted to mark the origin! So I asked for a 31x7 ellipse instead. It completely flubbed it, and for 31x9 too. When a model gives a really good answer, does that just mean it’s seen the problem before? When it gives a crappy answer, is that not simpl…

I wouldn't ask an LLM to output this directly. For an ellipse ascii I would guess that having it write a python program to generate it and then run it would work much better. Using claude sonnet 4.6 on a free account it seemed to work (sorry in advance if the hacker news formatting is horrendous) ⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀ ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀…

You can use two spaces at the beginning of each line to trigger the "code" mode. I tried to reconstruct your drawing, but perhaps I didn't guess correctly:

  ⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠢⠤⣄⣀
   ⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
   ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ 
   ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
   ⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
   ⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁
  ⠀⠀ ⠀⠀⠉⠙⠒⠢⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀
Edit: I had to delete the two first spaces or each line and replace them with newly typed spaces from my keyboard. Perhaps there is some white-space-unicode-magic-character that is confusing HN.

Re: Amateur armed with ChatGPT solves an Erdős problem

#349

Post by staticassertion »

petra wrote: post #329
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 don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???

In my experience, you can tell them "Don't stop working on this until complete" and they'll go for an hour or more.

Re: Amateur armed with ChatGPT solves an Erdős problem

#350

Post by IAmGraydon »

jeremyjh wrote: post #341
gorgoiler wrote: post #216

I asked ChatGPT to draw the outline of an ellipse using Unicode braille. I asked for 30x8 and it absolutely nailed it. A beautiful piece of ascii (er, Unicode) art. But I wanted to mark the origin! So I asked for a 31x7 ellipse instead. It completely flubbed it, and for 31x9 too. When a model gives a really good answer, does that just mean it’s seen the problem before? When it gives a crappy answer, is that not simpl…

No, that simply is not the case. The whole point of deep learning - and the reason it has been successful in so many domains over the last 20 years - is that generalization does occur. Leela will kick your ass at chess whether she's seen the position before or not, even if her search depth is set at 1 ply. In the case of LLMs, the compression ratio alone absolutely requires this.

So what do you think is the reason it could do 30x8 and not 31x7?
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