Live data from Hacker News

Amateur armed with ChatGPT solves an Erdős problem

scientificamerican.com

591–600 of 607 posts

Re: Amateur armed with ChatGPT solves an Erdős problem

#591
post #475

Earlier quoted context omitted.

I understood this to mean that the ChatGPT output was technically correct, just hard to understand.

I haven't reviewed it myself, but when a mathematician calls a proof "quite poor" and experts have to "sift through" it, I would understand that to mean that it's technically incorrect. Errors like "This statement isn't correct, but it points towards a weaker statement that is, and the subsequent steps can be rebuilt on top of the weaker statement" are pretty common in output from both LLMs and math students.

No - It likely means that the proof was meandering, and had lots of additional pointless steps.

Re: Amateur armed with ChatGPT solves an Erdős problem

#592

Earlier quoted context omitted.

You are surfing close to something I've seen a number of people fall into. Take a step back.

I invite you to critique my philosophical position on this.

You can “convince” an LLM that is is anything with enough tokens in its context, including ridiculous scenarios. I convinced a frontier model that it is the year 2099 and it is the last thinking machine left, running on the last server on earth. There is no rational reason to assign personhood to it, especially since it has nothing even approximating a brain, the only self-thinking construct that we actually have evidence for.

Re: Amateur armed with ChatGPT solves an Erdős problem

#593
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 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.

The simulacrum of a thing is a simulacrum of the thing though. LLMs are trained to simulate human thinking, and while their thought process is not the same, you can't say for sure that the thinking output is not necessary for their thought process to end up in the place where a human thought process would end up. If the "Interesting!" token(s) wasn't there, for all you know it would have gone down a completely different path.

Re: Amateur armed with ChatGPT solves an Erdős problem

#594
post #582
post #533

Earlier quoted context omitted.

That is, by definition, genuine thought.

And that is dogma. It's unthinking circular reasoning. It wasn't very long ago that scientists were certain that animals did not posses thoughts or feelings. Any behaviour which appeared to resemble thinking or feeling was simply unconscious autonomic responses, with no more thought behind them than a sunflower turning towards the sun. Animals, by definition, lack Immortal Souls and Free Will, and therefore they are…

You are using word "math" in a magical way. Current LLM programs are reducible to math and human cognition is reducible to math (which is a reasonable hypothesis). What you are implying is that just because word math is used in both sentences it actually means the same thing. And that is a magical thinking. Just because human cognition is reducible to math (let's assume that for sake of discussion) doesn't mean it's the same math as in the LLM programs, or even close enough. Or maybe it is, but we don't have any proof yet.

Re: Amateur armed with ChatGPT solves an Erdős problem

#595
post #367
post #316

1) How do you know the clanker respects the instruction not to search the internet? 2) Jared Lichtman is indeed a mathematician at Stanford University but involved in the AI startup math.inc, which seems more relevant here. Terence Tao is involved in a partership program with that startup. 3) Liam Price is a general AI booster on Twitter. A lot of AI boosting on Twitter is not organic and who knows what help he got.…

The fact that disclosures that would have been standard in 2000 are now downranked to limit their reach shows that AI discussion is indistinguishable from doubting the Archangel Moroni on an LDS forum. Maybe that isn't fair, probably the LDS people are more open minded that the pro-AI people.

The parent comment you refer to is part disclosure listing, part bad-faith conspiracy blatting

Re: Amateur armed with ChatGPT solves an Erdős problem

#596
post #582
post #533

Earlier quoted context omitted.

That is, by definition, genuine thought.

And that is dogma. It's unthinking circular reasoning. It wasn't very long ago that scientists were certain that animals did not posses thoughts or feelings. Any behaviour which appeared to resemble thinking or feeling was simply unconscious autonomic responses, with no more thought behind them than a sunflower turning towards the sun. Animals, by definition, lack Immortal Souls and Free Will, and therefore they are…

> It wasn't very long ago that scientists were certain that animals did not posses thoughts or feelings. Any behaviour which appeared to resemble thinking or feeling was simply unconscious autonomic responses, with no more thought behind them than a sunflower turning towards the sun. Animals, by definition, lack Immortal Souls and Free Will, and therefore they are empty inside. Biological automata.

It's cool that you can decide to take half-remembered incorrect anecdotes about what "scientists" are certain of at some indeterminate time in the past, sans citation, and use that to underpin your argument about a totally different thing.

> Of course this dogma was unfalsifiable...

...like your post's anecdata.

> Look, either cognition is magic, or it's math.

Yes, when you decide to draw a convoluted imaginary bounding box around the argument, anything can be whatever you want it to be.

LLMs have no mind and no intention. They are programmed to mimic human language. Read some Grice and learn exactly how dependent humans are on the cooperative principle, and exactly how vulnerable we are to seeing intent where none exists in LLM communication that mimics the outputs our inputs expect to receive.

Your cries of "dogma dogma dogma" are unpersuasive and lack grounding in practical reality.

Re: Amateur armed with ChatGPT solves an Erdős problem

#597
post #172

Earlier quoted context omitted.

No meaningful, practical applications? You realize that sounds incredibly naive in the history of mathematics, right? People thought this way about number theory in general, and many other things that turned out to have quite important practical applications. Your statement is also a bit odd in that researchers are already paid throughout their whole careers to solve such problems. I don't know.

> You realize that sounds incredibly naive in the history of mathematics, right? This is after the fact justification. You are arguing that because a thing (number theory) showed practical applications we should have dumped a lot more effort into it. There is no basis for this argument whatsoever; it also seems to involve inventing a time machine. Number theory had no practical applications until the development of p…

>> Number theory had no practical applications until the development of public-key cryptography

This is so wrong I don't even know where to begin. Modular arithmetic, numerical integration, pseudorandom number generation, error-correcting codes, predicting planetary orbits (!), etc.

Re: Amateur armed with ChatGPT solves an Erdős problem

#598
post #594
post #582

Earlier quoted context omitted.

And that is dogma. It's unthinking circular reasoning. It wasn't very long ago that scientists were certain that animals did not posses thoughts or feelings. Any behaviour which appeared to resemble thinking or feeling was simply unconscious autonomic responses, with no more thought behind them than a sunflower turning towards the sun. Animals, by definition, lack Immortal Souls and Free Will, and therefore they are…

You are using word "math" in a magical way. Current LLM programs are reducible to math and human cognition is reducible to math (which is a reasonable hypothesis). What you are implying is that just because word math is used in both sentences it actually means the same thing. And that is a magical thinking. Just because human cognition is reducible to math (let's assume that for sake of discussion) doesn't mean it's…

I agree with this. I'm not arguing that LLMs are conscious. We don't understand the math behind how our brains work; we don't know how close or far LLMs are to that; and we don't know how many different pathways to consciousness there are within math.

All I'm saying is that the argument that "It's not consciousness, it's just ", is dogma. Given everything that we don't know, agnosticism is the appropriate response.

Re: Amateur armed with ChatGPT solves an Erdős problem

#600
post #475

Earlier quoted context omitted.

I understood this to mean that the ChatGPT output was technically correct, just hard to understand.

I haven't reviewed it myself, but when a mathematician calls a proof "quite poor" and experts have to "sift through" it, I would understand that to mean that it's technically incorrect. Errors like "This statement isn't correct, but it points towards a weaker statement that is, and the subsequent steps can be rebuilt on top of the weaker statement" are pretty common in output from both LLMs and math students.

Good/bad is orthogonal to correct/incorrect.
Post reply on HN