Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

chatgpt.com

Post reply on HN
Print view View original

41–50 of 681 posts

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#41

Post by hyperhello »

sdwr wrote: post #15
vb-8448 wrote: post #2

Maybe it's silly, but from someone who is ignorant on this topics, what are the consequences of this kind of "discoveries"? Is it something "revolutionary" or just another small brick that will pile up until something really "revolutionary" will happen?

It's an indicator of AI progress. The solutions aren't especially revolutionary, but no person had been able to solve them after decades of collective attempts.

To be fair I don’t think there were too many people really trying to. Symbolically, one could make a parameterization of the Jacobian determinant and then brute force a solution, if one had known such a polynomial existed in only three dimensions.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#42

Post by tetris11 »

napoleoncomplex wrote: post #21

This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.

crosses fingers "Low hanging fruit, low hanging fruit, low hanging fruit..." hyper-ventilates

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#43

Post by tetha »

Jun8 wrote: post #5

Similar to how Cypher puts it: I know this is “just” next token inference, matrix mult and just software, ie there’s no “intelligence” there BUT, looking at this convo … damn! The fascinating this is that the LLM is not acting as a tool here AFAIk, but very much like a colleague. I have no knowledge of the domain and have only PhD EE level math knowledge, so maybe my bar is too low.

I think the "But this is not intelligence because it is known math" is not a correct argument. It is unknown how the overall higher intelligence of humans works.

What I do notice however is that LLMs are becoming capable of doing an increasing part of the intellectual work I can do, and usually a lot faster.

Just today I presented an agent framework that can take an informal incident statement and propose infrastructure changes to fix it, all evidence backed. This did nothing I could not to, but it did all 5 test cases in 6 - 12 minutes each. I would have found all of the monitoring indications it did, but it would have taken me a day per test case. The LLM also included sass to silly tickets. ("This is not even worth spending monitoring resources on. It's obviously a configuration problem.")

That's how this is reading to me as well. It's just fast at slogging through a certain level of "simple" transformations.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#45

Post by Diogenesian »

IshKebab wrote: post #14
Jun8 wrote: post #5

Similar to how Cypher puts it: I know this is “just” next token inference, matrix mult and just software, ie there’s no “intelligence” there BUT, looking at this convo … damn! The fascinating this is that the LLM is not acting as a tool here AFAIk, but very much like a colleague. I have no knowledge of the domain and have only PhD EE level math knowledge, so maybe my bar is too low.

> there’s no “intelligence” there BUT There is clearly intelligence there. We have no way to recognise intelligence other than the appearance of intelligence and this very clearly displays that. It's also quite clearly different to human intelligence in some notable ways, but not in any that preclude describing it as intelligent. At least for normal non-pedantic definitions of the word.

[flagged]

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#48

Post by cyanydeez »

napoleoncomplex wrote: post #21

This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.

this sounds like like an open parenthesis (

without someone independently verifying it, it just dangles there

...

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#49

Post by doctoboggan »

Similar to the story of George Dantzig, who was late to class and solved two open problems in statistics because he mistook them for homework, I think the current batch of frontier LLMs are chained up by knowing which problems are supposed to be unsolved. If they're let free (probably via some targeted RLHF) we might get a flurry of solutions to open problems.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#50

Post by squidbeak »

nozzlegear wrote: post #34
IshKebab wrote: post #14

Earlier quoted context omitted.

> there’s no “intelligence” there BUT There is clearly intelligence there. We have no way to recognise intelligence other than the appearance of intelligence and this very clearly displays that. It's also quite clearly different to human intelligence in some notable ways, but not in any that preclude describing it as intelligent. At least for normal non-pedantic definitions of the word.

That's not clear at all. What's clear is that this is a very smart man who knows how to use this tool well.

I'd say an entity capable of instructing one of the leading mathematicians of his era is pretty clearly intelligent by any reasonable measure - however it might be arriving at its output.
Post reply on HN