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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
11–20 of 681 posts
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#12It’s endlessly fascinating to read the AI transcript of an expert who _really_ knows how to cut to the chase. It just shows how much you can potentially squeeze out of these models. I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise (emphasis on progression and usage patterns, not absolute skill, obv I don’t match that): sho…
It reinforces how to "learn AI" is to first master the problem domain.
I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#13I wish you'd share some conversations from experienced programmers too. How do they ask questions?
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#14Similar 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.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#15Maybe 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.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#16"I’ve activated Pro. Can you continue to look for a potential geometric explanation of the X_3 ~ A3 miracle that avoids coordinates or other unmotivated constructions ?" Another satisfied customer!
I do the same kind of thing. "You're smarter now, time to try to cut down dumbo ChatGPT".
High IQ bros.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#17I'll have a blog post up tomorrow about it but the Jacobian Conjecture counterexample is a very funny cognitohazard for LLM assistants. It's a paradox for modern LLMs: they have enough math skills such that they can easily compute the Jacobian to formally verify the counterargument, but its own knowledge base is locked prior July 19th 2026 where all it knows is that the Jacobian Conjecture is unsolved and a random chat user providing such a proof is highly unlikely.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#18Similar 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.
Everyone uses "intelligence" to mean something slightly different, so for this to be a useful claim to make or refute we need to come up with new, intentionally-pedantic, terms (or new domain-specific definitions for vague existing ones).
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#19Can't even ctrl+f the conversation, wish openai would fix that
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#20It's reassuring to know that even a supergenius's ChatGPT session is one sentence from the human followed by 3 pages of LLM output.