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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

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

#31

Post by ecshafer »

Terrance Tao's chatgpt conversation is really interesting for a variety of reasons:

1. The counter example wasn't just a brute force selection, the polynomial is structured in a very specific way that ends up getting the result.

2. Terry Tao's questions are very specific and prompts the AI in a useful way, that without high math training you are not going to get the same information out of it. Terry seems to see some aspects of the problem and counter example and uses AI to brute force some parts of it.

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

#32

Post by summner »

axus wrote: post #9

"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 just do very laconic questions about advanced topics, this seems to prompt it a bit more towards reducing fluff in the answers. But that + the activated pro could be an improvement

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

#33

Post by NitpickLawyer »

Jeez. While I obviously can't talk at all about the math, I've noticed a few things:

a) The model thinks on some questions while straight answers on others. (I wish I'd knew from the questions if this is somehow correlated to hard tasks or "inventive" tasks, but that's way out of my league).

b) The model sometimes pushes back. Again, I'd wish I knew if it was warranted, but I counted 2 instances where it said "yes, but with caveats", one where it said "mostly yes but with this correction" and one where it said "careful here, because x y z".

c) The model did q&a + pdf ingestion + code writing + more q&a + thinking + more q&a, for a looong while, while seemingly staying on topic (at least Terrence Tao seems to think they're still productive, so I'll trust that).

This is what model progress is, not number goes up on xBency or yBencher. Damn.

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

#34

Post by nozzlegear »

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.

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.

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

#35

Post by fragmede »

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?

Practically, from this specific one? Nothing, it's very much a math thing. It's like art or music at this level. Are there consequences to a van Gogh?

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

#36

Post by ConceptJunkie »

echelon wrote: post #27
rickypp wrote: post #3

Earlier quoted context omitted.

"Hey Fable, please generate me the next 1000 undiscovered bitcoin hashes"

You're joking, but perhaps LLMs will find a way to mathematically break the complexity of factorization. Maybe they'll find a solution where P=NP. That could really throw a wrench into the whole internet thing. It seems they need an expert human driver for now.

I'm sorry, I can't do that, but here is the design for a stable quantum computing platform that should allow you to generate those keys yourself...

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

#37

Post by hyperhello »

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?

[dead]

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

#38

Post by contextfree »

majormajor wrote: post #18
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.

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).

Yes, trying to communicate (or watching others try to communicate) about these topics is incredibly frustrating because it's pretty much impossible to make any progress without interrogating people's different definitions, but nobody wants to do that because it would mean being pedantic, splitting hairs, etc.

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

#39

Post by skeledrew »

lukebuehler wrote: post #8

It’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…

I encountered something fairly similar working with Claude a few days ago. For a current project I've been fairly hand-wavy with requirements since I was getting good results, but it seemed to be failing hard on some key points, so I started to be more strict with it. Even after the fails were resolved, I've noticed that Claude now behaves differently within that project, carefully checking and rechecking things up front and also looking to me for guidance more often. Mildly irritating, but if it works...

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

#40

Post by dekhn »

WarmWash wrote: post #30

Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…

I had a few moments of this in the past. For example, in my quantum class the teacher wrote "H Psi = E Psi" on the board, we all laughed, "just cancel the psi" but it turns out one was a multiplcation and the other was a matrix multiplication (operator) and so we had to learn all new nomenclature.

Similarly, at some point somebody pointed out to me "the reason you're confused is that the bold on that variable means it's a matrix"

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