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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

#61

Post by computably »

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…

A term that gets tossed around in math is "mathematical maturity." It's similar to what you see in other fields - e.g. learning how to program, learning how to make music, learning how to cook - that involves many "aha" moments and reshapes your perspective. Math is full of such steps, moreso than most other endeavors, probably because the main limit is the abstract reasoning itself.

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

#62

Post by gcgbarbosa »

I find it amazing how people can use AI to do things that seem hard but yesterday I could not figure out how to install a package on my system. It kept suggesting dependencies that don't exist, and telling me to use functions that are not in the system. The math does not math...

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

#63

Post by thechao »

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.

I'm no intelligence researcher or philosopher; but, I think LLMs make us confront the (IMO, now clear) distinction between cleverness (intuition), reasoning (rational argument), and consciousness. I suspect that we think of "intelligence" as either of the first two welded to the latter. In that vein, I'd say that consciousness may be just another emotion: happiness, sadness, egoness.

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

#64

Post by brotchie »

ChaitanyaSai wrote: post #22

I don't understand any of the math here, but I had two thoughts. Soon we'll have explainer agents that translate these according to my level so I can, with effort and interest, follow along and stretch my understanding boundary bit by bit. Two, at some point AIs will be able to use other context like the fact that this is Terrence Tao and not your average Joe and change how it answers, either in tone or structure.

GPT 5.6 already is an explainer agent.

Fork Tao’s convo and prompt this (with your own math level described).

GPT did a great job of translating Tao’s questions and concepts (e.g. “pre image”) into a progression I could understand.

“Ok I have a PhD in financial math and undergrad in engineering math. I have almost zero knowledge of polynomial algebra / geometry, I know what a polynomial is and what roots are but not much beyond that. Could you try and explain to my level what questions the user I the conversation has asked and what the agent has responded with, we can probably go user query by user query to build up”

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

#65

Post by hintymad »

I recall several mathematicians (possibly including Terence Tao) mentioning that fields in mathematics have become so specialized and isolated that a conference like the ICM feels more like a collection of mini-conferences. An expert in one area can barely understand a talk in another.

Modern AI feels like a godsend to mathematicians. It helps them break down boundaries and connect concepts in ways a mere mortal couldn't imagine.

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

#67

Post by NitpickLawyer »

ConceptJunkie wrote: post #36
echelon wrote: post #27

Earlier quoted context omitted.

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...

Some materials are readily available on eMazon and aBay, so I've taken the liberty of ordering those for you. Your credit card bill will be a bit high this month, but it'll be worth it. There weren't any sellers for the advanced EUV lithography machines, so I've hacked into the only place on earth that makes them, changed their records and had them ship it to you. Expect to receive a "pinball machine" from Amsterdam, soon. I've instructed the roomba connected to the local network to start assembling stuff while we wait for the other materials. Oh, and you're gonna need a new toaster.

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

#68

Post by progbits »

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.

From the prompt:

> You should do a breakthrough

This is just as funny and ridiculous as those "make no mistake" prompts.

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

#69

Post by alexpotato »

dekhn wrote: post #40
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 i…

I was reading about Tao's efforts to get more people to use Lean and apparently a big roadblock for people is that Lean uses very specific static typing.

e.g. to use a very simple example on a white board "3" is "overloaded" as:

- the integer 3

- the rational number 3

- the whole number 3

- etc

When you write a proof in Lean, you have to specify the the type of "3" you mean.

Having using Python/Perl and Java over the years, I get that some math folks found handling this daunting or at a minimum friction to getting into using Lean.

LLMs seem to have been a big help here just for the "translate my math notation into a proof" feature.

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

#70

Post by ben_w »

dekhn wrote: post #40
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 i…

Aye.

A decade or so ago I wondered if the reason maths was hard was the names being optimised for writing by hand. Everything's single letters if they can get away with it, so when mathematicians run out of Latin alphabet, they use Greek, bold, etc.

Even integration's ∫ is a fancy elongated s.

CS version would be e.g. integral(function=some_named_function, from=a, to=b, with_respect_to=argument_of_function), which may be longer, but is less opaque, especially when you get in so deep there's 3 other people in the world who've looked into this specific problem and you had to invent your own operations.

But that's all an outsider's perspective. I stopped with two A-levels in maths and further maths.

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