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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

#121

Post by charcircuit »

thechao wrote: post #75
brotchie wrote: post #64

Earlier quoted context omitted.

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…

I want to be able to take a conversation and ask for subconversations as red pen annotations "on the side". The linear nature of the context tends to frustrate this.

There are already browser extensions similar to this.

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

#122

Post by anthk »

elviejo wrote: post #100
dekhn wrote: post #40

Earlier quoted context omitted.

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…

That is why Iverson invented APL. As a notation to get rid of all those inconsistencies in math notation. And for years he taught math classes with APL on the blackboard without computers. whether he succeeded, is debatable. But APL is definitely powerful, succinct and "regular". In APL you don't infer the operation from the types at all. × is elementwise, +.× is inner product /always/, on scalars, vectors, matrices,…

For something like APL modulo the Unicode symbols:

https://t3x.org/klong/

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

#123

Post by LearnYouALisp »

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.

"Gew on, lad!"

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

#124

Post by dachworker »

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…

The abstraction is by necessity. Our puny brains have only a very small working memory. The only way we can reason about many problems is by creating multiple levels of hierarchy. That is actually the essence of what mathematics is.

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

#125

Post by istrice »

NitpickLawyer wrote: post #33

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, b…

The "yes, with caveats" thing is boilerplate for both Codex and Claude since this current generation.

It's actually a bit annoying because it primes you to think that the caveats are real, but most of the time it's just something terribly obvious and not a real caveat, but the model probably has some system prompt that tells it to always consider caveats or something like that.

Same as the model starting every reply with a commitment to be "honest". LLMism are fun but I tend to just suppress them via AGENTS.md because they distract me

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

#126

Post by brap »

kingleopold wrote: post #103
brap wrote: post #58

Earlier quoted context omitted.

It’s crazy how much these companies invest in their models but when it comes to UX they do fuckall

UX is still very hard for any startup because top talent almost never work on UX.

I’m sure they can hire a whole team of world-class UX folks and it will pay for itself

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

#127

Post by LearnYouALisp »

Freedom2 wrote: post #117
taylorfinley wrote: post #114

Earlier quoted context omitted.

Came here to flag the same beat. It's wild to me Terrance Tao has to pay to talk to chatgpt, you would think it would be the other way around!

How would you envision ChatGPT paying Terrence?

"I have some tokens."

"What am I going to do with these?"

"Try to trade them up for a Volkswagen?"

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

#128

Post by missedthecue »

Freedom2 wrote: post #117
taylorfinley wrote: post #114

Earlier quoted context omitted.

Came here to flag the same beat. It's wild to me Terrance Tao has to pay to talk to chatgpt, you would think it would be the other way around!

How would you envision ChatGPT paying Terrence?

OpenAI giving him a fancy schmancy title to advocate for their product, such as in the way he is inadvertantly doing here.

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

#129

Post by jephs »

Freedom2 wrote: post #117
taylorfinley wrote: post #114

Earlier quoted context omitted.

Came here to flag the same beat. It's wild to me Terrance Tao has to pay to talk to chatgpt, you would think it would be the other way around!

How would you envision ChatGPT paying Terrence?

OpenAI hiring him as a consultant, obviously, which may well be the case.

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

#130

Post by gowld »

ben_w wrote: post #70
dekhn wrote: post #40

Earlier quoted context omitted.

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 ma…

Look up "APL" and "J".
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