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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

#71

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.

Math is full of such steps, moreso than most other endeavors, probably because the main limit is the abstract reasoning itself.

That, as well as how long we've been doing it (thousands of years!) and so how much of the more accessible parts we've explored very thoroughly.

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

#73
post #66

This was my conversation with ChatGPT 4 years ago: https://i.imgur.com/WPaWgzZ.png Where will we be in another 4 years? What a time to be alive!

I'm from the UK. What's in the image?

Me asking ChatGPT what values of x satisfy 0/x = 0. ChatGPT insists it has no solutions.

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

#74

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…

It can't be one language, and that's the big problem. It's inescapably a bunch of tiny DSLs. Once you see both the inconsistency and the necessity for inconsistency, it becomes much easier to just roll with it.

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

#75

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…

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.

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

#78

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.

But a property of intelligence is to know when to stop, if we treat intelligence as some sort of search and not some a priori intuition of the entire space. Seems kind of hard, if not impossible, to train for specifically that.

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

#80
post #66

This was my conversation with ChatGPT 4 years ago: https://i.imgur.com/WPaWgzZ.png Where will we be in another 4 years? What a time to be alive!

I'm from the UK. What's in the image?

ChatGPT repeatedly asserting that 0/x=0 is division by zero and therefore no value of x satisfies the equation.
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