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A digestion of the Jacobian conjecture counterexample

terrytao.wordpress.com

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Re: A digestion of the Jacobian conjecture counterexample

#21
post #7

Earlier quoted context omitted.

People are upvoting this because Tao is a celebrity.

He’s famous, but I don’t believe he is a celebrity, as he is not famous for his persona.

I just mean, anything Tao writes that is related to AI will get on the front page, because Tao represents the authoritative voice of reason using AI tools. And this website is primarily for AI news.

Re: A digestion of the Jacobian conjecture counterexample

#22
post #9

[flagged]

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

> Does asking "make no mistakes" actually change the output?

Why Teams Add "Make No Mistakes" to AI Prompts (And Why It Never Works)

https://jakemcmahon.github.io/medium-articles/make-no-mistak...

Re: A digestion of the Jacobian conjecture counterexample

#23
post #7

Earlier quoted context omitted.

People are upvoting this because Tao is a celebrity.

I'm upvoting this because it's interesting. I don't have to fully understand something to find it interesting.

In what way is it interesting compared to the myriad of other posts on this topic that has content you can understand?

Re: A digestion of the Jacobian conjecture counterexample

#24

Earlier quoted context omitted.

It will make mistakes if you tell it to, so I assume it will make no mistakes if you tell it not to.

When this news came out I amused myself by asking Claude to prove that 0.999... != 1. First it did so for the hyperreals. To do it for the reals I had to tell it it was allowed to make mistakes, although it didn't end up interestingly wrong - just very fuzzy and vague.

Fable, prove that for every positive integer n, repeatedly dividing by 2 if even or multiplying by 3 and adding 1 if odd will always eventually reduce the sequence to 1.

Re: A digestion of the Jacobian conjecture counterexample

#25

Earlier quoted context omitted.

I'm upvoting this because it's interesting. I don't have to fully understand something to find it interesting.

In what way is it interesting compared to the myriad of other posts on this topic that has content you can understand?

It's interesting because I like math, and typically posts like this generate a lot of interesting comments. Plus, in general, I'm wildly disinterested in the AI discourse that eats up 50-75% of the front page, so frankly anything that's slightly more interesting than that gets an upvote from me.

Re: A digestion of the Jacobian conjecture counterexample

#27

Okay. So what does this overturn, intuitively? Can we no longer assume that functions are differentiable at certain points, or something?

No. This is about polynomials. The assumption that the Jacobian is nowhere zero is what is doing so much of the work. This means the Jacobian must in fact be constant. But obviously there are many mappings whose Jacobians are not constant.

Re: A digestion of the Jacobian conjecture counterexample

#29

Earlier quoted context omitted.

In what way is it interesting compared to the myriad of other posts on this topic that has content you can understand?

It's interesting because I like math, and typically posts like this generate a lot of interesting comments. Plus, in general, I'm wildly disinterested in the AI discourse that eats up 50-75% of the front page, so frankly anything that's slightly more interesting than that gets an upvote from me.

You seem to be saying that you would upvote an empty article (or a gibberish article) with the title "Jacobian Conjecture Counterexample", is that right?
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