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Terrence Tao's blog is better than most textbooks and everyone has been using it for the past 20 ish years lol
A digestion of the Jacobian conjecture counterexample
71–80 of 150 posts
Re: A digestion of the Jacobian conjecture counterexample
#72Re: A digestion of the Jacobian conjecture counterexample
#73Earlier 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?
I consider it both interesting and important to stay informed on the capabilities and limitations of frontier AI models. I'm not a mathematician myself -- he might as well be speaking Martian for all I know -- but the opinion and experience of a leading authority in the math field is very relevant to staying abreast of the larger machine-intelligence field.
Re: A digestion of the Jacobian conjecture counterexample
#74reading through this I eventually realized a situation similar to my experience of it is what my dog sees if I attempt to explain Python programming to him.
The difference is your dog will never understand the Python code but you could probably understand this post in a matter of days or weeks if you really wanted to. Can we all please stop acting like this Terry guy is so special?
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Re: A digestion of the Jacobian conjecture counterexample
#75reading through this I eventually realized a situation similar to my experience of it is what my dog sees if I attempt to explain Python programming to him.
The difference is your dog will never understand the Python code but you could probably understand this post in a matter of days or weeks if you really wanted to. Can we all please stop acting like this Terry guy is so special?
I'm not sure if you're taking the piss or genuinely don't know who he is
Re: A digestion of the Jacobian conjecture counterexample
#76The introduction to this piece was easy to follow, but as soon as he got into recapitulating it with algebra he lost me (because I'm bad at math). But he includes the GPT5 prompts for his conversation, which are easier to follow: https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed...
> I'm bad at math ... he includes the GPT5 prompts for his conversation, which are easier to follow
You were kidding, right?
Re: A digestion of the Jacobian conjecture counterexample
#77[flagged]
You're not gonna believe what Paul Graham's blog or the discussion board related to it looks like.. straight out of the 90s. Forget LaTeX it doesn't even support images!
Re: A digestion of the Jacobian conjecture counterexample
#78The introduction to this piece was easy to follow, but as soon as he got into recapitulating it with algebra he lost me (because I'm bad at math). But he includes the GPT5 prompts for his conversation, which are easier to follow: https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed...
> Clearly one can get from Theorem 3 to Theorem 2 by composing with the isomorphism {X \cong {\bf C}^3} and using the previously mentioned fact that local injectivity implies non-zero constant Jacobian.
I mean, clearly, right?
You and me both, pal.
Re: A digestion of the Jacobian conjecture counterexample
#79Okay. So what does this overturn, intuitively? Can we no longer assume that functions are differentiable at certain points, or something?
I'm not a mathematian but I know enough linear algebra and vector calculus to understand the conjecture. This is my interpretation: Firstly, the determinant of the Jacobian is measuring if at any point the function is crushing space / flattening out. If the Jacobian is a nonzero constant everywhere this means that nowhere does the the function flatten out. A small change in X along any line will always produce a non…
Sounds like 3 more iterations on K3/Fable, and we'll able to ask it to break computational hardness assumptions like DLP?
Re: A digestion of the Jacobian conjecture counterexample
#80Earlier quoted context omitted.
The difference is your dog will never understand the Python code but you could probably understand this post in a matter of days or weeks if you really wanted to. Can we all please stop acting like this Terry guy is so special?
I certainly do not think that the average HN reader "could probably understand this post in a matter of days or weeks". I think the level of background information you need is something like an undergraduate degree in mathematics and at many universities that's probably not enough either.
There's a difference between understanding something and being able to do something. For example you can get a broad understanding of what calculus does in a matter of minutes: a derivative is just the rate of change of a curve, and an integral is the total area under a curve - you're practically there! Of course it'd take months of work to understand how to apply it yourself, let alone all the tricks involved, but a basic understanding of what stuff is, is very easy to obtain.
And I think that generalizes to math. Its normal presentation is completely impenetrable due to a large use of symbols and terms with no outside meaning (or, even worse, a meaning that contradicts the colloquial usage). But I think if we somehow resolved that issue, the average person would be fully capable of following along even if they're going to have to take everything at face value as opposed to being able to meaningfully understand the exact methods and tricks being used to get from A to B.