alt Hacker NewsHey do you want to hear about this cool new result in maths? Let's just speedrun a graduate course in all the prerequisites!
(I more or less do have the background to read these things, but it's super off-putting to start the article about a crazy new proof from a Fields medallist with an introduction to manifolds.)
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I'm reminded of a graduate course in Elliptical Curves where, late in the semester, we took a lecture to speedrun all the prerequisites and ideas of Perelman's [then new] proof of the Poincaré conjecture. It was wild but a lot of fun.
I mean that's pretty much just what Quanta does, if you don't like it I'd recommend reading a different publication. It's their whole shtick, simplifying complex news about science/mathematics just enough so that people completely unfamilar can get a general sense of what happened.
You can always just not read an article, particularly if it triggers you.
I think it's nice someone wrote about this, even if it's super technical and I cannot understand it completely.
I got it for free!
(EDIT: I'm sorry, this silly and dumb.)
"You want many folds!" We gottem!
(Shrug) It's a really nice introduction to manifolds, to the extent that's what it is. Really it's just an introduction to rational parameterization, which I'd never heard of but which at first glance seems extremely nifty.
It all gets pretty incomprehensible after that, but that's not the author's fault.
Do you have the background to do what QM/wiki does, but for HN?
Eg breakdown the explanation of the Hodge diamond on P6 of the paper LI5
Here's how en.wiki (with diagram!!) does it -- which I thought could have been handwaved better in TFA:
Mirror symmetry translates the dimension number of the (p, q)-th differential form h^(p,q) for the original manifold into h^(n-p,q) of that for the counter pair manifold.
(n=4 for the paper)
https://en.wikipedia.org/wiki/Homological_mirror_symmetry#Ho...
To call this an idea from string theory, is giving string theory too much credit (imho)