meiji163

A better description is "simple", not "easy".

"If you do not believe that mathematics is simple, it is only because you do not realize how complicated life is." -von Neumann

Some favorite math books

Intro to Smooth Manifolds, Lee -- sweeping intro to geometry with minimal prereqs, great at balancing the nitty gritty details with conveying intuition

A Course In Arithmetic, Serre -- classically terse and elegant intro to algebraic and analytic number theory. Goes from quadratic forms to Dirichlet's theorem to modular forms in a mere 100 pgs!

Princeton Lectures in Analysis, Stein & Shakarchi -- 4 books covering much of classical/modern analysis, they really shine in their discussion of applications

The large scale structure of space-time, Hawking & Ellis -- The most mathematically satisfying treatment of general relativity I've found. High points include proof of singularity theorems!

Spin Geometry, Lawson & Michelson -- Deep dive into the enigmatic "spin groups" and their applications in geometry. Also the only good (book) reference I could find on the index theorem

Milnor is a wonderful writer, in his books as well as his papers.

> I'm not sure how useful category theory actually is in the example cases.

It's hard to say that category theory is "applied" to this or that problem. you'll hear many mathematicians call it "abstract nonsense" half-jokingly. More than anything it's a unified way of talking about mathematical structures that gives you a certain point of view (which is where it might be useful).

The best book I've found for a non-math audience is Fong & Spivak, 7 Sketches in Compositionality.

In Theorem 1.1, f is a function of random variables, which might be where you're confused.

> doesn't that mean y is a predictable function of x

Sort of: as function of real numbers, sha256 is just some deterministic function. But point is its output "looks like" a uniform random variable for any reasonable input distribution i.e. as a function of random variables the input and output variables should have 0 correlation

Not only is the diagnostic framework a joke, it's the basis of immense amounts of iatrogenic harm [0]

[0] "Anatomy of An Epidemic", Robert Whittaker

+1 I recently read a The Idiot as well, another incredible work of his.

This article is a great example of what I'd call "mindless problematization" From what I've seen, this is you're trained to do in modern humanities departments. Take any seemingly obvious claim and "problematize" it.

It's telling that they do not say "nuance" it, rather it has to be made a _problem_. e.g. if you think "wilderness" is a thing you subscribe to a racist idea for "white male elites", if you think social media is affecting childhood development you're just caught up in the religious fervor of "scientized version of the biblical story of the Fall".

A whole lot of BS gets written this way, because these arguments have the superficial air of being subversive and contrarian.

I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.