orlandpm

> dedicated 60-vCPU server

How many of these are you paying for out of pocket??

Who is funding this? Sounds like a fun experiment but that’s a huge amount of compute if I understand correctly.

Well, all these closed surfaces you mention are (topologically) spheres. The theorem doesn’t apply to some other closed surfaces, like the torus, which does admit a continuous non-vanishing vector field.

Heard a mathematician friend call this the “hairy sphere theorem” once. At first I thought he was being a prude, but now I appreciate that the theorem is about spheres, as opposed to balls.

Yes! Draw an equilateral triangle with side length one. Then cut it in half and reason from there.

(2015)

Nice! I like the way you put this.

_Algebraic Topology_ by Allen Hatcher. This is quite an advanced book, but it was the first topology book I picked up and it blew my mind. Without a serious math background you may only be able to read the first parts (some of chapters 0 and chapter 1), but even so it may amaze you. It was insane to see how much mathematical machinery can be built up to understand concepts as simple as “space” and “continuity.” Then these tools can be used to quickly prove facts about mind-boggling higher dimensional objects.

_Introduction to Quantum Mechanics_ by David Griffiths. Not CS or Math, but an amazing book because if you sit down and work through it it gives you a manageable intro to a completely non-intuitive and mysterious scientific field. Prerequisites are “only” multivariable calc and linear algebra.

_Algebra_ by Michael Artin. This was the book I decided to grind through at the right time to learn abstract algebra and get better at rigorous proofs, and it was worth it. Part of why I loved this book and subject is because it feels dry and mechanical at first, but if you work on it long enough you can see the beautiful bigger picture come together.

_Introduction to Topological Manifolds_ by John M. Lee. This was another “right book at the right time” for me. The title is a bit jargony, but it is a rigorous introduction to the foundational objects of modern geometry (namely topological spaces and manifolds in particular). Great warm-up for the first book on my list.

_Algebra: Chapter 0_ by Paulo Aluffi. Weird title, but the first few chapters are the best perspective on abstract algebra I’ve seen. He focuses early on categories in a useful and philosophically interesting way, which is unique.

_Gravitation_ by Misner, Thorne, and Wheeler. Didn’t read the whole thing, but this book taught me a tensor is just a higher-order linear function. Who knew? Most physicists give really crappy explanations of tensors. Also I love that this book, affectionately known as the “phone book”, is so heavy that one imagines spacetime curving around it.

After I understood monads, I didn't write a short blog post about how simple they are. In fact, I took the opposite approach and am writing a ~500 page book about them :).

In seriousness, there's a lot that goes into appreciating a concept like a monad, especially if you want to combine the FP understanding with a rigorous mathematical understanding (monoid in a category of endofunctors approach). My new book is coming out next year with No Starch Press, and my goal is to give programmers a serious but doable introduction to abstract algebra, in the case that they care about this kind of stuff. Ping me if you want to read some early chapters and give feedback! [email protected]

I don’t think most PhD physicists know what a diffeomorphism is.