An Infinitely Large Napkin [pdf]

This document reminds me of the kinds of things I wrote at a smaller scale when I'd self-teach math. The usual pattern was:

- I don't know how X works.

- I collect several sources about X and try to understand it.

- I put in a lot of effort to understand X by reading all these sources repeatedly. I try to do exercises, do calculations, etc. I'm desperately seeking the moment it "clicks".

- I finally kinda sorta "get" X.

- I feel, "why didn't anybody simply explain X in this way?" / "why was everybody so overly formal?" / "why was everybody so overly informal?"

- I'm motivated to write a short note about X that makes it (allegedly) easier to understand X.

- I write it, and I realize it's actually hard to weave together a narrative that doesn't over- or under-assume prerequisites, that captures nuance, that has good examples, etc.

- "There are 15 competing standards."

The Infinitely Large Napkin is a really cool consolidation of a ton of undergrad/early grad pure math topics. It's so incredibly expansive in its scope and, if it were in book form, I'd have been ecstatic to have it as a 16 year old.

But paging through it, I find that they're very much in the style of quasi-formal lecture notes. A lot of topics are mentioned by their formal definition, and it's followed by a very anemic (if any) discussion, sometimes preceded by a very informal (sometimes humorous) introduction. Often such definitions are immediately followed up by a relatively technical exercise that presumes a fully synthesized understanding of material preceding.

In my view, this isn't the kind of book you work through. It's not "math distilled". Instead, it can serve as a great diving-off point for a new subject, or an inspiration to know where to look further on a given subject, or even a useful document to find a topic that piques your interest. Other books like this are those of yore that were encyclopedic in nature, such as:

- VNR Concise Encyclopedia of Mathematics (1975–1989) edited by Gellert et al. The math here doesn't get terribly advanced (complex and numerical analysis), but it's a good, expansive treatment to dive into.

- Mathematics From the Birth of Numbers (1997) by Jan Gullberg: This is another grand tour of math, albeit "only" to differential equations.

- The Princeton Companion to Mathematics (2008) edited by Timothy Gowers. This is a massive book that covers just about everything, up to and including some of the latest problems in mathematics. It's 1000 dense pages. (There's also the Princeton Companion to Applied Mathematics edited by Nicholas Higham.)

- The CRC Encyclopedia of Mathematics (1999) by Eric Weisstein. This is an anti-digitization of the Wolfram MathWorld into book form. Expansive, and also famous for some of the drama around its copyright. :)

How many of you upvote this pretenting to find some day the time and spirit to read and learn from it, but perfectly knowing that will never happen. I'm one of them unfortunally, gosh!

Is Github becoming the best place to host pdfs nowadays?

This reminds me of All the Mathematics You Missed (But Need to Know for Graduate School), which is a nice brief introduction to various undergrad maths topics

https://www.amazon.co.uk/All-Mathematics-You-Missed-Graduate...

I'm too dumb for this, and how popular it is here gives me anxiety

This quite literally points out a thousand things I havent fully understood about mathematics in a concise manner.

https://news.ycombinator.com/item?id=20168936 (2019, 33 comments)

https://news.ycombinator.com/item?id=30302291 (2022, 18 comments)

Is there a version of this with narrower margins? I can’t see well and need larger fonts