Best diagrams in any mathematical paper ever. Previous discussion [1] from a year or so ago.

[1] https://news.ycombinator.com/item?id=7655487

I found figure 2 needlessly confusing, as it showed the individual components overlapping, it was hard to visually separate them.

Also, needing a key to identify "blue dot" and "red dot" is amusing.

Brilliant use of napkin.js.

For the curious, yes this is actually a thing [1].

[1] https://github.com/napkinjs/napkinjs

Don't miss the compelling sequal, "Division by four".

http://arxiv.org/abs/1504.01402

This has probably one of the most amusing paragraphs of a math paper I have seen:

"We made it hard for ourselves in order to show a method that works for all n. It would have been more natural to take n = 3, which is the crucial test case for division. If you can divide by 2, and hence by 4, there is no guarantee that you can divide by 3; whereas if you can divide by 3, you can divide by any n. This is not meant as a formal statement, it’s what you might call a Thesis. We chose n = 4 instead of n = 3 because there are four suits in a standard deck of cards, and because there is already a paper called ‘Division by three’ [2], which this paper is meant to supersede."

Also worth noting, these two papers have the same lead author.

"∗John Conway collaborated on the research reported here, and has been listed as an author of this work since it was first distributed in 1994. But he has never approved of this exposition, which he regards as full of ‘fluff’"

That's weird; I thought Conway was a big fan of fluff (and while the reader is enjoying the fluff, he sneakily introduces the highly non-trivial.)

Edit: well the paper is fairly chatty, I guess that turns some people off (it can obscure the argument.)