One of the great joys of mathematics is the incontrovertible feeling that you’ve understood something the right way, all the way down to the bottom.

That’s how Ellenberg eloquently explains the appeal of mathematics. This book contains many examples of how mathematical thinking can lead to deep understanding of a lot of things, from statistics to politics to perspective. Nuggets of insight are everywhere — the discussion of statistical significance should be read by everybody. (In the meantime, you can get the gist from the XKCD cartoon Significant, which Ellenberg also cites.)

Apart from all the maths, there’s also an unexpectedly enlightening explanation of the thoughts and motivations of Antonin Scalia, the (in)famously arch-conservative US Supreme Court judge. I feel that I now understand the logic behind his uncompromising views. It may be flawed logic based on false premises, but at least I can see now how Scalia thought he was making sense.

This book overlaps a bit with Charles Siefe’s Proofiness, but is probably more explicitly mathematical. Which is a good thing! (See the quote at the top of the page.)