As someone who majored in math in college, this essay did an excellent job of communicating ideas that I've struggled to explain to family and friends who practically flinch when I tell them I studied math.
If you connected with this essay (or, perhaps, if you did not), I highly recommend checking out a book called 99 Variations on a Proof, by Philip Ording. It is an enjoyable, easy to understand journey through the art of making a mathematical argument by way of showing the many forms such an argument can take.
Hadn't seen The Cauchy-Schwartz Masterclass, but after a quick glance around, it seems to be very different from 99 Variations on a Proof.
The book I'm recommending is pretty far from a textbook. Rather it is an Exercises in Style type book that explores many different ways to express a mathematical proof of the same simple fact. Some of the proofs are whimsical, and others offer genuine insight. Many cover the ways that such mathematical discussions would have taken place in earlier historical periods.
In other words, 99 Variations is more like a jaunt through mathematics culture rather than a book that focuses on actual mathematical content.
I'll take a look at this book, though, because it looks quite good!
I'm in the reverse position: I have TSCM on my shelves but all I know of 99VoaP is what I can tell from Amazon's look-inside feature. My impression is the same as yours: the two books are very very different. TSCM is very much a book that intends to teach the reader some nontrivial mathematical ideas and techniques. 99VoaP sticks with a single rather elementary proposition and shows lots of ways of looking at it.
The book The Cauchy-Schwartz masterclass was crucial in the first paper I published, introducing the concept of Schur convexity. I am indebted to that great book.
If you connected with this essay (or, perhaps, if you did not), I highly recommend checking out a book called 99 Variations on a Proof, by Philip Ording. It is an enjoyable, easy to understand journey through the art of making a mathematical argument by way of showing the many forms such an argument can take.
https://www.amazon.com/99-Variations-Proof-Philip-Ording/dp/...