Tasten - Riechen - Schmecken Book

This is a short but very dense fix-up of four lectures given by Weyl on the eve of his departure from the Institute for Advanced Study at Princeton, wherein he builds motivation for the mathematics of symmetry out of real-world examples: art, biology, crystals, atoms, and spacetime. And it's meaty stuff: the difficulty spikes sharply towards the end of lecture 2, and anyone without a broad undergraduate level understanding of math and science might feel left behind.

Part of that is a modern trend away from focusing so severely on Euclidean geometry (as in, straight from Euclid) in primary education. Another part is a rather different mathematical vocabulary that modern (high level) mathematics has simply left behind: as just one example, Weyl calls a 2-d matrix (a, b; c, d) of numbers "unimodular" whenever the "modul" ad-bc is 1 or -1. Modern mathematicians still use the term "unimodular," but ad-bc is the "determinant" of the matrix. Thank or blame the Bourbaki group for the vocabulary changes, probably.

Nevertheless, there are lots of provocative ideas in these lectures, and several important works named as avenues for further reading. Weyl's comment that Galois theory is the relativity theory for a finite set of numbers blew me away, for example... but mathematical maturity is required!

Compared to another book in the "Princeton Science Library" series - WHY BIG FIERCE ANIMALS ARE RARE, by Paul Colinveaux - SYMMETRY doesn't quite hit the "general reader" sweet spot, and so merits 3½ out of 5 stars, rounded down. If you do pick it up, expect to need to read it more than once.