Math is the hidden secret to understanding the world

I love this book, and I often recommend it to teachers, because teachers need to be aware of metaphors and how they use them. I actually discovered this book after I was done preparing this TED talk, only to discover the many similarities between my ideas and theirs.

This is a beautiful and easily accessible book about the art of doing mathematics and the beauty of mathematical proofs. It is the constructive counterpart to Lockhart's 25-page essay from 2002, "A Mathematician's Lament," where he (rightly) criticized how math too often is taught schools (not only in the US). In his book Measurement, he gently guides you into thinking like a mathematician.

This a gem. The authors set forth to shed light on what mathematics really is, both in a philosophical, but also historical, perspective. It describes in a beautiful way what the mathematical experience is like, and what it is like to be a mathematician.

The title says it all. Although this book at times is very wordy and rambling, I love the way the authors drive home the argument that it is through analogies and metaphors that we create and develop concepts and thought.

I have been a fan of John Stilwell's book for a long time, and this is his most recent one. I love it! It is a beautifully written account of the main branches of mathematics, with both history and proper mathematics. Even though many of Stilwell's books are written for a wider audience, they also contain more advanced mathematics (but explained in a very clear way) compared to other books in the same category. This book also very nicely covers more recent developments, like reverse mathematics.

This is a lovely book about numbers and properties of numbers. The authors expertly communicate deep and profound connections and truths about numbers and mathematics. The book is also filled with numerous insightful illustrations.

I read this book as a student, and it probably changed my life. It made me aware of how pervasive the use metaphors is in our language and our thinking. Ask yourself this question about your own language: How can you separate between metaphors and non-metaphors?

This is an absolute classic! Not only does it contain an incredible number of beautiful illustrations, but each curve in the book is characterized in extremely many different ways. Whereas one characterization might be neat and elegant for one curve, the same characterization might but cumbersome and tedious for the next. It is really nice to see the multitude of perspectives for each curve.