Klein Project Blog

January’s Book of the Month is Mathematics for the Million: How to Master the Magic of Numbers by Lancelot Hogben. First published in 1936 and reprinted many times.

From the Prologue: “The customary way of writing a book about mathematics is show how each step follows logically from the one before without telling you what use there will be in taking it. This book is written to show you how each step follows historically from the step before and what use it will be to you or someone else if it is taken. The first method repels many people who are intelligent and socially alive, because intelligent people are suspicious of mere logic, and people who are socially alive regard the human brain as an instrument for social activity”

Chapters:
Mathematics in Remote Antiquity
The Grammar of Size, Order, and Shape
Euclid as a Springboard
Number Lore in Antiquity
The Rise and Decline of the Alexandrian Culture
The Dawn of Nothing
Mathematics for the Mariner
The Geometry of Motion
Logarithms and the Search for Series
The Calculus of Newton and Leibnitz
The Algebra of the Chessboard
The Algebra of Choice and Chance

December’s Book of the Month is Historical Topics for the Mathematics Classroom by J.K. Baumgart, D.E. Deal, B.R. Vogeli, A.E. Hallerberg, eds., published by the National Council of Teachers of Mathematics.

This book has a summary of the history of each major branch of mathematics (Number, Computation, Algebra, Geometry, Trigonometry and Calculus) followed by brief essays on specific topics of significance within each branch. The last two chapters of the book give a brief, integrated view of the direction of mathematics development over the last century.
Originally published in 1969, and updated in 1989, the book continues to offer high school and university teachers an excellent tool for their own development.
(Adapted from a review by Tim Keenan).

November’s Book of the Month is Geometry and the Imagination by Hilbert and Cohn-Vossen. First published in 1952.

The AMS website says: “This remarkable book has endured as a true masterpiece of mathematical exposition. … The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.
[It] is full of interesting facts, many of which you wish you had known before. … The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in . …
One of the most remarkable chapters is “Projective Configurations”. … Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. …
A particularly intriguing section … is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? … The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! …”