Euclid’s Window

Although geometry is a fixture in the school curriculum of the United States, there is very little knowledge of its history or appreciation of its immense contributions to human advancement. Leonard Mlodinow’s response is a lively and relatively non-technical discussion of geometry focusing on, but not limited to, the contributions of five men: Euclid, who organized and systematized Greek geometry; Rene Descartes, who applied algebraic methods to geometrical problems; Carl Friedrich Gauss, who discovered the concept of non-Euclidean space; Albert Einstein, who discovered the curvature of space; and Edward Witten, one of the major contributors to string theory. Mlodinow’s goal is to demonstrate that geometry was and remains “the window to understanding our universe.”

Mlodinow carefully places each mathematician’s work in its historical context and traces the influence of one upon another. Although the history is organized around the five men and the revolutions in mathematical, scientific, and even philosophical thought they triggered, it is a relatively complete history. He is careful to fill in the large gaps in the chronology and provides vivid descriptions of the lives of the mathematicians.

Euclid’s Window lacks a bibliography, but Mlodinow does provide notes for the sources of quotations and other information. These notes show that Mlodinow utilized many of the standard sources in the history of mathematics and personal interviews for the contemporary period. His discussions of the twentieth century are more informed than those of the earlier periods, where his sources are dated and have been superseded. Nonetheless, he has succeeded in providing the general reader with a new and exciting way of looking at an old subject.