The King of Infinite Space: Euclid and His Elements

Berlinski (Infinite Ascent: A Short History of Mathematics) has written a number of books on math, science, philosophy, and related topics. His new book is a tribute to the classical Greek mathematician whose treatment of the fundamentals of geometry, his Elements, has been studied (with pleasure or anguish) by millions over the past 2,000-plus years. Berlinski obviously savors the work of Euclid, but he finds room for quibbles with what he considers the fuzziness of Euclid's axioms and definitions. His side remarks are often humorous (a welcome and unusual touch in a book dedicated to an analysis of an ancient mathematical treatise). He also flavors his discussion with quotes from mathematicians of more recent centuries. In particular he tells of the 19th-century mathematicians who were brave enough to develop non-Euclidean geometries that violate Euclid's fifth axiom.