The King of Infinite Space: Euclid and His Elements by David Berlinski

In high school, I never knew how ancient the proofs of geometry were. I worked with points, lines, and planes without feeling I was part of a continuum, enjoying how new the ideas of logic applied to shapes and spaces felt. Only years later did I read about Euclid and how for over 2000 years his axioms had been applied in mathematics, engineering, and philosophy.

According to David Berlinski in his book The King of Infinite Space: Euclid and His Elements, the writings of Euclid have held up very well, withstanding many who have tried to disprove his propositions. Only the parallel postulate from his book The Elements continues to trouble as no one has been able to definitively prove or disprove it. Euclidean geometry was the only geometry until the middle of the nineteenth century when non-Euclidean geometry rose to explain some phenomena not previously explained.

In picking up this small volume, I hoped to learn more about Euclid himself, but there is little to know. Like Shakespeare, it is his writing that has survived to inspire new generations of scholars, many of whom still swear by him. Though it has been many years since I studied geometry, I found I could follow most of the text of The King of Infinite Space and enjoyed puzzling about negative numbers, infinity, and our ability to test theories about real things on geometrical models. I had to use a dictionary to read several pages, but my vocabulary may expand from the effort.

Berlinski, David. The King of Infinite Space: Euclid and His Elements. Basic Books, 2013. 172p. ISBN 9780465014811.