Reviews: Books

What: Euclid's Window
How: Non Fiction
Who: Leonard Mlodinow
When: 2001
Grade: A

This wonderfully chatty book describes the history of Geometry (and related subjects) from Ancient Greece to modern America.

Most people tend to believe the those of a literary bent can't be interested in maths, but for me, it was a real toss up which one I would take to university. It's not infrequently that I wish I'd gone with maths, if I'm honest.

I did maths up to A Level, and I found the Euclidean chapters of the book easy to follow. I think, even if I hadn't, I wouldn't have found it hard to deal with. Mlodinov follows the history of maths thoroughly, showing how each mathematician, philopher and scientist made the next step. I was interested to learn how later zero was invented, or the use of symbols such as + and - came into use, or the invention of graphs.

This easy flow made it much simpler to grasp the non-Euclidean mathematics. It's telegraphed from an early chapter that there are great flaws in Euclid's assumptions, but they can neither be proved nor disproved. After centuries of wrestling with this, different mathematicians make a leap and decide to simply start with different assumptions, and maths suddenly gets weird. And yet, it makes more sense. Euclidean geometry doesn't work when applied to the curve of our planet; non-Euclidean elliptical geomatrey does.

The author uses his family to illustrate examples of various theories, but he does not become bogged done in the equations. The book is not intended as a textbook, nor will it teach you mathematics, but it allows you to grasp the ideas behind complex theories. This is Popular Science, not a degree course, and the familiar stye is singularly appropriate, with cheerful observations about the habits of famous figures and the attitudes of the profession. It shows you why string theory is such a big thing in modern physics without burying you in the how.

I devoured this book, and I've already lent it to a friend. I thoroughly reccommend it to everyone other than physicists or mathematicians!