Mathematics and the Search for Knowledge

This is by far one of the best science books for the layman I have ever read, and I enjoyed reading it. I especially liked the discussions of the cultural context inwhich Copernicus, Kepler, Galileo, and Newton worked. The break that Copernicus made with common sense AND religous dogma is so great as to boggle the mind even today. And Kepler's determination that the Earth's orbit is an ellipse, again defies belief, since it was done before calculus was invented, or the law of Gravity determined. I highly recommend this book to anyone who enjoys a good science read.

This is a good, basic introduction to the history of math, but its promise of engaging philosophical issues falls short. It's not until Chapter XII that Kline really engages the philsophy of mathematics, but then attempts to cover a lot of ground in a short span, and the distinctions and groupings Kline forms of different thinkers' conceptions of mathematics leads to strange bedfellows; particularly Kline's claim that Wittgenstein is basically a mathematical empiricist and yet believes that mathematics is a human creation. To my mind there's an inherent contradiction there. Most bothersome, however is the almost entire lack of proper footnotes. Some of the most interesting quotes will be difficult (if not impossible) to find b/c Kline only tells us the author of the quote and oftentimes doesn't even include the author in the bibliography! In particular I'm thinking of a fascinating quote from Evariste Galois - Kline gives no indication of where I can find it! Still, I have to give this book a 4 just b/c it's a good introduction that reads rather quickly.

By reading this short book, you will absorb a good foundation in both Mathematics and Physics. You will also acquire an infinite respect for Newton, Maxwell, and Einstein. In all cases, these geniuses developed theories regarding natural phenomena that often could not so readily be observed (if at all).

Morris Kline's thesis in this extraordinary book is stated clearly in the final words of his preface, and then presented through a historical survey throughout. Here are the key words, "Contrary to the impression students acquire in school, mathematics is not just a series of techniques. Mathematics tells us what we have never known or even suspected about notable phenomena and in some instances even contradicts perception. It is the essence of our knowledge of the physical world. It not only transcends perception but outclasses it."As far as I'm concerned, Kline makes his case. And I am one of those who received the erroneous impression in school that he mentions -- of course, I never managed to pay much attention in math classes, but that was only partially my fault.If you are at all like me, and suspect you might have missed something in your misspent youth, get this book.