This book was recommended to me by a friend I have known since third grade. He was also my neighbor for most of my childhood. We both shared an interest in computers and science back in high school, and thanks to the wonders of the internet, are still able to keep in touch. Randall, known as Randy back in the day, told me he had read this book several times since discovering it in college. I was a little puzzled, given the topic, why one would be inclined to read such a book multiple times. Most non-fiction, which this book is, rarely warrants more than one read.
I quickly understood why he read it so many times. I took a fair amount of math classes in college – calculus I,II, and III, differential equations, combinatorics and linear algebra. I even took modern physics as an elective after taking the physics courses required for my engineering degree. I taught algebra and geometry at Mt. Zion High School in Georgia for a year. I am not a mathematician by any means, but I have a strong background in math. This book had me re-reading pages and questioning concepts I had previously taken for granted. In calculus it is common to find the values of equations as the value of a variable in that equation approaches infinity. I just accepted that infinity was a really huge number. I never considered that one infinity could be bigger or smaller than another infinity or that there could be dispute over whether something could be infinitesimally small.
This book describes the infinitely small and large in great detail, its practical applications and how these concepts historically came into being. The author spends a great deal of the book discussing the mathematician Kurt Gödel, specifically. The author even had visited with Gödel on more than one occasion. Gödel was known for his Incompleteness Theorem. The practical application of this theorem basically discounts that there can ever be an all-encompassing “theory of everything”. Its application to an infinite universe basically points to the truth that it is not possible to know everything about such a universe. Physicists since Einstein’s time have been searching for this Universal Theory. If Gödel’s theory is applied to our universe as we understand it, such a theory will never be found.