The book that I read for our "book club," if you will, is Journey Through Genius by William Dunham. First of all, I would like to say that this is a great book. It is absolutely filled with information about not only some of the greatest proofs of all time, but also about the mathematicians themselves, the culture in which they lived, and the era in which they studied. That being said, I also want to add that this is not a book that you read for leisure in the evenings to relax. I would say that it is almost more of a book to read in spurts, not all at once. I say that because, though the information is extremely interesting, it would take an incredible amount of time to read through the entire book and actually have made sense of it all. I really loved the fact that the contents laid out the specific sections dedicated to particular proofs, theorems, and mathematicians. This allows the reader to skip around to the proofs that might be the most interesting to them at a particular time and truly dive in. That's the thing about this book. It's not about a joyful afternoon swim, but a rapids of facts and explanations that seem crazy to "dive into," but once you come out at the end of any of these rapids, you find yourself with a smile on your face. This is the beauty of mathematics at its finest. As described by the author, mathematics is not simply about practical application, memorization, or finite use. Rather, mathematics is like a Rembrandt a Picasso, a masterpiece. Something that is not only practical but visually and logically pleasing. Logic, in fact, is noted in this book as being one of the only prevailing pieces of history. Science changes and is replaced. Medical practices from centuries ago are naive attempts at best of something great, but the logic behind a tried, tested, and true proof of a theorem prevails over the centuries.
I would recommend this book to anyone who has an interest not just in the application of a theorem or how the proof is derived, but how these things are affected by the culture of the region, era of time, and specific personalities of the mathematicians who discovered them. If you are someone who is looking for a to the point, concise, and application geared explanation of some of these proofs, I would say this is not the book you are looking for. This book is not so much about learning a theorem or proof as it is discovering the theorems and proofs. So one might ask, "What is the difference between learning and discovering?" Well the answer to that is quite simple. There is a certain appreciation and fulfillment that comes from discovering something, while learning offers merely the satisfaction of a good grade, a praising note, or a gold star. The gratification in learning spawns from the reward, whereas the gratification in discovery spawns not only from the reward, but also the journey, hence the title of the book, Journey Through Genius. It is not titled, Genius Explained, How To Be a Genius, or Guess What This Theorem is Used For! And that is for a very good reason.
At the beginning of this blog I said that this book is not a leisurely read, but I have come to the conclusion that leisure, much like beauty, is in the eye of the beholder. For many mathematicians, like those mentioned in this book (Euclid, Archimedes, Euler, etc) these things may be one in the same.