Customer Reviews

Euclid in the Rainforest: Discovering Universal Truth in Logic and Math

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4 star:		(1)
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2 star:		(1)
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I should start by saying that I didn't read this book to learn anything about mathematics; I already knew all the math in it. But I have long been interested in ways to present math ideas to people who aren't strong in math. Mazur's approach of putting the math into stories sounded interesting.

For example, in the section on Euclid, Mazur starts with a story about soldiers in the Amazon rain forest trying to pull a truck out of a gully. This involves a bit of trigonometry, which leads to a discussion of the Pythagorean Theorem. But it's not really about geometry; it's about how mathematicians approach problems and how they prove their solutions and even what it means to say that some mathematical statement is true. Mazur illustrates this by showing two non-mathematicians struggling with the theorem, trying to arrive at a solid proof, whatever that means. How they arrive at the proof, and what it means for something to be a proof, are just what this book is about.

Who, other than a teacher of mathematics, can profit from this book? The target audience consists of people who don't have much math education but are interested. But there is significant use of diagrams, numbers, and algebra. (By algebra I mean the rules of arithmetic; you don't have to be able to solve equations.) If you have "math anxiety" you might have trouble getting past that. Then again, the chatty style is designed to ease you through, so you might give it a try.

You might decide that my review would be more useful if you knew a bit more about my background. If so, click on my name at the head of this review.

Properly presented, the fundamental truths of mathematics are easy to understand. By that I mean that if they are presented in the appropriate non-technical language and with simple examples, then almost anyone can understand them. Mazur does this and does it very well. Much of the mathematics in this book is also philosophical in nature. A great deal of ink is spent in describing Zeno's famous paradox, "proving" that motion is impossible. His development of the solution to the paradox can be understood by anyone possessing the most rudimentary of mathematical backgrounds.
The role of proof in mathematics is also discussed, with questions raised as to what actually constitutes a proof. Mathematicians have debated this point since the Greeks invented the concept of the mathematical proof, and this is a good recapitulation of that debate. I consider it very healthy for the math profession to admit to the laity that mathematical proof is not necessarily fixed in concrete. It is also a point of significant honesty to admit that proofs that were considered correct for centuries contained flaws that were discovered and repaired.
There are three sections to the book:

*) Logic
*) Infinity
*) Reality.

The chapter "Does Math Really Reflect the Real World?" makes a point that often astounds mathematicians and others that work in the physical sciences. Namely, that mathematics does describe the real world, not only well, but often astonishingly well. New mathematical concepts are invented and considered to be purely abstract, there being no current practical application. However, as science progresses in other areas, that "purely abstract" idea suddenly has uses in the real world. Of course, the real world does have its flaws. It is impossible to create the perfect circle, the well-balanced coin and die do not exist and there are times when we cannot measure a value to enough decimal places to get true predictability. Those situations are also covered, which is important, as it points out that even the best mathematics does not give us absolute predictability. Fortunately, nearly all of the time, the good enough is in fact really good enough.
This is one of the best popular mathematics books that I have ever read; it covers the fundamentals that need to be covered and at a level that nearly everyone can understand.

Published in Journal of Recreational Mathematics, reprinted with permission

I purchased this book a couple of weeks ago and can hardly put it down. I work in the area of operation research for the Navy and have recently decided to become a highschool math teacher. There are so many interesting examples of math in this book and great stories to boot. This book is an excelent example of how math can be entertaining. I would recomend it to anyone who wants to have a better understanding of math.

This book is an utter joy to read. Mazur gently leads the reader into mathematics through delightful adventure stories. I confess that I bought the book for its cover after reading the accolades on the back jacket, something I rarely do; but how could anyone refuse such an interesting title? Just read the first few pages and you are in for a whirl of a ride through rainforests of wonderfully explained math, made easy by Mazur's gentle approach. This is a unique book-one that is poetically written with a constant reminder that math is everywhere. Open it anywhere and jump in for a delightful ride. The journey gets a bit bumpy somewhere near chapter 5, but if you hold on tight, the jaunt is worth it, for it comes out at a clearing under the awesome rainbows of understanding and delightful colors of literary satisfaction.

This book might as well be called Love Stories about Mathematics. As as example, in the first few pages he is talking about a stranded truck in the Venezuelan jungle. How strong a winch do you need to pull the two ton truck up the hill? When you are pushing on the truck while being eaten by bugs, I don't know I'd think much about the simple trig problem. Or, in a horse race, from how far behind can a horse catch and pass the leading horse?

Dr. Mazur loves mathematics, math for itself, math just for its elegance. And he brings it across in this book. I can remember in my own math studies when I first got to differential calculus. It was like new worlds opening. It was like what other people tell me about the first time they heard Beethoven's Fifth.

What I could never have done was bring out the excitement, the fascination, the love that Dr. Mazur does in this book.

It is a rare occasion one happens upon such a beautiful and inspiring book. It's a work of art - as anyone who has ever tried to write anything from a simple essay, to a scientific paper - could tell you. This book is an amazing piece of writing, in which rigorous mathematical deduction and poetry dance together in perfect harmony.

I've never been to the Venezuelan rainforest, but mathematician Joseph Mazur made me feel as if I had taken an expedition up the Orinoco River in a hot 1960 summer. I have never been to Paris either, but I felt as if I was in Café Luxembourg while a famous professor explains a proof to a young American thirsty for knowledge.

The young American (young Dr Mazur) is the reason I loved this book, because his adventures and discoveries are so fascinating and true. Not only does he make me see what he sees (ah, all those wonderful places!), he also makes me feel and get excited about the same things he feels. There is much more going on than just trips all over the globe, and he tells you all about it.

Young Joseph Mazur and his friends travel and have a lot of fun while pondering mathematical theoretical questions and discovering the truth all around them. Every trip is an initiation into another chapter of history of mathematics, whether it is trigonometry, geometry, set theory or probability.

Euclid in the Rainforest is filled with interesting characters like Zeno, Achilles, Riemann, Cantor, and Dr. Mazur makes them all seem as real as the people in your hometown. Every time you meet on one of these characters you discover something new, they all teach something about logic, infinity and reality.

This book reminds me of a Bildungsroman, a journey of learning and self discovery, and yet you get the feeling that all that could happen today, it could very well be your own story:
"...anyone who loves to bring nature and humanity closer together will remain a logician of sorts; an observer who can deduct answers; a mathematician who can handle infinity; a scientist who can accept chance. A Euclid in the rain forest ".

My only complaint is that I read the whole thing in only two days, as I couldn't put it down. Since the book cost $15.00, this comes to $7.50 per day. I was expecting a book on mathematics to take me at least a week, which would have been only $2.14 per day. Other than that, it was terrific. Mazur keeps a focus on really basic questions like, "what is truth, anyway." This sounds esoteric, but it leads to some excellent takeaway revelations. To put it another way, you don't merely learn some new facts about math, you have the opportunity to get a clearer understanding of science as well as mathematics. For instance, I had always thought of "junk science" as inferior to peer-reviewed science because their analytical processes - deduction, induction, inference, observation, etc. - were different from one another. Mazur forces you to look at a process known as "plausible reasoning" that is the hallmark of the very best peer-reviewed science, which leads to better understanding of the validity of scientific theories and laws. In my letter to the author, I told him that, "I have always been a sceptic, but now I know why I am a sceptic." I highly recommend this book to anyone who is a little sceptical - and all good scientists are a litte sceptical - about some modern scientific "discoveries." Thank you, Joe Mazur.

Dr. J. G. McCully.

This is a good book. You just read page after page without any brain-twisting theories. Facts and stories about math are lucidly presented. A soft way to teach truths about math and logic.

I found this remarkable little book in a 'bargain basket' at a bookstore in Panama City. I took it with me to Kuna Yala where I was staying in a Kuna village without electricity, running water, or much else. Thus I had a lot of very quiet time to read it. Parts of it were very difficult for me, but the overall message of the book is wonderful.

For some reason there are 'Post Modern' scholars (sic)(Stanley Fish of Florida International University is one) who want to reserect the old canard of 'science is merely faith' as a criticism of recent books on faith by scientists and others (Sam Harris, Richard Dawkins, Christopher Hitchens).

While this book does not directly address the issue of `faith vs. science', it is a explanation of the scientific method and the cleanest example of why science is not based on faith, does not require faith, and, in fact, can be demonstrated to be counter to faith based beliefs.

When I was an undergraduate in the late Pleistocene I took a philosophy course in which the instructor took the position that `Science,' `Religion,' and `Philosophy' were equally valid approaches to understanding reality. I didn't do well in the course because I kept objecting to his basic premise. While my training is in biology I have been trying to learn Particle Physics and Cosmology in recent years and am even more convinced that science is fundamentally divorced from other approaches.

Even if you are not going to a tropical island for a week, get this little book. You will probably enjoy it and will come away with a much better appreciation for how science works and how scientists think.

I agree with the review from Mr.Strasser as found below. The book intention seems not to enlighten any mathematical foundations or concepts but rather to find universal truth in math by peeling the layers each culture places on our understanding. I was thrilled with the book but it seems to leave the intended point about 5 chapters from the end. Started out thrilled but ended disappointed.