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Euclid in the Rainforest: Discovering Universal Truth in Logic and Math Hardcover – October 4, 2004

ISBN-13: 007-6092035879 ISBN-10: 0131479946 Edition: 1st
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Editorial Reviews

Review

“Devoid of complex proofs and dense mathematical language; instead, the author has drawn upon his experience as a formative teacher to create a book rich in content that connects with real-world experiences.” —Library Journal

“Joseph Mazur brilliantly explores the symbiotic relationship between the physical and the mathematical worlds…A stylish and seductive book that convinces the mind even as it delights the soul.” —PEN American Center

--This text refers to the Paperback edition.

From the Back Cover

"How does one summarize a book about rainforest adventures, probability, the Café Luxembourg, Euclid, and prime numbers? This is an absolutely delightful book, full of insight, suffused with gentle humor–a picaresque novel of mathematics. What do we mean by proof and persuasion in the most symbolic of fields, Mazur asks, and responds with stories that effortlessly guide us to the heartland of reason. This is a fabulous book, in all senses, from beginning to end."

—Peter Galison, Mallinckrodt Professor of the History of Science and of Physics,
Harvard University, author of Einstein's Clocks, Poincairé's Maps

"Euclid in the Rainforest is beautifully written and packed with insights into how mathemeticians convince themselves they are right. Mazur is a talented teacher who knows his subject inside out, and his delightful stories take his readers to the heart of mathematics–logic and proof. This original and charming book is accessible to anyone, and deserves major success."

—Ian Stewart, Professor of Mathematics, University of Warwick, author of Math Hysteria, and Flatterland

"My chief regret after more than forty years of trying to teach concepts in mathematics and statistics to biology students is that I did not have Mazur's book available. It should be assigned reading for all undergraduates in science."

—R. C. Lewontin, Alexander Agassiz Professor, Harvard University

"Mazur is an excellent storyteller. Euclid in the Rainforest is a warm and creative masterpiece that reveals the spirit of mathematics."

—Tadatoshi Akiba, Mayor of the City of Hiroshima

"Mazur has a wonderfully engaging writing style, and a marvelous feel for the interface between the physical world as we experience it every day and the mathematical one. This book is a pleasure to read."

—Joseph Harris, Chair, Department of Mathematics, Harvard University

"Mazur's Euclid in the Rainforest is written with warmth and a lifetime's attachment to the things of this world and the forms of the world it manifests. Here are the pleasures of sitting with the author, as a young man, learning his craft in a Greenwich Village cafe from an old professor; and later on, teaching the craft in turn to an eight-year-old. Inspiring stuff. By overhearing such conversations as these, the reader too is led to savor the beauties of mathematics."

—Robert and Ellen Kaplan, co-founders of The Math Circle, and co-authors of The Art of the Infinite: The Pleasures of Mathematics

"Delightful, full of insight, suffused with gentle_humor–a picaresque novel of mathematics."

—Peter Galison

How do we know that something is true? How do we know that things really are what they seem? Many people think math and science are the ultimate authorities on reality. Math defines abstract, universal truths; scientific truths are established by experiments in the real world–but underlying both kinds of knowledge is logic. In Euclid in the Rainforest, Joseph Mazur examines the three types of logic that are the basis of our knowledge about the world we live in: the classical logic of the Ancient Greeks, the weird logic of infinity, and the everyday logic of plausible reasoning that guides all science today.

Through tales of great moments in the history of math and science, stories of students making discoveries in the classroom, and his own quirky adventures in the Greek Islands, New York, and the jungles of South America, Mazur illuminates how we uncover truth in the tangled web of our experiences–and convince ourselves that we are right.

Euclid took the incipient logic of his time to new heights with his magnificent geometry, the whole edifice of which is built on just five assumptions. That logic rigorously defined proof, cleverly avoiding problems with infinity that were introduced when the Pythagoreans discovered that the diagonal of a square could not be measured and Zeno of Elea used infinity to argue that motion is logically impossible. It would be almost two millenia, though, before a good understanding of the logic infinity emerged and made all kinds of technology possible. Plausible reasoning–which is based on the math of probability– lets us assess the general conclusions we derive from specific cases in scientific studies. It gives us the confidence to believe that a conclusion reached today will be true tomorrow, ultimately driving scientific, and human, progress.

In lucid, ebullient language, Mazur, a professor of mathematics for over thirty years, makes the fundamentals of the three fundamental types of logic widely accessible for the first time. Deeper questions at the heart of the process of discovery are laid bare: What does it mean to believe a proof? Where does the finite end and the infinite begin? How can we be sure that the statements we make about the material world are accurate? Exposing the surprising roles of intuition, belief and persuasion in logic and math, Mazur tells a real-life detective story that has been going on for millenia: the pursuit of ultimate truth about our world, our universe, and ourselves.


© Copyright Pearson Education. All rights reserved.

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Product Details

  • Hardcover: 352 pages
  • Publisher: Dutton Adult; 1 edition (October 4, 2004)
  • Language: English
  • ISBN-10: 0131479946
  • ISBN-13: 978-0131479944
  • Product Dimensions: 6.5 x 1.2 x 9.3 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #1,224,431 in Books (See Top 100 in Books)

More About the Author

His full name is Joseph Conrad Mazur. His mother bought a used copy of Lord Jim in London on her way from Vienna to America, thinking that if she could read it with a dictionary it might improve her English. Like Mazur's mother, Conrad was Polish-born, so she felt that English written by a Pole must be easy to understand.

JOSEPH MAZUR is Professor Emeritus of Mathematics at Marlboro College where he has taught a wide range of classes in all areas of mathematics, its history and philosophy. He holds a Ph.D. in mathematics from M.I.T., and is a Guggenheim Fellow. He is the author of Euclid in the Rainforest: Discovering Universal Truth in Mathematics (Finalist of the 2005 PEN/​Martha Albrand Award and chosen as one of Choice's 2005 Outstanding Academic Titles of the Year) and the editor of the recently republished classic by Tobias Dantzig, Number: The Language of Science. He is the author of The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space (Plume), What's Luck Got to do With it?, (Princeton), and Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers (Princeton).

Customer Reviews

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Most Helpful Customer Reviews

36 of 36 people found the following review helpful By Edward F. Strasser on November 30, 2005
Format: Hardcover
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.
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Format: Hardcover
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.
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14 of 15 people found the following review helpful By Warren C. Chisler on July 13, 2005
Format: Hardcover
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.
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10 of 12 people found the following review helpful By T. Jefferies on February 7, 2005
Format: Hardcover
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.
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11 of 14 people found the following review helpful By John Matlock on November 18, 2004
Format: Hardcover
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.
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