JOSEPH MAZUR

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

Euclid in the Rainforest is a Finalist for the PEN: Martha Albrand Award for First Nonfiction. Also, It has been selected as an Outstanding Academic Titles of the Year 2005 by the library journal "Choice."

“Logic as an academic and intellectual discipline can be overwhelming and dry. But writing with the general reader or undergraduate student in mind, Mazur (mathematics, Marlboro Coll.) successfully explores how mathematical logic and proof are essential building blocks to understanding knowledge and universal truths. In brief chapters, he draws on the philosophy and geometry of the ancient Greeks and incorporates historical vignettes and personal narratives to examine the three types of logic (classical logic, plausible reasoning, and infinity) that we use to determine whether something is true.

Mazur clearly demonstrates how the validity of arguments and truthfulness can be revealed through the rules of logic, debate, and the principals of mathematics. Although there are some simple diagrams and figures, his text is devoid of complex proofs and dense mathematical language; instead, the author has drawn upon his experiences as a formative teacher to create a book rich in content that connects with real-world experiences. Suitable for large public and academic libraries.”
“In Euclid in the Rainforest, one can see Euclid as a metaphor for the sterile and the methodical--the logical, but mechanistic stacking of proven result upon proven result to arrive at an end that is unassailable by anyone, anywhere, anytime. On the other hand, the rainforest conjures up complexity, richness, unexpected sightings and multiple pathways to the clearing called ‘clarity.’ In Joseph Mazur’s book, you find these metaphors juxtaposed. Readers become the traveling companions of someone part geek and part Indiana Jones; it is an enjoyable trip.”
“This charming book radiates love of mathematics... and of life. Mazur (mathematics, Marlboro College) weaves elementary explanations of a wide range of essential mathematical ideas into narratives of his far-ranging travels. Trekking into the rainforest of Venezuela, conversing in a café (cafe) in Paris, touring the Greek islands on a luxury yacht, and other adventures--they all serve as backdrops to careful treatments of the Pythagorean theorem, Boolean algebra, non-Euclidean geometry, Zeno's paradox, the Law of Large Numbers, the Continuum Hypothesis, etc. Along the way Mazur explains topics such as the difference between mathematical and scientific induction and others of metamathematical nature. The chapter subtitled ‘The Role of Intuition and Belief in Mathematics’ illustrates his approach to mathematics as more than formulas and theorems by relating the human side of Jordan's travails when proving his Curve Theorem. Another example is his historical account of the quest to prove the Parallel Axiom.

The value of the extensive bibliography is greatly enhanced by guiding comments. The index is unusually complete. This book is a treasure of human experience and intellectual excitement. One wonders how many of today's students can appreciate its value. Summing Up: Highly recommended. All levels.”
“Joseph Mazur does readers the great service of setting the arcane ideas and procedures of mathematics back in the world where they belong, the market-place, the smoky café, the classroom, the laboratory, the sidewalk, the sailboat, the rainforest. He reminds us how beautiful they are, how compelling, without letting us forget that they have their tragic moments as well as various lead and walk-on roles in the human comedy.”
“Joe Mazur holds an MIT doctorate in mathematics, but his history of the search for universal truths in logic and math has a narrative charm that will make it appealing even to the average educated reader. Euclid in the Rainforest paints a sweeping history that identifies three central ideas of logic that have guided Western thought for the past 2,500 years. By situating his theories in stories set first in the rainforests of Venezuela and then on the Mediterranean coastline, Mazur draws us into explorations that might otherwise seem hopelessly obtuse or irrelevant.”
"How does one summarize a book that is about rainforest adventures, probability, the Cafe 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."
“My chief regret after more than 40 years of trying to teach concepts in mathematics and statistics to biology students is that I did not have Mazur's book avaliable. It should be assigned reading for all undergraduates interested in science.”
“Euclid in the Rainforest is beautifully written and packed with insights into how mathematicians convince themselves they are right. Joe Mazur is a talented teacher who knows his subject inside out, and his delightful stories take his readers effortlessly to the heart of mathematics--logic and proof. This original and charming book is accessible to anyone, and deserves major success.”
"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. The book is a pleasure to read."
"Joe 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 much 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.”
“Mazur is an excellent storyteller. Euclid in the Rainforest is a warm and creative masterpiece that reveals the spirit of mathematics.”

Ever since the appearance of Lancelot Hogben’s Mathematics for the Million and Courant & Robbins’ What is Mathematics, mathematicians who believe not only in the practical importance but also the aesthetic beauty of the subject, and who have the gift of good expression, have written books accessible to the layman. The book under review is one such work....
A beginning student reader of this book will find that he is learning mathematics painlessly as if he is reading a book of stories....
The book deserves to be assigned as supplemental reading to all undergraduates taking science classes.

The Motion Paradox

From The New Scientist
"THIS is one of the most fascinating science books I have ever read. It tells the story of the 2500-year quest to gain an understanding of the slippery concept of motion. Beginning with the Greek paradoxes that showed that motion is utterly impossible, the book progresses through Galilean relativity, Einsteinian relativity and superstring theory, finally coming up to date with the still unresolved question of whether space and time are continuous or grainy. Joseph Mazur has succeeded in telling a fresh and untold story with clarity and style."

From Publisher's Weekly
"The Greek philosopher Zeno sought to reveal that motion and speed were logical impossibilities; one of his famous four paradoxes argued that a moving object can never reach its destination, because it must first travel half the distance, then half the remaining distance, and so on. In this entertaining, informative diversion, Mazur (Euclid in the Rainforest) spins out the discoveries of the mathematicians and scientists who have grappled with the riddles of time and space over the last two millennia, from Aristotle up to Heisenberg and contemporary string theorists. Yet for all their answers, the fundamental premise that motion is an illusion created by consciousness still remains. Many elements of the story, such as the astronomical breakthroughs of Galileo and Tycho, or the simultaneous development of calculus by Leibniz and Newton, have been discussed in greater detail in other recent books. But Mazur spins a good yarn, and his conversational tone holds readers' attention even as the mathematical formulae pile up in later chapters." Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

From Booklist
"Zeno's four paradoxes have bamboozled the greatest mathematical minds, for he purported to prove that motion is impossible, a conclusion somewhat at variance with experience. In this history of puzzlement over the paradoxes, mathematician Mazur begins by imagining Zeno stumping the entire ancient-Greek brain trust except for Aristotle, who offered refutations of Zeno. With Aristotle's own notions of motion refuted by Kepler, Galileo, and Newton, Zeno enjoyed a brief renaissance but seemed tamed once more by calculus and its mathematical tool kit. Motion and time again were continuous, not infinitely divisible, which is the underlying assertion that lets Zeno claim that fleet-footed Achilles can never catch up to a tortoise that has a head start. Then, as Mazur relates, Planck's discovery of the quantum, and Einstein's of relativity, restored Zeno's paradoxes to philosophical relevance. Entrained with some requisite algebra, Mazur's account achieves an entrancing verbal clarity in its discussion of the success and limits of mathematically modeling motion, and itself is a fine example of popularizing a famous philosophical mind-bender." Copyright © American Library Association. All rights reserved