Euclid in the Rainforest: 5discovering Universal Truth in Logic and Math Hardback - 2004

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.--Ian Stewart, Professor of Mathematics, University of Warwick, author of Math Hysteria and FlatterlandHow do we know that something is true? How do we know that things really are what they seem? Everyone knows math defines abstract, universal truths, and that 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 all our knowledge of 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. 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 millennia, however, 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. true tomorrow, that investments of time and money are worthwhile, and so ultimately drives 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 something is true when chance plays so great a role in the universe? 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 millennia; the pursuit of ultimate truth about our world, our universe, and ourselves.(c) Copyright Pearson Education. All rights reserved.