This book is ideal for a smart, but mathematically-untrained adult who wants orientation to some interesting and useful mathematical concepts, as well as a portal to mathematical epistemology. A little high school algebra and geometry, even if it's fairly dusty, is plenty of background to appreciate the explanations here. Author Mazur builds his discussions of deduction, induction, probability, and plausibility into a series of autobiographical and historical anecdotes, within sections titled "Logic," "Infinity," and "Reality." I really appreciated his explanation of transfinite numbers, a modern math concept that has always eluded me. The book has an apparatus with useful directions for further reading.

Some of the little stories in the book were ones I found difficult to credit, but perhaps that was a savvy way of giving the reader a motive to further ponder the notion of plausibility!

"Whimsical" and mathematically "rigorous" are two concepts that seldom apply to the same book, but they do to Joseph Mazur's "Euclid in the Rainforest." ("Goedel, Escher, Bach" comes to mind.)

Mazur develops three separate way of thinking mathematically: the classical logic of the Greek geometers, the weird logic of infinity, and probalistic logic.

He takes us through several proofs of the Pythagorean theorem. He distinguishes between logical induction and mathematical induction and then illustrates the latter with proofs that (1) the square root of 2 is irrational; (2) there is not a largest prime number; (3) between every 2 rational numbers there is an irrational number; (4) between every 2 irrational numbers there is a rational number; and (5) that the cardinality of the irrational numbers is greater than that of the rational numbers.

He also shows Cantor's proof that the real numbers are uncountable. Finally, he adds some counterintuitive examples of probability theory and a discussion of decision making under uncertainty and the normal curve.

Mazur tries to make the rigor painless by illustrating some of the proofs in the context of anecdotes about some of his quirky travel and teaching experiences. That technique can be annoying in the hands of a less skill writer, but I think Mazur pulls it off rather well. All in all, a pleasant read for the non-mathematician.

JAB ( )

Gentlest of intros to mathematical thinking, diluted with personal anecdotes.