In this accessible and illuminating study of how the science of mathematics developed, a veteran math researcher and educator looks at the ways in which our evolutionary makeup is both a help and a hindrance to the study of math.
Artstein chronicles the discovery of important mathematical connections between mathematics and the real world from ancient times to the present. The author then describes some of the contemporary applications of mathematics – in probability theory, in the study of human behavior, and in combination with computers, which give mathematics unprecedented power.
The author concludes with an insightful discussion of why mathematics, for most people, is so frustrating. He argues that the rigorous logical structure of math goes against the grain of our predisposed ways of thinking as shaped by evolution, presumably because the talent needed to cope with logical mathematics gave the human race as a whole no evolutionary advantage. With this in mind, he offers ways to overcome these innate impediments in the teaching of math.
"It is a rare occasion that a prominent mathematician takes a look at his discipline from a distance and offers his views on how mathematics has evolved, through its interaction with the 'real' world, in parallel to the evolution of the human brain. Artstein has the knack of presenting original and deep ideas in a pleasant, often-humorous, style using simple and direct language. Thus the book will be equally enjoyable to the scientist, who will encounter in it thought-provoking questions, and to the lay reader, who will gain a view of what mathematics is all about and how it has attained its present state of the art."
– Constantine Dafermos, professor of applied mathematics and Alumni-Alumnae University Professor, Brown University
"An absolutely brilliant work by an outstanding mathematician! It addresses very important issues about mathematics and nature, with many deep thoughts, analogies, unknown (to me) facts, fantastic humor, numerous real-life examples – you name it! The book is written so nicely that it is difficult to stop reading. I believe it will be a great pleasure for everybody (including mathematicians) to read this wonderful piece. Enjoy reading!"
– Boris Mordukhovich, Distinguished University Professor, Wayne State University
"In this intriguing book, the author guides us through the evolution of mathematics from ancient times to the present day. As the title suggests, it is through encounters with the real world that we understand mathematics and can develop it further. The thoughts and views expressed are original and novel. Take, for example, the argument that the logic of deductive mathematics, which was established by the Greeks and is used to this day, is in fact 'antievolutionary.' But introducing such topics only enlivens the presentation. And it is worth noting that no background in mathematics is required for the reader; the only 'requirement' is the reader's curiosity."
– Marshall Slemrod, professor emeritus, Department of Mathematics, University of Wisconsin
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Zvi Artstein is the Hettie H. Heineman Professor of Mathematics at The Weizmann Institute of Science, where he has worked for over thirty-eight years as a scientist, a teacher, and an administrator. He is the author of more than 120 scientific articles published in peer-reviewed journals.