A compelling journey through history, mathematics, and philosophy, charting humanityas struggle against randomness

Our lives are played out in the arena of chance. However little we recognize it in our day-to-day existence, we are always riding the odds, seeking out certainty but settlingareluctantlyafor likelihood, building our beliefs on the shadowy props of probability. "Chances Are" is the story of manas millennia-long search for the tools to manage the recurrent but unpredictableato help us prevent, or at least mitigate, the seemingly random blows of disaster, disease, and injustice. In these pages, we meet the brilliant individuals who developed the first abstract formulations of probability, as well as the intrepid visionaries who recognized their practical applicationsafrom gamblers to military strategists to meteorologists to medical researchers, from blackjack to our own mortality.

Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into ten languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely scintillating."
In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it.
"Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean?

Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works.

In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.

Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.

The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

Who hasn't feared the math Minotaur in its labyrinth of abstractions? Now, in Out of the Labyrinth, Robert and Ellen Kaplan--the founders of The Math Circle, the popular learning program begun at Harvard in 1994--reveal the secrets behind their highly successful approach, leading readers out of the labyrinth and into the joyous embrace of mathematics. Written with the same wit and clarity that made Robert Kaplan's The Nothing That Is an international bestseller, Out of the Labyrinth offers an engaging and practical guide for parents and educators, and a delight for anyone interested in sharing the pleasures of mathematics. The Kaplans begin by describing the state of modern math education--the lockstep acquisition of "skills," "number facts," and "mad minute" calculations. Instead, they argue, math should be taught as the highest form of intellectual play, an endeavor to be explored and enjoyed by children (or adults) of any age. One by one, they dismantle the many barriers to appreciating mathematics, from the self-defeating belief that mathematical talent is inborn, to the off-putting language of mathematics, to the question of why anyone should care. They show, for instance, that mathematical ability is not a matter of inborn genius, but of doggedness and attention. Even Einstein admitted that "I know perfectly well that I myself have no special talents. It was curiosity, obsession, and sheer perseverance that brought me to my ideas." Enhanced throughout with puzzles, practical equations, and colorful anecdotes from their own classrooms, Out of the Labyrinth will delight readers with its engaging exploration of mathematics. It will allow students, parents, teachers, and others to wrestle with the accessible mysteries of math--and discover their inner math genius.