Robert Kaplan’s The Nothing That Is: A Natural History of Zero
was an international best-seller, translated into eight languages. The Times
called it “elegant, discursive, and littered with quotes and allusions from Aquinas
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.