Zero: The Biography of a Dangerous Idea is a nonfiction popular science book written by the American journalist Charles Seife and originally published in February 2000 by Viking, a division of Penguin Random House. Zero was Seife’s debut book, though he had done freelance work on miscellaneous topics in science, mathematics, and technology for various magazines and journals. He is currently a professor of journalism at New York University and has received acclaim for both his freelance work and several additional books. In Zero, Seife surveys the origins and history of the idea of zero in philosophy, mathematics, and science. The major themes of the book are that the idea of zero is perilous, that zero unlocks the mysteries of nature, and that zero and infinity are intertwined. Zero won the 2001 PEN/Martha Albrand Award for First Nonfiction Book and was a New York Times Notable Book.

This study guide refers to the September 2000 edition released by Penguin Random House.

Summary

As Seife explains in Chapter 0, Zero is a chronological survey of the concept of zero, broadly conceived to include not just the mathematical number but philosophical nothingness and the scientific vacuum (empty space). Seife considers the history of zero inseparable from the history of infinity. Zero is also a story about those individuals—mathematicians, philosophers, theologians, mystics, astronomers, physicists, and others—who wrestled with zero throughout the centuries.

Chapter 1 examines the earliest number systems of humanity, explaining why zero wasn’t needed by ancient counters. Seife introduces readers to the Greek, Babylonian, and Mayan counting systems, identifying the earliest appearances of zero. He then analyses why zero was not merely ignored but feared by ancient peoples.

In Chapter 2, Seife discusses Pythagoras, emphasizing his mystical obsession with numbers and shapes and his ignorance of zero. He discusses Zeno’s paradox at length and then attends to Aristotle and philosophy, which biased Western thought against zero for centuries. He also talks about Archimedes and the difficulties of the Western calendar that have resulted from the rejection of zero.

Chapter 3 describes Eastern philosophy and early Indian counting systems’ receptivity toward the ideas of zero and infinity. Seife shows how zero also fared well in Islamic civilization, Arab counting systems, and Jewish thought. He turns back to the West to note the earliest questionings of Aristotelianism and indicates that zero first infiltrated Western thought through Fibonacci.

Chapter 4 explores how various individuals brought notions of zero and infinity into Renaissance thought, giving special attention to René Descartes’s invention of the coordinate plane and Blaise Pascal’s discovery of the vacuum and probabilistic argument for believing in God.

In Chapter 5, Seife returns to Zeno’s paradox and outlines the series of mathematical advances that led to the discovery of calculus. He explains how calculus as initially conceived by Newton and Leibniz relied on division by zero but eventually overcame this paradox through D’Alembert’s notion of limits.

Chapter 6 guides readers through a series of complex mathematical innovations—imaginary numbers, projective geometry, the Riemann sphere, and set theory—that exposed how zero and infinity intertwine. Seife shows how the mathematicians responsible for these innovations reacted to these bizarre new ideas.

Chapter 7 considers the impact of zero in the physical sciences. Seife examines the discovery of absolute zero and the development of thermodynamics and statistical mechanics. He describes a paradox in the early study of light and how Max Planck and Einstein unwillingly revolutionized physics to resolve the paradox, inventing quantum mechanics and general relativity, respectively. Seife also discusses the Heisenberg uncertainty principle, the Casimir effect and zero-point energy, and black holes, emphasizing the integral roles of zero and infinity in these phenomena.

In Chapter, 8 Seife shows that zero is at the forefront of modern scientific inquiry into the fundamental nature and origin of the universe. He discusses how string theory resolved the tension between quantum mechanics and general relativity by taming zero but remarks that the theory remains untestable and therefore speculative. Seife then describes how a series of discoveries led to the consensus that everything had a beginning—the Big Bang, ground zero of the universe.

Chapter ꝏ explains that thanks to zero the universe will expand forever. Seife concludes by recapitulating the basic outline of his history of zero and summarizing the reasons that zero was and is a significant idea.

The book ends with five appendices that elaborate on some of the concepts introduced in earlier chapters. Illustrations throughout the book also aid readers with comprehension of abstract or difficult ideas.