What is Zero: The Biography of a Dangerous Idea about?

The number zero seems self-evidently harmless, but Charles Seife's history argues that zero has been, at various points, theologically threatening, mathematically subversive, and philosophically destabilizing. The book traces zero's biography from its origins in Babylonian and Indian mathematics through its transformation of arithmetic, calculus, and physics, and into quantum mechanics and cosmology, where the infinities and zeros of modern physics continue to raise deep conceptual problems.

The early chapters are cultural history. Ancient Greek mathematics had no zero because the Greeks found the concept incoherent — nothing cannot be a number. The Church in medieval Europe was hostile to zero partly because zero implied a void, and the void was theologically problematic in a cosmos created by God. Indian mathematicians were less constrained by these metaphysical commitments and developed zero as a number with its own arithmetic rules. Arab traders carried the Hindu-Arabic numeral system, including zero, into Europe, where it transformed commerce and science.

The mathematical chapters are more substantive. Seife explains how zero and infinity are always paired — you cannot have one without the other — and how this pairing causes problems. Division by zero is undefined; multiplying zero by infinity produces any number you like, or none. These indeterminacies appear at the heart of calculus (the derivative is a ratio of two zeros) and at the heart of physics (quantum field theory and general relativity both generate infinities that have to be managed by mathematical techniques that amount to subtracting one infinity from another). Seife argues that zero and infinity represent the points where mathematics touches genuine mystery.

The book is short and readable and occasionally oversimplifies. Seife is a journalist, not a mathematician, and some of the later physics is handled quickly enough that specialists will wince. But as an introduction to why a number matters — to the history of counting, to the development of calculus, to the structure of modern physics — it's unusually effective. Zero is one of those concepts that seems obvious until you look at it closely, and then stops seeming obvious at all.