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PRELUDE

In a scene in the American political drama The West Wing, two senior government aides stare in disbelief at a slide in a presentation. A group of cartographers is attempting to explain that the map of the world, the map they have known and trusted all their lives, is just one of many. And it is flawed. "Are you saying the map is wrong?" asks one aide incredulously.

No map of the planet is accurate: it's simply not mathematically possible. The surface of a sphere cannot be transformed into a two-dimensional drawing without distortion. But, as the cartographers explain, the map they are looking at promotes a Eurocentric view of the world. Europe appears to be larger than South America, but South America is actually twice as large. Germany is located in the middle of the map when it's actually in the northernmost quarter of Earth. All this time, our view of the world has been distorted.

The map was drawn by Flemish cartographer Gerardus Mercator in the sixteenth century. It was originally intended for sailors crossing oceans, not for policy wonks considering geopolitics. It has been passed down from generation to generation, solidifying its place as the dominant map, giving people across the planet the impression that this is what the world looks like, not that it is just one perspective.

The history of mathematics is similar. Despite mathematics' reputation as the study of fundamental truths, cold hard calculations and irrefutable proofs, it has not escaped the powerful individuals and structures that have shaped truth and knowledge. Far from it: in fact, the history of mathematics has accumulated biases over thousands of years—from the way certain mathematics and mathematicians are revered to the stories we tell about its origins. It is time this pattern was reexamined and the story retold.

When we, Kate and Timothy, first met to discuss a joint book project, we hadn't anticipated where it would lead. Sipping tea in a bookshop in Charing Cross, London, we talked about our shared love of mathematics and agreed that we should write an approachable history of the subject. Drawing on Kate's expertise as a mathematical historian and Timothy's mathematical and journalistic credentials, we thought it would be straightforward.

We were wrong. The more we delved into the history of mathematics, the more we uncovered about the way it has been distorted. And the more we felt compelled to do something about it.

The origins of mathematics are beautifully varied. Rather than ideas springing up in one location, variations have often appeared throughout history, demonstrating just how powerful the human propensity to reason really is. Ideas ignore national borders, so often mathematics has spread from one place to another alongside trade and cultural exchange. However, the progress of mathematics is not linear. It has gone forward and backward, jumped around the planet, gone off on tangents, on adventures and sometimes down dead ends. And it is much the richer for it. Despite its reputation for logical progressions, mathematics is a far more chaotic affair.

However, this is not how the story of mathematics is usually told. The ancient Greeks are put on a pedestal as somehow being the originators of modern mathematics, yet so much of what is now incorporated into our global knowledge comes from many other places too, including ancient China, India, and the Arabian peninsula. This assumption that the European way of doing things is superior didn't originate in mathematics—it came from centuries of Western imperialism—but it has infiltrated it. Mathematics outside of ancient Greece has often been put to one side as "ethnomathematics," as if it were a separate subject altogether, a side story to the real history.

As we worked our way through thousands of years of mathematics, almost everything we thought we knew was challenged in one way or another. Some well-known stories ended up being misrepresentations and others complete fabrications. Many mathematicians and mathematics have wrongly been excluded from history. Over the following pages, we will reveal some of the ways in which the story of mathematics has been warped. The real story is one of a truly global endeavor. Mathematics is about ideas and inventing ways to think them through to their conclusions. Diversity of thought isn't just important in mathematics, it is fundamental.