A clear, entertaining development of the number systems required in any course of modern mathematics.

“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal

Why do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.

The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.

Learning meets wonder when you invite numbers to come play in your imagination! First think of One peeking out from the night Like a point, or a dot, or a shimmering light. But when One finds a friend to run from or run to, Then we can’t call both “One”—that new One must be Two! And should you want something to go in between, You’ll need a new number, a number like Three. Four makes a square when it’s standing around, But what would you see if it flies off the ground? And then when another new One comes to mind, Yell out its name if you know it . . . it’s Five! Do you like the way that these numbers are sounding? Then join our adventure to count beyond counting! Hello Numbers! What Can You Do? is not like any other counting book. As each “new One” appears on the scene, the numbers’ antics hint at ever-deeper math. Young readers ages 3 to 6 will not only count along, but begin to wonder about symmetry, angles, shapes, and more. Written by the mathematician-and-poet team Edmund Harriss and Houston Hughes, and illustrated by longstanding New York Times artist Brian Rea, this rollicking, rhyming book will take you to a whole new world of numbers.

A clear, practical, first-of-its-kind guide to communicating and understanding numbers and data—from bestselling business author Chip Heath. How much bigger is a billion than a million? Well, a million seconds is twelve days. A billion seconds is…thirty-two years. Understanding numbers is essential—but humans aren’t built to understand them. Until very recently, most languages had no words for numbers greater than five—anything from six to infinity was known as “lots.” While the numbers in our world have gotten increasingly complex, our brains are stuck in the past. How can we translate millions and billions and milliseconds and nanometers into things we can comprehend and use? Author Chip Heath has excelled at teaching others about making ideas stick and here, in Making Numbers Count, he outlines specific principles that reveal how to translate a number into our brain’s language. This book is filled with examples of extreme number makeovers, vivid before-and-after examples that take a dry number and present it in a way that people click in and say “Wow, now I get it!” You will learn principles such as: -SIMPLE PERSPECTIVE CUES: researchers at Microsoft found that adding one simple comparison sentence doubled how accurately users estimated statistics like population and area of countries. -VIVIDNESS: get perspective on the size of a nucleus by imagining a bee in a cathedral, or a pea in a racetrack, which are easier to envision than “1/100,000th of the size of an atom.” -CONVERT TO A PROCESS: capitalize on our intuitive sense of time (5 gigabytes of music storage turns into “2 months of commutes, without repeating a song”). -EMOTIONAL MEASURING STICKS: frame the number in a way that people already care about (“that medical protocol would save twice as many women as curing breast cancer”). Whether you’re interested in global problems like climate change, running a tech firm or a farm, or just explaining how many Cokes you’d have to drink if you burned calories like a hummingbird, this book will help math-lovers and math-haters alike translate the numbers that animate our world—allowing us to bring more data, more naturally, into decisions in our schools, our workplaces, and our society.

Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.