In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements.

Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory.

The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and ­creativity.

The Inka Empire stretched over much of the length and breadth of the South American Andes, encompassed elaborately planned cities linked by a complex network of roads and messengers, and created astonishing works of architecture and artistry and a compelling mythology—all without the aid of a graphic writing system. Instead, the Inkas' records consisted of devices made of knotted and dyed strings—called khipu—on which they recorded information pertaining to the organization and history of their empire. Despite more than a century of research on these remarkable devices, the khipu remain largely undeciphered.

In this benchmark book, twelve international scholars tackle the most vexed question in khipu studies: how did the Inkas record and transmit narrative records by means of knotted strings? The authors approach the problem from a variety of angles. Several essays mine Spanish colonial sources for details about the kinds of narrative encoded in the khipu. Others look at the uses to which khipu were put before and after the Conquest, as well as their current use in some contemporary Andean communities. Still others analyze the formal characteristics of khipu and seek to explain how they encode various kinds of numerical and narrative data.

There is no question that native cultures in the New World exhibit many forms of mathematical development. This Native American mathematics can best be described by considering the nature of the concepts found in a variety of individual New World cultures. Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways. Native American Mathematics, edited by Michael P. Closs, is the first book to focus on mathematical development indigenous to the New World.

Spanning time from the prehistoric to the present, the thirteen essays in this volume attest to the variety of mathematical development present in the Americas. The data are drawn from cultures as diverse as the Ojibway, the Inuit (Eskimo), and the Nootka in the north; the Chumash of Southern California; the Aztec and the Maya in Mesoamerica; and the Inca and Jibaro of South America. Among the strengths of this collection are this diversity and the multidisciplinary approaches employed to extract different kinds of information. The distinguished contributors include mathematicians, linguists, psychologists, anthropologists, and archaeologists.

“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