Cloth $30.00 ISBN: 9780226646985 Will Publish September 2021
E-book $29.99 Available for pre-order. ISBN: 9780226647036 Will Publish September 2021


A Philosophical History of Number and Humanity from Antiquity to the Present

David Nirenberg and Ricardo L. Nirenberg


David Nirenberg and Ricardo L. Nirenberg

432 pages | 1 halftone | 6 x 9 | © 2021
Cloth $30.00 ISBN: 9780226646985 Will Publish September 2021
E-book $29.99 ISBN: 9780226647036 Will Publish September 2021
Ranging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity.

Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity?

These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schrödinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.
Introduction: Playing with Pebbles
1 World War Crisis
2 The Greeks: A Protohistory of Theory
3 Plato, Aristotle, and the Future of Western Thought
4 Monotheism’s Math Problem
5 From Descartes to Kant: An Outrageously Succinct History of Philosophy
6 What Numbers Need: Or, When Does 2 + 2 = 4?
7 Physics (and Poetry): Willing Sameness and Difference
8 Axioms of Desire: Economics and the Social Sciences
9 Killing Time
10 Ethical Conclusions
Index of Names
Review Quotes
Joachim Frank, Columbia University, Nobel Prize in Chemistry
“Ricardo and David Nirenberg, father and son scholars of mathematics and history, have teamed up in a breathtaking voyage examining the foundations and limits of knowledge in western thought. Not content with secondary sources, they have translated from the literature in their original languages: Arabic, French, German, Greek, Hebrew, Italian, Latin, and Spanish.  In particular, they target mathematics and the natural sciences, and the way the concepts of sameness and differences affect our understanding of the natural world. But in the process, the authors touch upon many other facets of human endeavor, all named after their Greek roots: poetry, philosophy, psychology, economy.  Along this wildly entertaining journey, we meet dozens of erudite thinkers, scientists, and writers such as Anaximander, Al-Fārābī, Fyodor Dostoevsky, Ludwig Wittgenstein, Werner Heisenberg, and Rainer Maria Rilke. The book arrives just in time to give us ammunition as attempts are being made to put truth itself into the supercollider. It is a source of inspiration and comfort to learn how the far-flung ideas about numbers, our existence, and the world we live in have been debated in the past.”
James J. Heckman, the Henry Schultz Distinguished Service Professor of Economics at the University of Chicago, Nobel Memorial Prize in Economics
“This is an erudite and insightful exploration of the collision between two distinct ideas: sameness and difference. The authors brilliantly unify wide-ranging bodies of thought across millennia around this theme. They forcefully and eloquently demonstrate why this dichotomy  matters today and how deeply it shapes our vision of the world and the actions we take.”
Hent de Vries, the Paulette Goddard Professor of the Humanities, New York University
"Drawing on a broad range and telling selection of examples from economics, quantum physics, literary studies, and more, the Nirenbergs combine their strength as a professional medievalist and a mathematician, respectively, to take the reader on a guided, remarkably enthralling tour through the universe and universals of formalization. Beautifully and engagingly written, this book will greatly appeal to a wide, interested reading public and change the critical terms of debate regarding mathematical versus other forms of reasoning in the natural, social, and human sciences as well as literature and the arts, even ordinary life, for years to come."
For more information, or to order this book, please visit
Google preview here

Chicago Manual of Style

Chicago Blog: Mathematics and Physics

Events in Mathematics and Physics

Keep Informed