The Waltz of Reason

The Entanglement of Mathematics and Philosophy


By Karl Sigmund

Formats and Prices




$41.00 CAD



  1. Hardcover $32.50 $41.00 CAD
  2. ebook $19.99 $25.99 CAD

This item is a preorder. Your payment method will be charged immediately, and the product is expected to ship on or around December 19, 2023. This date is subject to change due to shipping delays beyond our control.

"A mind-bending jaunt … that makes clear in fascinating detail how math is more than a sum of its parts" (Publishers Weekly)

“Let no one ignorant of geometry enter here,” Plato warned would-be philosophers. Mathematician Karl Sigmund agrees.

In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund’s wit and humor shine as brightly as his erudition.

The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have molded our thought and founded our world.

  • “[L]overs of philosophy and human behavior who are at the very least math-curious will be captivated by the author’s investigations of game theory, the social contract, the classic prisoner’s dilemma and, of course, the looming question of whether computers are truly intelligent, even potentially conscious.”
    Los Angeles Times
  • "[Sigmund] writes clearly and with subtle wit, making The Waltz of Reason highly readable... [and] well worth a dance."
    American Scientist
  • “[D]oes the imaginary number i actually exist, or did we invent it? Could an alien civilization develop an alternate form of mathematics, or would they inevitably develop the same one we have? Sigmund’s witty tone inspires readers to delve into those questions and others.”
    Physics Today
  • “Sigmund takes readers on a mind-bending jaunt through game theory, gambling systems, and more. This makes clear in fascinating detail how math is more than a sum of its parts.”
    Publishers Weekly
  • “An erudite, witty, tongue-in-cheek and wide-ranging discourse on philosophy and mathematics, a Gödel, Escher, Bach for the 21st century.”
    Christof Koch, PhD, author of The Feeling of Life Itself
  • “A delightful historical tour of the interplay of Mathematics and Philosophy.”
    Brian Skyrms, University of California, Irvine
  • “Mathematics and Philosophy have always been great dance partners throughout human history. Karl Sigmund is the perfect companion to lead readers on this merry dance. His combination of deep mathematical and philosophical knowledge combined with his entertaining prose will have readers waltzing through this wonderful book.”
    Marcus du Sautoy, author Around the World in Eighty Games
  • “Lucid, readable, and fascinating. Karl Sigmund acts as our friendly guide to topics as diverse as the meaning of numbers, the limits of computers, and the impossibility of a fair voting system. Highly recommended!”
    Ian Stewart, author of What’s the Use?

On Sale
Dec 19, 2023
Page Count
448 pages
Basic Books

Karl Sigmund

About the Author

Karl Sigmund is a professor emeritus of mathematics at the University of Vienna. One of the pioneers of evolutionary game theory, he has authored several other books on mathematics and philosophy, including Games of Life and Exact Thinking in Demented Times. He lives in Vienna, Austria. 

Learn more about this author