King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry

King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry

The notion of “geometry” brings to mind circles, triangles, the Pythagorean Theorem. Yet geometry is so much more; indeed, it governs much of our lives-from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And there can be no better guide to the majestic reach of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.


Many of the greatest names in intellectual history were geometers—Archimedes and Einstein among them—and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter’s special contributions—his famed Coxeter groups and Coxeter diagrams—have been called “tools as essential as numbers themselves.”


Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter’s vision.


But Coxeter’s greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and algebraic.

View the TVOntario documentary, “The Man Who Saved Geometry”


“Siobhan Roberts has achieved something extraordinary in this book, a paean to a geometer and all geometry. It tells a brave, compelling story. It comprehends a whole universe— our universe — of kaleidoscopes and crystals, groups and symmetry, bicycles and snowflakes, music and movement.It is lucid, beautiful, and exalting.”

—James Gleick, author of The Information

“Roberts’ book really soars in its description of Coxeter’s work and his ability to visualize space, to communicate the poetry of geometry and to inspire other mathematicians, physicists and artists…”

—Nathan L. Harshman, Chicago Tribune

“What emerges loud and clear in King of Infinite Space is that Siobhan Roberts understands Coxeter’s spirit very deeply. She understands what drove him, and she knows just how to put into words the fire that always inhabits a great mathematician’s soul.”

—Douglas Hofstadter, Indiana University, author of Gödel, Escher, Bach

“What a wonderful world Siobhan Roberts evokes through this scientific portrait of the inimitable geometer, Donald Coxeter…. Like the fine and thoughtful sketches of Jeremy Bernstein and James Gleick, Roberts succeeds beautifully in crossing mathematics with the quirky, imaginative, and productive life of one of our greatest modern mathematical thinkers.”

—Peter Galison, author of Einstein’s Clocks, Poincaré’s Maps

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