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King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry Hardcover – September 19, 2006


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Product Details

  • Hardcover: 320 pages
  • Publisher: Walker & Company; First Edition edition (September 19, 2006)
  • Language: English
  • ISBN-10: 0802714994
  • ISBN-13: 978-0802714992
  • Product Dimensions: 1.4 x 6.4 x 9.3 inches
  • Shipping Weight: 1.6 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #823,206 in Books (See Top 100 in Books)

Editorial Reviews

From Publishers Weekly

During the latter half of the 20th century, geometry largely fell out of favor within the mathematical community. As Canadian journalist Roberts so well describes in her first book, Donald Coxeter (1907–2003), a University of Toronto mathematician, almost singlehandedly preserved and advanced the discipline through hard work and acute insights. His impact has been felt in a wide variety of fields and acknowledged by the likes of Buckminster Fuller and M.C. Escher. Coxeter also helped transform mathematics education to bring geometry back into the mainstream. This change is critical because, as Roberts explains, a robust understanding of geometry is essential for progress in disciplines from crystallography to cosmology, and from video graphics to immunology. Given Coxeter's long life and career, his biography, in large part, tells the story of mathematics in the 20th century as well as a human portrait of a man who—despite his royal title—was a "humble, hands-on geometer." Roberts, who won a National Magazine Award for a Toronto Life profile of Coxeter, puts most of the technical material in appendixes, so the text is readily accessible to a general audience. 70 b&w photos and diagrams. (Sept.)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

From Booklist

The mathematics of shape and space, geometry was not professionally hip during the career of H. S. M. Coxeter (1907-2003). As Roberts elaborates in this warm but not uncritical portrait, the visual and intuitive aspects of geometry did not attract a field headed in more abstract directions. By the 1950s, a group of French mathematicians mounted the barricades against geometry under the slogan "Death to triangles!" Coxeter took notice but no heed of the radicals, content with his fertile imagination that yielded new geometrical papers up to his nineties. Though keeping geometry vibrant was not Coxeter's intent, it was the effect as, over time, his discoveries came to be useful to architect Buckminster Fuller, string theorists, and Godel, Escher, Bach (1979) author Douglas Hofstadter, who contributes a preface. Roberts accessibly explains the cruxes of Coxeter's discoveries and his place in mathematics history, while her narrative of Coxeter's personal life depicts an aloof but amiable character a bit deficient in the parenting department. With Coxeter appraised by peers as a modern Euclid, Roberts' biography bears inclusion in the popular mathematics collection. Gilbert Taylor
Copyright © American Library Association. All rights reserved

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Customer Reviews

4.3 out of 5 stars
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Above all, the book is well written and entertaining.
Grant Cairns
An enjoyable biography of one of the 20th century's great mathematicians.
L. King
It's amazing how one encounters things without really trying.
J. Guild

Most Helpful Customer Reviews

14 of 15 people found the following review helpful By Megan Jones-Smith on April 20, 2007
Format: Hardcover
In the interest of full disclosure, I must admit from the start that I started to read this book because of the tireless promotion of Glenn Smith, my father-in-law, friend of Coxeter and passionate geometer (who also happens to be quoted in the book). I even went to U of T, even if my studies kept me far from the mathematics department. But although geometry was my least favorite of all the maths in school, with Glenn's passion for this book there was no way I could continue to ignore my husband's copy lying in the living room. I had to pick it up and see for myself just what his excitement was all about.

I expected to be in over my head, possibly bored, reading it more out of curiosity than intrinsic interest. But after the first few pages I was hooked. This book, while delineating the history of geometrical inquiry, is also a captivating narrative of Coxeter's life. This is the story of a man who pursued his passion with his own quirks and habits, told in a way that rendered him human to me even as it allowed me to fully understand why he is considered a genius in his field.

Yes, there were certain paragraphs full of mathematical explanations where I had to simply breath deep and hope that whatever on earth that meant had no direct impact on the unfolding of the narrative at large. The abundance of footnotes were also awkward at first, a sign that the author wasn't sure if her audience would be academic or popular, but after a while they faded from my attention as I became engrossed in Coxeter's story.

By the end, I was ready to pull out the Zome tools and mirrors so that I could start building models and see if I, too, could see in four dimensions or more. So far I'm still stuck in the regular three, but with the inspiration of Coxeter to guide me there's always hope.
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10 of 10 people found the following review helpful By Jonathan Choate on April 16, 2007
Format: Hardcover
Siobhan Roberts' King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry is by far one of the best math related books I have read in years. Admittedly I am a geometer at heart, but it was far more than the mathematical content of the book which excited me. First of all, the author provides a detailed and very human look at the life of a world class mathematician. We follow Coxeter's career from Trinity College to the University of Toronto with stops along the way at Berkeley and the Institute for Advanced Studies at Princeton. Secondly, we get a good look at how and why geometry fell out of favor in the twentieth century, thanks in good part to efforts of Bourbaki, the French mathematics critical montoring group. Thirdly, we see how Coxeter developed many of his important results in a way that is accessible to anyone with a decent secondary mathematical background. The book contains seven appendices and an extensive set of endnotes all of which I found to be both very readable and very helpful. The author does a nice job of showing how the concept of symmetry was central to Coxeter's work in second, third, fourth, and higher dimensions. I found particularly interesting Coxeter's admiration for the work of M. C. Escher but as hard as Coxeter tried he could not get Escher to understand the mathematical significance of his own art work. During the later part of the book, the author shows how Coxeter's work has been used in a variety of fields both inside and outside of mathematics: Buckminster Fuller, in his work with geodesic structures, was inspired by Coxeter's polyhedral theories; Macarthur Fellow Jeff Weeks employed Coxeter's work with higher dimensional polytopes in developing his theories on the shape of the universe.Read more ›
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12 of 13 people found the following review helpful By R. Hardy HALL OF FAMETOP 500 REVIEWER on January 21, 2007
Format: Hardcover
Here is an unlikely candidate for real-life hero: a geometry professor. H. S. M. "Donald" Coxeter, a classical geometer interested in shapes, lines, vertices, polygons and the visualization of such geometric entities, saved the world from being overtaken by formalists who wanted to algebra-ize everything in geometry. Coxeter is not well known by most people; his geometry encompassed higher dimensions than most of us can think about. But he was truly a hero for the mathematicians who knew him and worked with him, and he did make differences in their discipline that have proved to have surprisingly widespread and even practical results. He has had the good fortune, four years after the end of his long life, to be the subject of a full and admiring biography _King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry_ (Walker) by Siobhan Roberts. Roberts is a journalist who interviewed Coxeter himself over a period of two years toward the end of his life, and has interviewed many leading mathematicians and scholars who were the best ones to explain the exalted status in which Coxeter is held. Roberts's book is not a geometry text; she give analogies about Coxeter's work and hints at its themes rather than going into any mathematical detail, so even if you are intimidated by mathematics, you can get an idea of Coxeter's thoughts and just why he was such a revolutionary. This makes not only for an interesting biography, but an agreeable tour of just how mathematics has gotten done in the past few decades.

Coxeter, born in London in 1907, was one of the mathematicians that broke the rule that doing math is a young man's game. He did make his first discoveries when he was thirteen, but was active until his death in 2003, still writing, proving, and presenting.
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