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King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry Hardcover – 30 Oct 2006

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Product details

  • Hardcover: 399 pages
  • Publisher: Walker & Company (30 Oct. 2006)
  • Language: English
  • ISBN-10: 0887842011
  • ISBN-13: 978-0887842016
  • ASIN: 0802714994
  • Product Dimensions: 16.3 x 3.8 x 24.4 cm
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 756,891 in Books (See Top 100 in Books)

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"'Tells a brave, compelling story...of kaleidoscopes and crystals, groups and symmetry, bicycles and snowflakes, music and movement. It is lucid, beautiful, and exalting.' James Gleick, author of Chaos and Faster "Her beautifully written tribute is rich in details about Coxeter's long life and his colourful interactions with the world's top mathematicians. I found it impossible to stop reading." Martin Gardner, author of The Ambidextrous Universe. "A lively view of the history of mathematics while weaving the story of Donald Coxeter, a broad-minded genius who built an important bridge between two opposite extremes of mathematical creation - the pictorial world of classical geometry and the ideal world of abstract algebra." Freeman Dyson author of Disturbing the Universe" --This text refers to an out of print or unavailable edition of this title.

About the Author

Siobhan Roberts won a National Magazine Award for her profile of Donald Coxeter. She lives in Toronto. Click here for the author's website. --This text refers to an out of print or unavailable edition of this title.

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3 of 4 people found the following review helpful By Rerevisionist on 17 Jun. 2010
Format: Paperback Verified Purchase
Biog of Coxeter, a Canadian professor who flourished in the 1960s and was famous for having 'saved geometry'. Famous amongst mathematicians, at least. His books were and I expect still are on university maths reading lists. The authoress is Canadian, and it's her first book. It has to be said she hasn't been bold in her comments. For example it's not entirely clear what Coxeter's life work really amounted to. Nor does she try to tackle the highly disputable elements which seem taken for granted by these people, on such things as multiple dimensions and groups (defined in ways not in conformity with the usual meanings, I'd guess deliberately), geometry of curved surfaces - which has been given a sort of fantasy ethereal feel, and the extremely simple and therefore implausible derivation of e=mc squared.

Coxeter seems to have been happiest with extensions of the Platonic solids (in 'Regular Polytopes'), and related activities, such as the standard system for describing crystals (by their nodes etc), geodesic domes, possible implications for molecular structure, and so on. There's quite a bit on domes (which he didn't invent) and buckminsterfullerene, a form of carbon generated by evaporating carbon in a vacuum whereupon the atoms because of carbon's valency of 4 tend to like as sheets, but by default curl round. Whether anyone's found a use for this, seems not to be known by Roberts. Another thing Coxeter didn't find was Penrose's simple-seeming slightly asymmetrical tiles.

Coxeter used algebra rather heavily and extended into regions where he then tailed off and others' expertise ruled. His book of 'twelve essays' hardly sold any copies. There are quite striking accounts, if you read between the lines, of inter-departmental and inter-university rivalries.
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3 of 4 people found the following review helpful By Michael Sharpe on 21 July 2007
Format: Hardcover
'Donald Coxeter, the Man Who Saved Geometry' is the book's subtitle, so you can guess Siobhan Roberts wanted to write a 'conspiracy bio' with the hero (with all his personal flaws) proving his point before the judgement of his peers, that the old ways really are the best.

So the book's material includes a lot of context about 'geometry'- the knowledge and the practice, the mathematical community's heroes/heroines and villains/ villainesses, and even 8 Appendices, one of which is entitled 'Crystallography and Penrose Toilet Paper'. The narrative flips back and forth in the TV documentary style, starting and ending with Coxeter as he was just before his death on 31.3.03, aged 96.

With a foreword and more by the great Douglas Hofstadter, in-text photos including some Escher masterpieces directly influenced by Coxeter, and meticulous sourcing and bibliography, I enjoyed the book immensely apart from the Hollywood leanings - the Penrose connection is a tasty journalistic snippet, but it just don't belong....So, great that such a biography gets written, good that a Toronto-based journalist with mathematical contacts of the calibre of John Horton Conway and Marjorie Senechal gets to do it, bad that a reprint revising some minor typos (Saversnake Forest?!?!) hasn't been released in paperback yet!
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Amazon.com: 18 reviews
17 of 18 people found the following review helpful
Yes, there's math, but there's a whole lot more too 20 April 2007
By Megan Jones-Smith - Published on Amazon.com
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.
12 of 12 people found the following review helpful
The Geometer's Geometer 16 April 2007
By Jonathan Choate - Published on Amazon.com
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.

One theme that occurs again and again throughout the book is that Coxeter's work was always characterized by his excellent taste, his sense of beauty, and the exquisite simplicity of his mathematics. I hope that anyone who reads this book will run out and get copies of Coxeter's three wonderful books: Introduction to Geometry (2nd edition 1989), Regular Polytopes( 1973 ), and Geometry Revisited ( 1967 ) (co-authored with Samuel Grietzer ) . Finally, the author has shown how Coxeter's efforts have helped rekindle people's interest in geometry. Many prominent people in the mathematics community, such as Douglas Hofstadter and John Conway, have been inspired by Coxeter's work and are helping to revive interest in this beautiful subject. This is a book that should be read by everyone who teaches geometry and by anyone who has any interest in the way in which some of the most elegant work in mathematics during the last century evolved.

Siobhan Roberts has been working with members of the York University Mathematics Department to put together a web site for the book. The site is still under construction but an early version can be found at [...]
14 of 15 people found the following review helpful
A Mathematical Hero 21 Jan. 2007
By Rob Hardy - Published on Amazon.com
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. He was a student at Cambridge, and in 1936 he immigrated to Toronto and took a teaching post at the university there, where he remained for the rest of his life. There are many descriptions of cranky mathematicians in these pages, but Coxeter was never like that. A fellow mathematician said, "He was almost courtly. He was very gentle, even when he managed to show you that you were thinking like an idiot." He had the archetypal lack of interest in any practical applications of his ideas, appalled that his lovely theories could be sullied by practical utility. He firmly believed in pictures, visualization, and intuition, putting himself successfully at odds with the formalists who had inspired the New Math that was taught in grade schools forty years ago. His insistence on visual appeal linked him to M. C. Escher who incorporated mathematical ideas into his art. Coxeter even wrote explications of certain Escher prints; that he did so gratified the artist, but privately the non-mathematician Escher said that the "hocus-pocus text is no use to me at all." Coxeter also had a close, not always collegial, relationship with Buckminster Fuller, whose geodesic domes he admired.

Coxeter's professional life was without reproach. His family life was much less than perfect. Part of the problem was that he had all the bumbling of an absent-minded professor, causing his wife Rien to screech names at him in her native Dutch. Coxeter conceded, "I was not able to love Rien as fully and completely as one should his wife," but when she developed Alzheimer's, he took uncharacteristically close care of her bathing, dressing, and feeding. Neither of their two children had interest in mathematics. His daughter "ran hot and cold on his status as a mathematical legend," but escorted the elderly Coxeter to his last conferences. She said, "Dad would hate to be equated with Elvis Presley, but Elvis gave people some moments of joy, happiness, inspiration. And if that's what Dad's work does for these people, that's wonderful. Personally, I get more from Elvis Presley." She isn't the only one, of course, but Roberts's delightful biography can't help but show even non-mathematicians just how important a figure Coxeter was. Do not fret that you don't understand all the math here. Coxeter once admitted that even in the geometry that he loved, "There are so many branches of the subject in which I am almost as ignorant as the proverbial man in the street."
8 of 9 people found the following review helpful
Coxeter deserves better... 2 Jan. 2009
By Librum - Published on Amazon.com
Format: Hardcover
Let me say at the outset, I was very excited when this book came out. It was awhile before I got around to reading it, and in the interim my expectations grew. Having just finished KoIS, I am sad to say, my expectations were greatly disappointed. SR may have written a fine magazine profile (I haven't read it; I can't say; but I don't doubt she did), but as (evidently) neither a mathematician nor a historian(/biographer) by training, she was not, in my view, up to the task of developing a book length treatment of her subject. The opening chapters of KOIS read as competent if uninspired biography. Coxeter strikes me as perhaps not the most scintillating of biographical subjects. But judging from his massive scholarly output, and the influence he has exerted on several generations of mathematicians and scientists in disparate fields, he is a patently fascinating intellectual subject. Clearly SR knows this too, and tries admirably to convey as much. But to do her subject true justice, she would have needed to delve far more deeply into his scholarship, and the fundamentals of his discipline, than she is able to. I can only hope that Conway or Hofstadter or Dyson or some other deeply knowledgeable -- and sympathetic -- Coxeterian will take up the challenge of writing a real scientific biography of HSM. He richly deserves one.

One additional criticism of KoIS: in its concluding several chapters, KoIS nearly abandons its subject altogether, and roves randomly over topics in the geometry of biochemistry and physics. These are fascinating topics, to be sure, but a) RS treats them only superficially and b) their connection to Coxeter is far from clear. The subtitle of the present book seems to suggest that but for Coxeter advances in biochemical and string theoretical thinking might never have occurred. Really? I don't doubt Coxeter's key role in keeping geometry alive in the mathematics of the 20th century. But he was not THE only geometrist of the era nor THE only geometry-minded mathematician or scientist. SR is practicing an annoying kind of hyperbole here that is all too common in popular-science treatments. These closing chapters, then, read almost entirely as a kind of filler, chock full of interesting details, but of only tangential relation to the topic at hand: Coxeter's life and work.

Having come down on KoIS rather negatively, I do credit SR with taking this project on. She clearly has great affection for Coxeter the geometer and the man, and the density of her endnotes (a bit excessive to be sure) attest the hard work she did in the library and on the phone. She is an engaging writer and will doubtless do fine work in the future. That said, both the biography and the intellectual biography of HSM Coxeter have yet to be written. I look forward eagerly to reading them one day.
4 of 4 people found the following review helpful
Unfashionable math 1 Mar. 2007
By N. Kobayashi - Published on Amazon.com
Format: Hardcover
Is geometry dead? For most of us, geometry is but a faint memory of school days, an old-fashioned toy collecting dust cast in a corner of our childhood memories. So old-fashioned indeed that geometry was indeed pronounced dead by a group of French mathematicians, Bourbaki. In fact we find in this first book by Siobhan Roberts that geometry was already falling out of fashion when the protagonist of her work, Dr. Donald Coxeter, chose the subject to be his lifelong pursuit. What he made out of it for his extremely long and fruitful academic career, therefore, is an indispensable lesson that one's passion and talent would eventually lead to extraordinary achievements regardless of the trendiness of the nature of one's target subject.

"King of Infinite Space" is about a mathematician who reinvented and reinvigorated geometry. It will be a delight to anyone with basic understanding of geometry, but readers' enjoyment does not depend on it. It can be read also as an arresting biography of a lonely scholar who sought solace in the beauty of mathematics while being emotionally alienated by his family. Instead of his wife, it seems as if geometry was his partner of life, bringing him many joys and even unexpected interactions with artists such as M.C. Escher or with George Odom, an admirer and a resident in the Hudson River Psychiatric Center in upstate New York who kept sending Dr. Coxeter numerous models.

For the rest of us less endowed with mathematical talent, this book offers a glimpse to life and mind of a genius. The unfashionableness of his research subject seems to have been compensated by the longevity of his academic career -- he was writing new papers well into his nineties. Offering also a digested and concise version of the rich history of geometry, Roberts' work is a wonderful choice to a wide range of readers.
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