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King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry
"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." ―Brian Greene, author of The Elegant Universe The word "geometry" brings to mind an array of mathematical circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; 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 as Siobhan Roberts elegantly conveys in The King of Infinite Space , there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century. Many of the greatest names in intellectual history―Pythagoras, Plato, Archimedes, Euclid― were geometers, 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 by other mathematicians "tools as essential as numbers themselves," but his 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 rational. 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. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.
399 pages, Hardcover
First published January 1, 2006
6 people are currently reading
315 people want to read
About the author
Siobhan Roberts
4 books30 followersWhile writing the Conway biography, Siobhan Roberts was a Director’s Visitor at the Institute for Advanced Study, in Princeton, and a Fellow at the Leon Levy Center for Biography, at the CUNY Graduate Center in New York City. In 2017 she won the JPBM Communications Award for Expository and Popular Books, bestowed by the American Mathematical Society and the Mathematical Association of America (putting her in good company with previous recipients James Gleick and Sylvia Nasar, among others).
She also wrote and produced a documentary film about Coxeter, The Man Who Saved Geometry, for TVOntario’s The View From Here (September 2009).
As a journalist, she writes for Newyorker.com, New York Times "Science Times," Quanta, and The Walrus. Her profile of the one-hundred-year-old mathematician Richard Guy was included in The Best Writing on Mathematics 2017 (Princeton University Press).
At various times she has contributed to The Globe and Mail, The Guardian, The Mathematical Intelligencer, Maisonneuve, Canadian Geographic, and Smithsonian, among other publications. She has won a few National Magazine Awards—writing about “the river of dust” at the National Archives in Ottawa, the occasion when the FBI came calling at Winnipeg’s level-4 National Microbiology Laboratory, and Donald Coxeter’s final journey, to a geometry conference in Budapest at the age of ninety-three.
She also wrote and produced a documentary film about Coxeter, The Man Who Saved Geometry, for TVOntario’s The View From Here (September 2009).
As a journalist, she writes for Newyorker.com, New York Times "Science Times," Quanta, and The Walrus. Her profile of the one-hundred-year-old mathematician Richard Guy was included in The Best Writing on Mathematics 2017 (Princeton University Press).
At various times she has contributed to The Globe and Mail, The Guardian, The Mathematical Intelligencer, Maisonneuve, Canadian Geographic, and Smithsonian, among other publications. She has won a few National Magazine Awards—writing about “the river of dust” at the National Archives in Ottawa, the occasion when the FBI came calling at Winnipeg’s level-4 National Microbiology Laboratory, and Donald Coxeter’s final journey, to a geometry conference in Budapest at the age of ninety-three.
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Displaying 1 - 25 of 25 reviews
July 4, 2008
It pains me to dislike a well-written book. The writing is elegant, concise, eloquent, appears thoroughly researches, and the book well-structured. While I was reading it, I wasn't struck with sufficient annoyance or revulsion that I felt compelled to, say, throw it across the room. But so little was I moved to care about its subject (H.M.S. "Donald" Coxeter, the "King of 20th Century Geometry," inventor of Coxeter diagrams, Coxeter groups, polytope cataloguer, and academic/author of 3 influential geometry texts) that I found myself reluctant to keep returning to it. Life's just too short and the universe of literature too vast to waste in unenlightening tedium. So let me spare you the pain.
I usually pick up biographies to gain insight on subject matter with which I am not wholly familiar, learn background and historical context of those whose ideas and accomplishments I admire, or simply be inspired by or vicariously enjoy the subject's presumably impressive achievements. I mean the narrative arc tends to be predictable: biographies are basically the story of a prodigious talent who emerges from obscurity, weathers personal challenges, and leaves a lasting legacy. It's the detail that makes it worthwhile.
Not here. Looking for insight or new appreciation of patterns (which I love) and shapes? Alas, Donald Coxeter's major achievements and encounters with more recognizable names (Albert Einstein, M.C. Escher, Buckminster Fuller, Douglas Hofstadter, John Conway) while brought to light, mostly occur in the context of dull, one-sided correspondence. Coxeter was known as a champion of graphic, rather than algebraic demonstration of geometric principles and concepts (this is what appealed his work to Fuller, Hofstadter, and especially Escher). Ironically, because this book largely lacked accompanying illustrations to operationalize how his diagrams, groups, kaleidoscopes, etc. worked, I couldn't really appreciate the (I guess?) complex ideas or their significance.
His life itself was unexceptional. A Brit born into privilege in London in 1907, Coxeter grew up in relative social isolation imposed largely by his interest in music and math (steered toward the latter as he was deemed by the likes of Holst and Stanford to show no particular compositional talent); followed the usual academic trajectory of college, grad school, fellowship, minor paper publication, placement at and ultimate university tenure (at the unremarkable University of Toronto), and a career teaching classes, attending conferences and symposia, writing papers and compiling these into textbooks; and remained professionally productive in this way until his death in 2003. He was a teenager during WWI, had to enter the workforce at the height of the Great Depression, was an accomplished mathematician who would know many of the players in the Manhattan Project, and a teaching professional during the strife of Vietnam, etc., and yet appears touched by none of these events, living a life almost entirely devoid of drama. Yay, him.
Perhaps his personal life offered inspiration? Nope. While apparently a nice enough guy in person and privately an advocate for social justice, he was so self-absorbed that even he had to admit he "was not able to love [his wife] as fully and completely as one should." (p. 143) Or his kids, who "lodged a formal complaint with their parents about the tension and lack of affection in their household." (p. 145) And his legacy? Upon his death, the University of Toronto thought so highly of his impact and accomplishments that... his position was not filled. There is apparently no geometry-specialist currently on the U of T staff. As the author writes, "mathematical traditions usually do not reside in isolated individuals." Yet, the University of Toronto apparently has plenty of company among the world's academic institutions in choosing "not to invest in the future of classical geometry." (p. 359) Ho-hum.
So, did Coxeter somehow manage to synthesize and frost the Euclidean cake for all time? I wouldn't really know, though I'm told his professional work does indeed form a vital part of contemporary understanding of symmetry with practical implications for contemporary research ranging from string theory to data mining. All I can say is that if in fact Coxeter wrote the book on classical geometry, and if that's what you're interested in, then pick up one of those books instead of this pointless biography.
I usually pick up biographies to gain insight on subject matter with which I am not wholly familiar, learn background and historical context of those whose ideas and accomplishments I admire, or simply be inspired by or vicariously enjoy the subject's presumably impressive achievements. I mean the narrative arc tends to be predictable: biographies are basically the story of a prodigious talent who emerges from obscurity, weathers personal challenges, and leaves a lasting legacy. It's the detail that makes it worthwhile.
Not here. Looking for insight or new appreciation of patterns (which I love) and shapes? Alas, Donald Coxeter's major achievements and encounters with more recognizable names (Albert Einstein, M.C. Escher, Buckminster Fuller, Douglas Hofstadter, John Conway) while brought to light, mostly occur in the context of dull, one-sided correspondence. Coxeter was known as a champion of graphic, rather than algebraic demonstration of geometric principles and concepts (this is what appealed his work to Fuller, Hofstadter, and especially Escher). Ironically, because this book largely lacked accompanying illustrations to operationalize how his diagrams, groups, kaleidoscopes, etc. worked, I couldn't really appreciate the (I guess?) complex ideas or their significance.
His life itself was unexceptional. A Brit born into privilege in London in 1907, Coxeter grew up in relative social isolation imposed largely by his interest in music and math (steered toward the latter as he was deemed by the likes of Holst and Stanford to show no particular compositional talent); followed the usual academic trajectory of college, grad school, fellowship, minor paper publication, placement at and ultimate university tenure (at the unremarkable University of Toronto), and a career teaching classes, attending conferences and symposia, writing papers and compiling these into textbooks; and remained professionally productive in this way until his death in 2003. He was a teenager during WWI, had to enter the workforce at the height of the Great Depression, was an accomplished mathematician who would know many of the players in the Manhattan Project, and a teaching professional during the strife of Vietnam, etc., and yet appears touched by none of these events, living a life almost entirely devoid of drama. Yay, him.
Perhaps his personal life offered inspiration? Nope. While apparently a nice enough guy in person and privately an advocate for social justice, he was so self-absorbed that even he had to admit he "was not able to love [his wife] as fully and completely as one should." (p. 143) Or his kids, who "lodged a formal complaint with their parents about the tension and lack of affection in their household." (p. 145) And his legacy? Upon his death, the University of Toronto thought so highly of his impact and accomplishments that... his position was not filled. There is apparently no geometry-specialist currently on the U of T staff. As the author writes, "mathematical traditions usually do not reside in isolated individuals." Yet, the University of Toronto apparently has plenty of company among the world's academic institutions in choosing "not to invest in the future of classical geometry." (p. 359) Ho-hum.
So, did Coxeter somehow manage to synthesize and frost the Euclidean cake for all time? I wouldn't really know, though I'm told his professional work does indeed form a vital part of contemporary understanding of symmetry with practical implications for contemporary research ranging from string theory to data mining. All I can say is that if in fact Coxeter wrote the book on classical geometry, and if that's what you're interested in, then pick up one of those books instead of this pointless biography.
Read
November 11, 2013Very disappointed! Picked this up on a whim during a library trip. I adored Simon Singh's book, "Fermat's Enigma", and expected this to be similar.
However, the writing was poor -- it read more like a long college term paper than a real book -- and there was no central story to build this book around. I read 30 pages of disorganized mathematical anecdotes and promptly gave up.
Additionally (and frankly), Roberts does not have the professional knowledge to evaluate the source material. She's a journalist (and maybe a very good one, I have no idea either way), and thus is limited to reporting speculative connections as fact and resorting to hero-worship of Coxeter.
Consider "Fermat's Enigma" for comparison. Singh has a PhD in particle physics from Cambridge. While his formal training does have substantial differences from pure number theory, he understands the ideas behind Fermat's Last Theorem very well and can express them in a way that non-professionals can understand. He can sift through the junk to find the gold. Roberts simply cannot. Again, I don't mean to insult her, but this topic does not suit her!
However, the writing was poor -- it read more like a long college term paper than a real book -- and there was no central story to build this book around. I read 30 pages of disorganized mathematical anecdotes and promptly gave up.
Additionally (and frankly), Roberts does not have the professional knowledge to evaluate the source material. She's a journalist (and maybe a very good one, I have no idea either way), and thus is limited to reporting speculative connections as fact and resorting to hero-worship of Coxeter.
Consider "Fermat's Enigma" for comparison. Singh has a PhD in particle physics from Cambridge. While his formal training does have substantial differences from pure number theory, he understands the ideas behind Fermat's Last Theorem very well and can express them in a way that non-professionals can understand. He can sift through the junk to find the gold. Roberts simply cannot. Again, I don't mean to insult her, but this topic does not suit her!
May 12, 2010
Siobhan Roberts writes an arresting biography of a key 20th century mathematician. In most authors hands it would have been a dull read, but she enhances the biography with the whole drama of geometry being neglected by contemporary mathematicians (it still is), and tells a wonderful anecdote of accompanying Coxeter on his last public talk. As a fan of polyhedra and symmetry, Coxeter is an important figure to me, and I'm grateful he got the biography he deserved. A documentary is about to be released, and Siobhan is next writing a bio of John Conway, possibly the most brilliant and accessible mathematician of our day and the mathematician who most inspires me.
July 28, 2025
This was a very detailed biography of Donald Coxeter. From the book jacket, we learn the author, Siobhan Roberts, is writing this as her first book. And sadly, that is evident.
The book begins very early in Donald's life. We learn of Donald's skill at music and mathematics. We also learn that his musical skill was quickly recognized as good but almost certainly never achieving levels of greatness.
We do see Donald's obsession and passion for geometry in all that he did. We also see his family effectively integrated into the story of his life. Sometimes biographies can rely too heavily on other people, but we get a good, cursory introduction to those figures and how they affected Donald's life.
The mention of Donald and all the mirrored viewing mechanisms he created were fascinating. It gave him a human, quirky personality that allows the reader to recognize Donald's eccentricities.
We also get to see Donald begin to explore the dating scene. Well, that is just covered at a very rudimentary level, but I expect this is ideal because he was not as obsessed or consumed with human interaction as he was with his geometric exploration. Also, some very rudementary presentation and analysis of his work is covered. This is at a very good level because anything beyond that low level would be beyond the scope of the book and the interest of the reader.
We do see some of the projects that Donald worked on and the people that Donald worked with. This is interesting and covered at a reasonable depth as well.
The book does mentions new math repeatedly. It clearly depicts the minimization of geometry in the teaching of this new math--very effective in the context of the book. This does show how negative that particular aspect of new math was.
The book wraps up with the end of Donald's life. And somehow, these final two chapters of the book flow better. Perhaps it was the awareness that the struggle (both Donald's struggle with life and my struggle to get to the end of the book) were coming to a close.
In short, this is not a pleasant read. As for specifics, I can only suggest the book is arranged chronologically, but there is no theme that connects one scene to the next. Furthermore, the writing style is very plain. Thankfully, it is not bad writing, but there's nothing captivating or even interesting about it. Ultimately, I would be hard pressed to recommend this book to anyone.
The book begins very early in Donald's life. We learn of Donald's skill at music and mathematics. We also learn that his musical skill was quickly recognized as good but almost certainly never achieving levels of greatness.
We do see Donald's obsession and passion for geometry in all that he did. We also see his family effectively integrated into the story of his life. Sometimes biographies can rely too heavily on other people, but we get a good, cursory introduction to those figures and how they affected Donald's life.
The mention of Donald and all the mirrored viewing mechanisms he created were fascinating. It gave him a human, quirky personality that allows the reader to recognize Donald's eccentricities.
We also get to see Donald begin to explore the dating scene. Well, that is just covered at a very rudimentary level, but I expect this is ideal because he was not as obsessed or consumed with human interaction as he was with his geometric exploration. Also, some very rudementary presentation and analysis of his work is covered. This is at a very good level because anything beyond that low level would be beyond the scope of the book and the interest of the reader.
We do see some of the projects that Donald worked on and the people that Donald worked with. This is interesting and covered at a reasonable depth as well.
The book does mentions new math repeatedly. It clearly depicts the minimization of geometry in the teaching of this new math--very effective in the context of the book. This does show how negative that particular aspect of new math was.
The book wraps up with the end of Donald's life. And somehow, these final two chapters of the book flow better. Perhaps it was the awareness that the struggle (both Donald's struggle with life and my struggle to get to the end of the book) were coming to a close.
In short, this is not a pleasant read. As for specifics, I can only suggest the book is arranged chronologically, but there is no theme that connects one scene to the next. Furthermore, the writing style is very plain. Thankfully, it is not bad writing, but there's nothing captivating or even interesting about it. Ultimately, I would be hard pressed to recommend this book to anyone.
March 3, 2012
This book tells the story of an important but largely unknown mathematician. Roberts is a fine writer, and I enjoyed reading her stories about Coxeter: his history, his work, the people he influenced. There's not much technical information here (at least not in any depth), but there is a great deal about the history of geometry, particularly in the 20th century. It's a fascinating subject, and I was encouraged to look for more of Coxeter's writings (I had already read a couple of his books and found them challenging but inspiring).
I would have given this book a higher rating but for one major annoyance: Roberts' use of foot- and endnotes. There are over 70 pp. of endnotes, many footnotes, and 8 appendices. I think this abundance speaks to some trouble she had in organizing her material. Many of the endnotes (probably a majority) are citations of source, but some are substantial expositions that perhaps would have worked better as either footnotes, or should have been incorporated into the main text. As it stands, reading the book was often an annoying exercise of flipping back and forth between the text and the notes at the end, sometimes losing track of what was going on in the main story because of the length of the expository note.
I'll admit that this entire subject of how to organize foot- and endnotes is a pet peeve of mine. My own preference is that endnotes should be reserved for source citations only, and that footnotes should be limited as much as possible in both number and length. But clearly many authors (or editors) don't feel this way, so my peeve will continue to get its exercise.
I would have given this book a higher rating but for one major annoyance: Roberts' use of foot- and endnotes. There are over 70 pp. of endnotes, many footnotes, and 8 appendices. I think this abundance speaks to some trouble she had in organizing her material. Many of the endnotes (probably a majority) are citations of source, but some are substantial expositions that perhaps would have worked better as either footnotes, or should have been incorporated into the main text. As it stands, reading the book was often an annoying exercise of flipping back and forth between the text and the notes at the end, sometimes losing track of what was going on in the main story because of the length of the expository note.
I'll admit that this entire subject of how to organize foot- and endnotes is a pet peeve of mine. My own preference is that endnotes should be reserved for source citations only, and that footnotes should be limited as much as possible in both number and length. But clearly many authors (or editors) don't feel this way, so my peeve will continue to get its exercise.
January 12, 2012
Probabilmente il nome di H.S.M.Coxeter non dice molto alla maggior parte delle persone, ma confido che tra i miei lettori la percentuale salga, non foss'altro che per tutte le citazioni ai suoi lavori fatte da Martin Gardner. Questa è la sua biografia, che percorre tutti i novantacinque anni di vita dell'uomo che da solo mantenne viva la fiammella della geometria classica nel corso del XX secolo. Avviso subito che il testo non è affatto pensato per un matematico, ma piuttosto per una persona che vede i matematici come una strana genìa, buona soamente per ricavarci su usa serie di gustosi aneddoti, di cui in effetti il libro è infarcito. Il risultato finale, almeno dal mio punto di vista, è piuttosto deludente, anche perché il testo divaga qua e là senza riuscire a seguire un percorso continuo - non che Coxeter abbia avuto chissà quale vita turbolenta, essendo rimasto per piu di sessant'anni a Toronto - e non fa capire la sua importanza nel panorama mondiale; insomma, la Roberts ha perso un'occasione. La traduzione è scorrevole, anche se a pagina 277 il cerchio di cui si parla è "dei" (non "a") nove punti: ma è anche vero che non fa parte del curriculum di geometria che ti insegnano a scuola o all'università.
Currently reading
September 17, 2007The topic is interesting. I am still slogging through this book. Not an easy read.
June 18, 2017
methodical
dnf
February 8, 2018Coxeter's book had a big impact on my understanding of polyhedra and polytopes, but this bio wasn't quite enough to hold my interest.
January 13, 2025
Singularly boring.
August 7, 2018
Behold a Fearless Symetry
An enjoyable biography of one of the 20th century's great mathematicians. It shines is in its description of Coxeter's interaction and influence with other luminaries including Veblen, Wittgenstein, Lefshetz, Conway, Escher, Bourbaki (the author holds back for a while, playing into the deception that Bourbaki is a group, not an individual), Buckminister Fuller, Hofstatder and others. The time at Princeton has its moments but at best Coxeter was at Fine Hall at the same time as Einstein and Von Neuman, but that's about it.
The book does drag when it delves into his marriage to Rien Brouwer and his politics. Coxeter was a pacifist but an armchair one. His most dramatic act was to walk out on a talk at Hart House by George H. Bush along with about half the faculty. It picks up again when discussing the relevance and importance of his work to such diverse areas as logistics, immunology and molecular structures, telecommunications, string theory and ultimately the shape of the universe. Geometry is incredibly important to physics as parallel to every symmetry that you find in n-dimensions there is believed to be a corresponding conservation law. They become one and the same.
As I grew up in Toronto and was a student who took several courses in the Math department at UofT I found it interesting how Coxeter had in various ways indirectly affected my own life. As a teenager I spent many happy hours figuring out magic squares and other puzzles in his edited version of H. Rousse Ball's The Moscow Puzzles: 359 Mathematical Recreations). I still have my copy of Father Magnus Wenninger's Polyhedron Models which I used to create numerous stellated polyhedra and hang them in my room and give them as gifts. Father Wenninger corresponded with Coxeter and is mentioned in the book, however you need to delve into the End Notes to get more of the details. Coxeter had already retired when I entered the University of Toronto. Apparently he was glad that the department had hived off Computer Science. I wound up with a minor in Applied Math where it w not required to take a computer course, though I did learn SPSS in order to chug out statistics and that proved to be fairly useful.
There's some good understandable coverage of some mathematical concepts such as Coxeter numbers and diagrams. Siobhan Roberts communicates the sense that Coxeter kept the field of geometry alive, but the lack of successors is troubling.
Coxeter's life message would be about the importance of diagrams and visual geometry as a foundation of Western intellectual thought. He apparently disliked computers and never learned how to use one though there is one short excerpt that says that he set a problem for his calculator - either it was a TI programmable, or he did a combinatorial calculation and had a great deal of faith that it hadn't died on him as it worked out the answer overnight. What I find paradoxical about this is that towards the end of his life (and he was quite active) some of the most interesting descriptive work in geometry was in computer generated graphics for GIS, Engineering and Film.
In classic tradition the Quadrivium - Arithmetic, Geometry, Astronomy and Music along with the Trivium - Grammar, Logic and Rhetoric, formed the basis for a liberal education. As the book notes, we've somehow lost the idea that Mathematical Thinking is part of that. Looking over my eldest's options for electives in University I was appalled to find that other than an Astronomy course there wasn't a single course in Math or Science offered. More Coxeter, please.
An enjoyable biography of one of the 20th century's great mathematicians. It shines is in its description of Coxeter's interaction and influence with other luminaries including Veblen, Wittgenstein, Lefshetz, Conway, Escher, Bourbaki (the author holds back for a while, playing into the deception that Bourbaki is a group, not an individual), Buckminister Fuller, Hofstatder and others. The time at Princeton has its moments but at best Coxeter was at Fine Hall at the same time as Einstein and Von Neuman, but that's about it.
The book does drag when it delves into his marriage to Rien Brouwer and his politics. Coxeter was a pacifist but an armchair one. His most dramatic act was to walk out on a talk at Hart House by George H. Bush along with about half the faculty. It picks up again when discussing the relevance and importance of his work to such diverse areas as logistics, immunology and molecular structures, telecommunications, string theory and ultimately the shape of the universe. Geometry is incredibly important to physics as parallel to every symmetry that you find in n-dimensions there is believed to be a corresponding conservation law. They become one and the same.
As I grew up in Toronto and was a student who took several courses in the Math department at UofT I found it interesting how Coxeter had in various ways indirectly affected my own life. As a teenager I spent many happy hours figuring out magic squares and other puzzles in his edited version of H. Rousse Ball's The Moscow Puzzles: 359 Mathematical Recreations). I still have my copy of Father Magnus Wenninger's Polyhedron Models which I used to create numerous stellated polyhedra and hang them in my room and give them as gifts. Father Wenninger corresponded with Coxeter and is mentioned in the book, however you need to delve into the End Notes to get more of the details. Coxeter had already retired when I entered the University of Toronto. Apparently he was glad that the department had hived off Computer Science. I wound up with a minor in Applied Math where it w not required to take a computer course, though I did learn SPSS in order to chug out statistics and that proved to be fairly useful.
There's some good understandable coverage of some mathematical concepts such as Coxeter numbers and diagrams. Siobhan Roberts communicates the sense that Coxeter kept the field of geometry alive, but the lack of successors is troubling.
Coxeter's life message would be about the importance of diagrams and visual geometry as a foundation of Western intellectual thought. He apparently disliked computers and never learned how to use one though there is one short excerpt that says that he set a problem for his calculator - either it was a TI programmable, or he did a combinatorial calculation and had a great deal of faith that it hadn't died on him as it worked out the answer overnight. What I find paradoxical about this is that towards the end of his life (and he was quite active) some of the most interesting descriptive work in geometry was in computer generated graphics for GIS, Engineering and Film.
In classic tradition the Quadrivium - Arithmetic, Geometry, Astronomy and Music along with the Trivium - Grammar, Logic and Rhetoric, formed the basis for a liberal education. As the book notes, we've somehow lost the idea that Mathematical Thinking is part of that. Looking over my eldest's options for electives in University I was appalled to find that other than an Astronomy course there wasn't a single course in Math or Science offered. More Coxeter, please.
June 4, 2021
A wonderful book. A biography more than a mathematical text, but if you have problems following the axiomatic structure of math books, the Bourbaki, which had a noted quote "Death to triangles", is part of the main reason why. Coxeter, and a few other visual thinkers, resisted this.
Siobhan Roberts has produced a very nice book which introduces what the French academy did to try to bring more respect to math. I have Marvin Marcus to thank for introducing the topic to me 3 decades earlier, so I had some preparation for reading King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry.
Geometry has a consider influence beyond Euclid and his axioms. And relativity theory and computer graphics show geometry isn't dead yet.
Roberts has also produced a 2nd enjoyable book about John Horton Conway: Genius At Play: The Curious Mind of John Horton Conway which I also recommend, which a Scientific American column on Mathematical Recreation introduced a cellular automata Game of Life which was very popular with some computists.
Siobhan Roberts has produced a very nice book which introduces what the French academy did to try to bring more respect to math. I have Marvin Marcus to thank for introducing the topic to me 3 decades earlier, so I had some preparation for reading King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry.
Geometry has a consider influence beyond Euclid and his axioms. And relativity theory and computer graphics show geometry isn't dead yet.
Roberts has also produced a 2nd enjoyable book about John Horton Conway: Genius At Play: The Curious Mind of John Horton Conway which I also recommend, which a Scientific American column on Mathematical Recreation introduced a cellular automata Game of Life which was very popular with some computists.
February 10, 2020
A challenging read if you are an outsider. Glad to have seen it through and left with thoughts about the geometry of intuition and vice versa
This entire review has been hidden because of spoilers.
May 29, 2025
ignited an interest in geometry
June 22, 2010
A great biography with enough technical overview on geometry to whet your whistle. It's not a sensational airport-bookstore sort of biography, which I guess at least one reviewer here prefers, but I found it engaging, enlightening and a joy to read. It spawned many side trips to Wikipedia for further exploration, and I checked out a copy of one of Coxeter's books to see how different classical geometry is from the analytical geometry I took in 8th grade.
February 5, 2009
I really enjoyed reading this. It wasn't an addictive read, but it did confuse me enough to make me think I liked math.
Coxeter did fascinating work with geometric shapes in multiple dimensions, including more than 3 dimensions. He divised a device with mirrors to replicate what it would be like to see in 4 dimensions.
Coxeter did fascinating work with geometric shapes in multiple dimensions, including more than 3 dimensions. He divised a device with mirrors to replicate what it would be like to see in 4 dimensions.
July 9, 2013
"Then again, as is said of pure mathematics, if it is beautiful and elegant, if it is good and profound, there is always the latent promise that it will open something up. Eventually, almost inevitably -- often inadvertently and unbeknownst to its inventor -- a beautiful piece of pure mathematics will fall into the pattern of crystallizing with an application in science."
December 26, 2011
This was a thoroughly enjoyable book about a subject that could have been very, very dry. Ms.Roberts is one to keep an eye out for, as she makes the people and the subject matter come alive. She helps us see the playfulness inherent in mathematics.
April 21, 2016
This is the first of my trio of books related to mathematical visualization.
Donald Coxeter kept alive the study of geometry, during a roughly fifty year period in the last century in which the dominant approaches to mathematics excluded the visual in favor of the algebraic.
Donald Coxeter kept alive the study of geometry, during a roughly fifty year period in the last century in which the dominant approaches to mathematics excluded the visual in favor of the algebraic.
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June 9, 2010This book is an absolute gem and should be on every science- and math-lover's bookshelf.
March 7, 2011
Biography of famous geometer H.S.M. Coxeter
August 10, 2015
Best biography of a geometer you will ever read.
January 28, 2017
"The man who saved geometry" - Well written book, but hard to stay super motivated to read it. I'm glad I did, though.
#bookclub
#bookclub
January 9, 2020
A promenade through the life of a man who loved and gave love to geometry.
Great set of references and a nice read.
Great set of references and a nice read.
Read
August 19, 2017Tema interessante (per chi è appassionato di matematica ovviamente) soprattutto perchè mostra quello che all'università viene ignorato: le vite degli uomini dietro le grandi scoperte matematiche.
Tuttavia, diversamente da altri libri sul genere, Aczel e De Sautoy su tutti, la narrazione non è molto accattivante e la semplice biografia non giustifica, per me, per ora, il proseguimento della lettura
Tuttavia, diversamente da altri libri sul genere, Aczel e De Sautoy su tutti, la narrazione non è molto accattivante e la semplice biografia non giustifica, per me, per ora, il proseguimento della lettura
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