Why Beauty Is Truth: The History of Symmetry

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Why Beauty Is Truth: The History of Symmetry

3.64 of 5 stars 3.64 · rating details · 246 ratings · 38 reviews

Hidden in the heart of the theory of relativity, quantum mechanics, string theory, and modern cosmology lies one idea: symmetry. Symmetry has been a key concept for artists, architects, and musicians for centuries, but as a mathematical principle it remained, until very recently, an arcane pursuit. In the twentieth century, however, symmetry emerged as central to the most...more

Paperback, 304 pages

Published April 29th 2008 by Basic Books (first published 2007)

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Jan 16, 2011 Cheryl in CC NV rated it 2 of 5 stars · review of another edition

The author messed up. He frets aloud about giving us lay-readers too much math, and still apparently didn't get a layperson to edit it for him. He avoids giving us equations, choosing instead to explain mathematical ideas in words - but the words are jargon. He explains what a square root is, and then just a few pages later expects us to readily agree that "the cubic x (to the third power) = 15x + 4 has the obvious solution x = 4." It does?? Ok, Stewart, who is your audience? I love mathematical...more

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Sep 13, 2010 Dav rated it 4 of 5 stars · review of another edition

While I don't feel I can claim anything close to truly grasping the concepts of mathematical symmetry after reading this book, I do feel I now understand the general structure of various forms of mathematics and how the built upon each other in order to reach the point we are at now. Specifically the point wherein the concepts of symmetry and group theory are being exploited by our most advanced scientists to understand our universe at a quantum level. This books starts at the beginning with the...more While I don't feel I can claim anything close to truly grasping the concepts of mathematical symmetry after reading this book, I do feel I now understand the general structure of various forms of mathematics and how the built upon each other in order to reach the point we are at now. Specifically the point wherein the concepts of symmetry and group theory are being exploited by our most advanced scientists to understand our universe at a quantum level. This books starts at the beginning with the first mathematicians and meanders through time following them as they develop from simple geometry to number theory and algebra up into complex numbers, quarternions on to group theory, Lie groups, topology and more.

This is a book for a general audience, so there is plenty of biographical content on the mathematicians which I sometimes found interesting but I often rushed through these sections as I found myself much more interested in trying to understand the math (although I should say that the lives of many famous mathematicians are more interesting that one might suppose). If there is a real shortcoming to this book it is the author's stated goal of including as few diagrams as possible (based on a publishing industry maxim that each diagram in a popular mathematics book decreases sales by a certain amount). I'm a visual person and often wanted to see concepts expressed graphically.

This book has certainly whetted my appetite for a deeper exploration of many of the mathematical concepts it reviewed! While dancing on an art car one night at Burning Man this year (where I spent a week finishing the book) I watched a grid of lasers mounted on our vehicle shine out on the dancing crowd below. The lasers were undergoing a rotational transformation driven by our dancing which sparked nearly an hour of trying to retrace my way through what I had learned in the book. I wasn't able to do it very well, and I'm a bit torn now between rereading it to see if the concepts settle in more firmly the second time or looking into finding individual books on the subjects (hopefully with plenty of diagrams and exercises).(less)

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Oct 09, 2012 Georges rated it 4 of 5 stars · review of another edition

Um livro fantástico sobre alguns conceitos matemáticos que foram a base da física moderna. Inicialmente inventados por loucos matemáticos que não sabiam para o que isso serviria, ou mesmo se algum dia suas invenções serviriam. Algumas partes românticas com matemáticos envolvidos em guerras e revoluções, disputas de amores e morte em duelos. Outras partes com o suspense de será que vai conseguir resolver? O livro tem alguns momentos muito difíceis onde explica as teorias da física quântica, corda...more

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Nov 28, 2008 Shane rated it 4 of 5 stars · review of another edition Recommends it for: Physicists and anyone interested in mathematics.

A very interesting history of the development of group theory and it's relationship to modern physics. This is not a mathematical history, but the story of the lives and ideas of the mathematicians and physicists that developed group theory. Those versed in mathematics might be frustrated by the lack of math, but a book that took the middle way between mathematical rigor and interesting history would have a very small audience.

There are a couple of small errors in the book. Stewart refers to Ei...more

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Jan 24, 2011 Koen Crolla rated it 2 of 5 stars

As advertised, Why Beauty Is Truth is a history of symmetry, briefly covering all of the usual suspects—the Babylonians, Euclid, Omar Khayyám, Cardano, Gauss, Lagrange, Abel, Galois, Lie, &c. up to modern group theory, then backtracking and going over Newton, Maxwell, Einstein, Schrödinger, Heisenberg, Wigner, Witten, &c. stumbling in the general direction of physical symmetries—with the usual variable amount of accuracy.

It also contains a very tiny bit of mathematics, for which Stewart...more As advertised, Why Beauty Is Truth is a history of symmetry, briefly covering all of the usual suspects—the Babylonians, Euclid, Omar Khayyám, Cardano, Gauss, Lagrange, Abel, Galois, Lie, &c. up to modern group theory, then backtracking and going over Newton, Maxwell, Einstein, Schrödinger, Heisenberg, Wigner, Witten, &c. stumbling in the general direction of physical symmetries—with the usual variable amount of accuracy.

It also contains a very tiny bit of mathematics, for which Stewart apologises profusely and continuously; the two pages of his first apology starting by repeating the sentiment that every equation halves the sale of a book and continuing with repeated assurances that the reader will not be expected to understand what such complicated symbols as √ and ² mean or even to look at any of the mathematics and really if you'd rather have a lie-down that's fine too.
Stewart has always been, to some extent, the sort of mathematician who's dreadfully embarrassed to be a mathematician (though to his credit, he does sort of stick up for his field in the closing chapter) and who seems to think that The Public uniformly hates mathematics despite the fact that part of it—the part that's his audience—clearly bought a book about mathematics. His endless apologies for the existence of his chosen field might be merely tedious, but the fact that his attitude also leads him to assume his readers never got past elementary-school mathematics and don't even remember most of that crosses into the offensive. I don't know who Stewart imagines his audience is, but he underestimates it.

The physics it contains is, if anything, worse. While the mathematics is too shallow and fragmentary to be understood by a reader who is not already familiar with them, it is, where it's not too vague to tell, at least broadly correct. Stewart's grasp on physics, though, is far less reliable; knowing that the speed of light in a vacuum is a matter of definition rather than measurement is one thing, but purporting to explain relativity and then not knowing that rotation is not just a matter of perspective or dismissing the luminiferous aether but then discussing the ``fabric of spacetime'' in the exact same terms, for example, is less excusable. Stewart is not a physicist; that does not exonerate him.

As such, it's probably most generous to treat Why Truthy is Beaut not as a work of popular mathematics or (especially) popular physics, but as one of popular history. As a book about history, the mathematics bit of it is basically interchangeable with any of a hundred other books written by mathematicians on the same general subject, and the physics bit is basically interchangeable with any of a hundred other books written by physicists on the same general subject, but if history is what you're after, its innocent inaccuracies, which would be more than acceptable in popular mathematics, destroy it.
In the end, there are many books covering roughly the same ground that are much better all around, including some written by Stewart himself. Why Beauty is Truth is not worth your time.

I'm sure I used to have more patience for Stewart; I don't know what happened.(less)

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Jul 18, 2009 Carl added it · review of another edition

Shelves: nonfiction, nonliterature, science

I have read a lot of science in the past few years but not much math. This humbling reading experience helps me realize just how little I know.

Here's a paragraph (page 168):

The four structures that Killing refers to are the Lie algebras su(n), so(2n), so(2n+1), and sp(2n) corresponding to the families of groups SU(n), SO(2n), SO(2n+1), and SP(2n): the unitary groups, the orthogonal groups in spaces of even dimension, the orthogonal groups in spaces of odd dimension, and the symplectic groups in

...more I have read a lot of science in the past few years but not much math. This humbling reading experience helps me realize just how little I know.

Here's a paragraph (page 168):

The four structures that Killing refers to are the Lie algebras su(n), so(2n), so(2n+1), and sp(2n) corresponding to the families of groups SU(n), SO(2n), SO(2n+1), and SP(2n): the unitary groups, the orthogonal groups in spaces of even dimension, the orthogonal groups in spaces of odd dimension, and the symplectic groups in spaces of even dimension. The symplectic groups are the symmetries of the position-momentum variables introduced by Hamilton in his formulation of mechanics, and the number of dimensions is always even because the variables come in position-momentum pairs. Aside from these four families, Killing claimed that exactly six other simple Lie algebras exist.

Whaaaa?

It is to Stewart's credit that I have a vague idea of what he's talking about, because before I started this book I would have lost him completely after the first "that". Other than my basic knowledge of syntax, which helps me by reinforcing that "Killing" and "Lie" are people and not common English words in this context, the rest of this skitters away from me like the shards of a glass I have dropped on the kitchen floor. I'm not putting that back together in any useful way!

I find it fascinating, though. The story of symmetry -- which just starts to coalesce in my head at around the aforementioned page, halfway through the book -- is in part the story of mathematicians: a collection of stubbornness, self-centeredness, genius, curiosity, focus, sour grapes, and flat-out bad luck.

What do I really understand now that I'm done? Not sure. But I do feel a bit of dawn creeping over the horizon now and then. Proceeding from the pure math section into the theoretical physics chapter didn't really click the symmetry light on as I hoped it would.

Of course, I picked up the book because I was curious about how I could apply its ideas to the study of literature! So far, I'm thinking this was a pipe dream....(less)

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Jul 14, 2008 DAVE ID rated it 4 of 5 stars · review of another edition

A crash course in Mathematical history focusing on symmetry told by a mathematician with an actual sense of humor and an ability to make all the in depth historical tidbits very interesting. A must read for all geeks.

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Dec 06, 2009 Hugh Williams rated it 3 of 5 stars · review of another edition Recommends it for: intellectuals who enjoy the history of math or physics

I would have enjoyed Why Beauty is Truth a lot more if I understood higher mathematics better. Stewart is an excellent writer, but I'm afraid the material is less approachable than he makes it out to be.

On the other hand, the historical side is quite accessible and comprises numerous deftly-told and intriguing stories.

The only criticism I would offer from a content standpoint is his dismissal of anything having to do with the so-called "fine tuning" arguments for the existence of God. More than...more

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Mar 13, 2013 Brett rated it 2 of 5 stars · review of another edition

Shelves: mathematics

This was a frustrating read. Parts in the first half of the book were insightful and very enjoyable. Unfortunately, large portions of the second half were simply beyond my intellectual firepower. The frustrating part was watching Stewart meander off into the postmodern mathematical wonderland of nonsense. Let me provide a paragraph typical of the last 100 pages:

"The exceptional group G2 also makes an appearance in the latest twist to the story, which Witten calls M-theory. The "M," he says, sta...more

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Aug 30, 2010 Deana rated it 3 of 5 stars · review of another edition Recommends it for: Anyone interested in the history of mathematics and physics, without getting tooooo mathy.

Recommended to Deana by: mom!

Shelves: nonfiction, 2010, owned-me

I really enjoyed the first half of this book. Ian Stewart is great at telling entertaining stories and getting me interested in mathematics, even without bringing up explicit equations or going too in depth. He gives the general ideas, just enough so you understand the concept, without going over our heads. And he's good at relating them to real world problems and examples, too.

During the second half of the book, though, the concepts quickly become more and more difficult to understand, even wit...more

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May 05, 2011 Cassandra Silva rated it 4 of 5 stars · review of another edition

Shelves: mathematics

I am trying to work my way through some mathematical studies and thought this would be interesting. It was a nice but also maybe boring? I usually like reading the histories of math and was excited at the onset by the Babylonian character first introduced. But then the author almost seemed to apologize for his style, dismiss the character and hurry off to the next one. He then adopts a style of quickly getting you interested in the character and then dropping them off at the dock before you get...more

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Dec 22, 2010 Elizabeth rated it 2 of 5 stars · review of another edition

While I enjoyed parts of this book, overall I was disappointed. I'm not a mathmatician, but I am well-educated and the jargon (and the formulas without explaining them) used by the author really created a barrier. There were MANY times when I would feel like I was finally getting what the author was writing only to miss out completely on the point due to the jargon used in the conclusion of an anecdote. In addition, the way the author organized his writing is not conducive to understanding, in m...more

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Apr 14, 2009 Russell rated it 5 of 5 stars · review of another edition

Another great maths book for the educated layman by Ian Stewart. It wasn't afraid to show equations - not to teach them to the reader but to get a feeling for how they look and what shape they are.
The last couple of chapters gave an interesting overview of how the physics Superstring theories use the mathematics of symmetry groups in their operation.

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Apr 07, 2011 Bryan Higgs rated it 4 of 5 stars · review of another edition

Shelves: mathematics, history-mathematics

"Why Beauty is Truth: A History of Symmetry" was the first book by Ian Stewart that I had read. I am now a convert. I own several of his books (he has reputedly written more than 50 books -- how does he find time?), and find every one fascinating.

Highly recommended!

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Jan 24, 2011 Greg Mathews rated it 4 of 5 stars · review of another edition

Amazing book! You will understand as much as you understand in math. For the concepts that you do not understand, you will get a rough estimate of what they are talking about. Still if you do not understand much the implications and history is fascinating!!!

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Jun 13, 2012 Hugo Luis rated it 3 of 5 stars · review of another edition

Un libro bonito de leer. La matemática llega a ser compleja y algunas cosas excedieron mi dominio pero, al final, creo que el mensaje me llegó integro. Siempre me ha sorprendido la capacidad del cerebro humano de trascender a las 4 modestas dimensioncitas a las que nos tienen limitados nuestras capacidades sensitivas.

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Apr 10, 2010 Converse rated it 2 of 5 stars · review of another edition

Shelves: mathematics, non-fiction

For symmetry read "invariant." Comprehensible through about the 19th century - more recent developments are not illuminated by Stewart's writing and result is incomprehensible technobabble.

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Jun 28, 2009 Eric rated it 3 of 5 stars · review of another edition

I couldn't follow much of the detail on how group theory gave modern physics a jump start into relativity, but it was an intriguing intellectual history nonetheless...

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Jul 21, 2010 Matthew rated it 4 of 5 stars · review of another edition

Don't let the cover fool you - this is a math book. A general interest math book, but it's a math book all the same.

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Dec 19, 2009 Lisa marked it as to-read · review of another edition

Why Beauty Is Truth: The History of Symmetry by Ian Stewart (2007)

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Sep 13, 2010 BAKU rated it 3 of 5 stars · review of another edition

Only read 3/4ths of this, the history parts, the math parts are still outside what I can understand

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Nov 06, 2010 Sophie rated it 3 of 5 stars · review of another edition

A fascinating look at various mathematicians in their pursuit of mathematical symmetry. Unfortunately for me, it became increasingly technical as the math moved towards quantum physics, and I lost the narrative thread through my own mathematical naiveté. But if you like math and challenges, definitely worth giving it a try!

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Jan 14, 2010 Carmen MC rated it 5 of 5 stars

Shelves: number-theory

"Mathematics and beauty"

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Jan 19, 2010 Jennifer rated it 2 of 5 stars · review of another edition

Shelves: nonfiction

I made it about halfway through-- right up to the diagrams about why you can't solve quintic equations-- when realized that I was more engaged when the author talked about the mathetmaticians' lives than I was about learning their mathematical reasoning behind how the history of symmetry really does equate to beauty. Ah, well, I tried!

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Sep 10, 2008 Jon Larimer rated it 4 of 5 stars · review of another edition

Decent history of mathematics and symmetry. A lot of layman's physics books (Brian Greene, Michio Kaku, etc) don't spend much time explaining the kind of symmetry they're talking about regarding quantum physics, but this book explains it well. I do think it ended too abruptly, not speculating much about the future.

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Oct 28, 2012 bekah rated it 2 of 5 stars · review of another edition

A fascinating concept.
Very well written, as always by Ian Stewart.

I just found this book really difficult to get through, and I'm not sure why.

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Mar 07, 2008 Margaret rated it 3 of 5 stars · review of another edition

I thought this would be an easier read, but it turned out to be a bit over my head. Probably a much better book if you're more into math and physics than I am. If you're looking for an easy read of a science or math book, this isn't it.

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Apr 18, 2012 Piya rated it 4 of 5 stars

Shelves: finished

Good history of the development of group theory and its application, but lacks the clear explanation of group theory itself (even just the basic),

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Jul 23, 2011 Ashley Blacquiere rated it 3 of 5 stars · review of another edition

An interesting survey, but it did not explore the mathematics to the depth that I was hoping.

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Jan 28, 2008 Vanessa rated it 4 of 5 stars · review of another edition Recommends it for: Those interested in math, math history

This is great for someone interested in math and the history of important mathematicians.

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About Ian Stewart

Ian Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

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