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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

3.89  ·  Rating details ·  1,317 ratings  ·  100 reviews
What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't ...more
Paperback, 368 pages
Published September 1st 2006 by Simon Schuster (first published 2005)
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 ·  1,317 ratings  ·  100 reviews

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Jun 15, 2017 rated it really liked it
Shelves: nonfiction
This book brought back some of the more fascinating things I learned in my upper division/graduate classes on group theory. It is approachable, yet I'm sure challenging to those without a mathematics background. I love thinking about the way-too-short lives of those brilliant mathematicians who invented group theory - the political and social environments at the time were rough, and what they accomplished was amazing. And symmetry is applicable to so many areas - it is a fascinating topic.
Jan 10, 2014 rated it really liked it
Shelves: non-fiction
This is a book about a genius. Livio quotes George Bernard Shaw early and appropriately to describe Abel and Galois: “The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.” (3) It is a very, very true statement.

Livio traces the development in mathematics over the broad strokes of history. It is a history of brilliant minds solving progressively more difficult algebraic equatio
Ami Iida
Aug 11, 2015 rated it really liked it
Shelves: math
it is written about symmetry and group theory.
they had made impressive upon the human being from math. .
There are lots of games coming from symmetry.
ex. tetris


15 puzzle

Rubik's Cube
you can play every games coming from symmetry. LOL LOL LOL
Jan 10, 2008 rated it liked it
This was definitely more readable than most of the books about math I have read. There was plenty in it that I didn't understand, but it didn't take away from the point of the book. Any mathematician who gets killed in a duel over a girl at age 20 after spending a year in prison for revolutionary activities is worth reading about...especially if he made a discovery that revolutionized mathematics.
Jan 01, 2020 rated it it was amazing  ·  review of another edition
How fascinating! What an intriguing start to the new year!
Mar 10, 2013 rated it really liked it
Shelves: sciences
This book is a comprehensive introduction to a very hard problem of mathematics : finding the general solution for a general equation, along with the story of two genius Niels Hendrik Abel and especially Evarist Galois. In my opinion, the author has spent much time to collect the documents related to Galois's life, so that he has described Galois's story truthfully in a very scientific way. That makes sense for the other books on Galois or the same topics always tried to describes Galois's story ...more
Mar 12, 2009 rated it really liked it
Shelves: science-math
I have a BA in physics, and even though this book is not a physics book, I learned just how much I didn't learn in my degree and how awful my teachers were. Livio obviously doesn't go into equations and mathematical derivations, but instead explains the reasoning behind them and how different branches of physics are actually connected (something they don't bother teaching you).
Dec 22, 2014 rated it liked it  ·  review of another edition
Shelves: black
This has got to be the geekiest book I've read in a long time. It's all about math, for goodness sake. How do you stay awake through a book on math? Well, the duel, and the murder mystery, and the tragic poverty, and the backstabbing, and the mental illness all helped.

Because it's not really a book about math, it's a book about mathematicians. Very different subject, really. There is the baffling tale, which I'm still not certain if I believe, that in 1500's Venice, mathematicians would face off
Jake Berlin
while this book has much more of a uniting scientific idea than the other livio i read (“brilliant blunders”), it’s actually much more scattered. is it a “big idea” book, or a biography of galois? why are there random throwaway chapters on evolution and music? there are absolutely some interesting ideas here - i would very much like to read a top-notch book about symmetry - but it mostly fails as a work of popular science writing.
Jul 16, 2008 rated it did not like it
Whoever wrote the copy for the jacket of this book should get a raise. The jacket makes you think the book will be really interesting, and instead it's more of a history of how certain mathematical equations finally were solved, the people who solved them, and how symmetry became an important part of mathematics. The first half of the book was VERY slow, and it wasn't until the author started actually talking about the "key" mathematicians and their life stories that it became interesting. Perha ...more
Oct 10, 2011 rated it liked it  ·  review of another edition
This book was a gift and I did not understand what I was about to read when I started it. It was not what I expected - a discussion of symmetry in nature. Instead, it was a history of symmetry, which heavy emphasis on the lives and theories of the mathematicians who perfected the theory. Written for a general audience, I struggled through some of the more challenging parts, but "click" of comprehension occurred when I resumed this book as it began a discussion on super string theory. Having just ...more
Mar 01, 2009 rated it it was ok
This book was a mixed bag.

The history of math parts were really interesting.

The exposition of Galois theory left a lot to be desired. It might be too complex for a lay book, but there's a lot about symmetry and physics that's presented at the level of "trust me, it works this way"!

The evolutionary bio bits were even worse.

I bet Ian Stewart's book on symmetry is better, but I'm all symmetried out for now.
Bryan Higgs
Apr 07, 2011 rated it really liked it
This was the first book I read about symmetry and its related mathematical topic, group theory, and it is excellent.

This book takes the same approach as many other similar books, focusing on the history (tragic in the case of Galois and Abel) and personalities, rather than the details of the mathematics.

This is a delightful read!

Highly recommended!
Ian Durham
Aug 03, 2011 rated it it was amazing
A truly remarkable book. It manages to convey the beauty of the mathematics while simultaneously telling a compelling story. One of the best books I've ever read. Honestly, my words just don't do it justice. I highly, highly recommend this book to anyone even if math isn't necessarily your cup of tea.
Jan 04, 2012 rated it it was ok
Shelves: history-of-math
The author is at pains to avoid actually presenting any of the mathematics. The subject is good. The storytelling is reasonably paced. But Livio just refuses to show us any of the actual subject matter. It is maddening.
Bill H
Dec 27, 2011 rated it really liked it
I really enjoyed reading this -- it's a bit scattershot, but in the way you can have a wide-ranging conversation with some stranger at a party and feel that the evening was well spent.
Charles Pearce
Jul 24, 2012 rated it liked it
Slow and dry at first. But it really picked up. It was a biography of the guy who came up with set theory. Now the physicists use it to explain the natural world.
Feb 22, 2010 rated it it was amazing
I enjoyed this book, and the glimpse of how many are involved in discovering a new equation.
Apr 12, 2013 rated it really liked it
Interesting book about mathematics.
Jeff Clark
Aug 09, 2018 rated it liked it
A slow build up, chapters 1-3. The chapter on Galois’s life, 5, is an excellent pamphlet sized biography of an extraordinary and tragic genius. It is the heart of this book and where the authors passion clearly lies. The chapters that bookend are good, one on Abel, another tragic mathematician and the second on groups (mathematical sense) in general. Chapters 7 & 8 are not in tone or content nearly as good as the 4, 5, & 6. The final chapter is not a fitting coda and attempts to tackle way too m ...more
Aug 20, 2017 rated it really liked it
3.5 stars. The book does a wonderful job in the beginning with the history of group theory and the biographies of its major contributors, but then gets a little bogged down when it attempts to delve into the applications in physics, chemistry, biology, and the social sciences. It can be excused given the high degree of abstraction that group theory quickly moves into, but it does subtract from the enjoyability of the book.
Feb 04, 2019 rated it really liked it
Recommends it for: the mathematically and physics curious
Interesting book, and mini-biographies of the all stars of mathematics over the years.

The subject matter is a bit over my head, but the writing is very good, the explanations understandable at a basic level, and the subjects interesting.

And now I know and have a basic understanding of mathematical symmetry and how it and group theory have been applied to physics to reach the current theories that I have run into periodially.
Jeffy Joseph
Jul 17, 2019 rated it really liked it
Shelves: non-fiction, science, math
It piqued my interest in Group Theory. I have added it to my to-learn list. This book is primarily a history book focusing on the development of group theory. The life story of mathematicians Abel and Galois, the pioneers who contributed to the development of field, forms a major chunk of the book. The unfortunate lives of these geniuses who died young had a cathartic effect on me. Its one of the best books that I read in 2016.
Nov 28, 2016 rated it liked it
Shelves: library, mathematics
I enjoyed this one for the most part, particularly the biographical sections on Abel and Galois. I ended up skimming or skipping sections in the beginning where it went into detail about symmetry, and later about applications of Group Theory to various fields of study. I read this mostly for the biographical sections, which were thorough but brief, due to the early deaths of both Abel and Galois.
Ray Savarda
Jul 23, 2017 rated it really liked it
good but not great.
Sort of light on the mathematics details, but a wide overview of the work on solving equations of various types that led to the discovery of the symmetries that led to the foundation of Group theory.
Good discussions of the trials and contributions of galois, abel and others.

Matthew Graham
Apr 22, 2018 rated it liked it
Good for the history of group theory until the 1960s but then rather rushes through developments since then, hinting at "amazing insights into the structure of finite groups and ... several of the most fascinating objects in the mathematical firmament" but providing no further detail. I would rather have had more on this than who killed Evariste Galois.
Sep 24, 2018 rated it liked it  ·  review of another edition
I enjoyed the first few chapters of this book quite a bit; but in later chapters, when the author began to discuss topics far outside of his realm of expertise, I didn't find the information presented to be credible. Also, I feel that the description of Galois as "romantic," which is repeated many times, is inaccurate.
Jan 26, 2020 rated it really liked it
Some parts were hard to track with, but overall it had a lot of interesting stuff. The tragic mathematicians were interesting. I wonder how many other little known stories like that exist. The stuff on symmetry was pretty cool. I wouldn't mind reading more on that. It's a bit dated now that the LHC has produced results that don't confirm supersymmetry and string theory.
Siddharth Shankar
Apr 19, 2020 rated it it was amazing
The best thing i like about this one is the concept of symmetry and how it was thought by Galois. What a mathematical genius to discover a breakthrough in maths just the night before his death. What a tragic life story. Its both moving and conceptually and information wise brilliant book. With Fermat's last theorem this is one of the best maths book.
It was interesting to be assigned a book for a math class, and this book has some truly fascinating information about math's relationship with other domains such as art, music, biology, etc. But Mario Livio is not a particularly talented writer, which makes this book kind of "meh."
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“The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature's design.” 5 likes
“Through the works of Weinberg, Glashow, and Salam on the electroweak theory and the elegant framework developed by the physicists David Gross, David Politzer, and Frank Wilczek for quantum chromodynamics, the characteristic group of the standard model has been identified with a product of three Lie groups denoted by U(1), SU(2), and SU(3). In some sense, therefore, the road toward the ultimate unification of the forces of nature has to go through the discovery of the most suitable Lie group that contains the product U(1) X SU(2) x SU(3).” 2 likes
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