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102nd out of 132 books
—
151 voters
The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
by
Mario Livio (Goodreads Author)
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
August 22nd 2006
by Simon & Schuster
(first published 2005)
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This is a fascinating book on symmetry written by an astro-physicist, Mario Livio. I fell in love with symmetry when I was in graduate school studying chemistry. I loved the concepts of reflection, rotation and inversion on simple molecules and how one could determine energy levels with these operations. As I moved from molecules I started to notice symmetry in Rachel's exquisite homemade quilts, in nature, in Bach's music, in art and architecture. So far this book is not about using symmetry in...more
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
I really liked this book. The historical tidbits were great; learning how self-important Cauchy was was especially fun. Unfortunately, Livio falls into the frequent popular-science trap of presenting horribly contrived analogies for some mathematical or scientific concept. Much worse is his example of the Play-Doh deformation group. It is not clear to me how one would define this in such a way that it is actually a group. For example, he needs to guarantee that no deformation sends two different...more
I mostly enjoyed this book, but like others have said, it's a mixed bag, with the book sort of going all over the place. I liked the digressions into the biographies of Galois and Abel, but by the time the book got to the last chapters, it was just too much of "and here's another example of symmetry!" for two pages, and then "here's another example of symmetry!" for another two pages. That said, I enjoyed large chunks of the book. A bit less breadth and a bit more depth would perhaps have been b...more
Solid if short biography of Galois and some other figures involved in the development of Group Theory. Galois was an interesting dude who makes all mathematicians over the age of 22 jealous for not developing their own field of mathematics by then and then not dying in a duel.
The good news, if you are a general audience, is that the mathematics content is light and easily digestible. The bad news is that if you want something deeper, well, take Group Theory. Livio doesn't go TOO deep into the su...more
The good news, if you are a general audience, is that the mathematics content is light and easily digestible. The bad news is that if you want something deeper, well, take Group Theory. Livio doesn't go TOO deep into the su...more
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
The book gave a good historical overview to group theory and the quintic equation, and that was interesting to me (though I would have liked to see a bit more of the mathematics behind them). I wasn't so enthralled with the application of symmetry to biology and evolutionary traits, as that doesn't really excite me, but I did like the discussions about relativity and theoretical physics. The book has, however, made me want to dig out my old college Abstract Algebra book and see what group-theore...more
I have long been fascinated by the life story of Galois, but I wasn't able to understand group theory, and could not fully appreciate his genius. I chose this book in hopes of solving this problem.
It certainly wasn't bad, but it was written at a lower level than I would have liked. I had to read through explanations of terms and ideas that I was already familiar with, which was frustrating, and while I liked the variety of topics that the book explored, the author often didn't discuss each topic...more
It certainly wasn't bad, but it was written at a lower level than I would have liked. I had to read through explanations of terms and ideas that I was already familiar with, which was frustrating, and while I liked the variety of topics that the book explored, the author often didn't discuss each topic...more
The equation in the title refers to the quintic, a fifth-degree polynomial. Livio traces the history of attempts to solve this equation (and lower-order equations), culminating in Evariste Galois brilliant proof and remarkable life. Galois was an committed Republican in mid-19th century revolutionary Frace and spent time in prison for his political activities. He was killed just months after his 20th birthday, possibly in a duel over a woman.
Livio's unpacking of Galois's life and proofs make fo...more
Livio's unpacking of Galois's life and proofs make fo...more
Livio takes a subject that one would think was exceptionally dull, i.e. Symmetry/Group theory, and brings the historical perspective that makes suitable for those who are not math geeks. He expertly gives the generalities of mathematical theory, so that Laymen can follow along.
I really wish more teachers would assign historical works to help students better understand that while math has generally been advanced one person at a time, that it is not unattainable or even not useful at the higher l...more
I really wish more teachers would assign historical works to help students better understand that while math has generally been advanced one person at a time, that it is not unattainable or even not useful at the higher l...more
The two big ideas in current mathematics, symmetry and group theory, are bound up in this book, with the drama of Abel's classic proof of the insolvability of fifth-order equations. Mixed in are wide-ranging ideas about the aesthetics of symmetry that have little or no relation to the mathematical topics Livio covers so beautifully, but the long detours are made palatable by the wealth of interesting details he summons up. Best, he makes a coherent narrative of the continuum of concepts that hav...more
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.
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.
A nice look into the intriguing world of symmetry and it's application in mathematics. The two "main characters" Galois and Abel are intensely interesting people and the bios of each provide a nice mid-book pause from the rest of the mathematically-based investigation into symmetry and group theory.
Not a deeply mathematical book by any means, but I'm also not a mathematician, so I found this beneficial to my enjoyment.
Not a deeply mathematical book by any means, but I'm also not a mathematician, so I found this beneficial to my enjoyment.
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!
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!
Livio takes us on historical journey in the development of mathematics. Starting with Babylonia and moving gracefully into the Middle Ages of Europe, he traces the lives of characters and the societies as they uncover the hidden treasures and develop the mathematical tools we use today. In the post Napoleon Europe, he takes special care and interest in the child prodigies Abel and Galois. Especially Galois. The heated revolutionary was killed at twenty in a duel but not before he put to paper id...more
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.
The title says it all, and once again Mario Livio manages to take a complicated subject and explain it simply and thoroughly while remaining engaging and entertaining. This is the guy you wanted teaching you in high school science class or first level college math or science classes in college. However, before you dive in, be forewarned: You should be at least a LITTLE conversant in science and math. You don't have to be a physicist to get it (after all, the book is written for the layperson), b...more
symmetry, beauty and an amazing story!!! one of the best books i have ever came across! Have been trying to finish it for years now, but i dont mind taking my time. its worth 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
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.
Wonderful short biographies of the men who mathematics the tool to unlock and describe creation.
Symmetry requires the laws of physics to be what they are.
Symmetry requires the laws of physics to be what they are.
The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio (2005)
Like reading five books , so much information. I keep picturing Galois ( group theory ) as being Elric from Full Metal Alchemist. ( Probably not far off really ) " ANYTHING can be transformed ! "
I enjoyed this book, and the glimpse of how many are involved in discovering a new equation.
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.
Aug 01, 2011
Ed Lavalette
added it
Not as good as the Phi book and much slower read.
Interesting book about mathematics.
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.
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).
Sep 25, 2012
Zed
is currently reading it
I've started this book, and while intrigued, have yet to get to the heart of the story. As one who uses group theory (in the context of vibrational spectroscopy) I have found the broader context most enlightening...but sadly the book requires returning to the library and I am a slow reader.
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Dec 28, 2011 05:37pm