
The Equation That Couldn't Be Solved
How Mathematical Genius Discovered the Language of Symmetry
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Narrated by:
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Tom Parks
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By:
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Mario Livio
About this listen
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 be solved.
For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory.
The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.
©2005 Mario Livio. (P)2017 Brilliance Publishing, Inc., all rights reserved.Listeners also enjoyed...
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Overall
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On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.
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An intriguing and underappreciated bit of history
- By Marino on 09-22-14
By: Amir Alexander
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Love and Math
- The Heart of Hidden Reality
- By: Edward Frenkel
- Narrated by: Mike Lenz
- Length: 10 hrs and 7 mins
- Unabridged
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In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.
By: Edward Frenkel
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The Impossible Man
- Roger Penrose and the Cost of Genius
- By: Patchen Barss
- Narrated by: Jonathan Beville
- Length: 11 hrs and 33 mins
- Unabridged
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When he was six years old, Roger Penrose discovered a sundial in a clearing near his house. Through that machine made of light, shadow, and time, Roger glimpsed a “world behind the world” of transcendently beautiful geometry. It spurred him on a journey to become one of the world’s most influential mathematicians, philosophers, and physicists. Penrose would prove the limitations of general relativity, set a new agenda for theoretical physics, and astound colleagues and admirers with the elegance and beauty of his discoveries.
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Flawed
- By Michael on 01-12-25
By: Patchen Barss
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The Universe Speaks in Numbers
- How Modern Math Reveals Nature's Deepest Secrets
- By: Graham Farmelo
- Narrated by: Hugh Kermode
- Length: 8 hrs and 38 mins
- Unabridged
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One of the great insights of science is that the universe has an underlying order. The supreme goal of physicists is to understand this order through laws that describe the behavior of the most basic particles and the forces between them. For centuries, we have searched for these laws by studying the results of experiments. Since the 1970s, however, experiments at the world's most powerful atom-smashers have offered few new clues. So some of the world's leading physicists have looked to a different source of insight: modern mathematics.
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Great story and narration, but lacks rigor...
- By James S. on 05-31-19
By: Graham Farmelo
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Shape
- The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
- By: Jordan Ellenberg
- Narrated by: Jordan Ellenberg
- Length: 14 hrs and 23 mins
- Unabridged
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If you're like most people, geometry is a dimly remembered exercise you gladly left behind in the dust of ninth grade. It's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face.
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Excellent, but not suited for an audiobook
- By Nemo71 on 06-21-21
By: Jordan Ellenberg
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A History of Pi
- By: Petr Beckmann
- Narrated by: Stephen R. Thorne
- Length: 6 hrs and 42 mins
- Unabridged
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The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress - and also when it did not, because science was being stifled by militarism or religious fanaticism.
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one of the best history books
- By Michael Wharton on 05-19-22
By: Petr Beckmann
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Math Mind
- The Simple Path to Loving Math
- By: Shalinee Sharma
- Narrated by: Shalinee Sharma
- Length: 5 hrs and 36 mins
- Unabridged
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Shalinee Sharma is one of the world’s top experts on math learning, but when she was in school, she sat in the back row, unsure if she could ever master the subject. Many of us buy into the idea that some people are innately good at math and others just won’t ever succeed at it—but it’s not true, and numeracy is as important as literacy when it comes to opening doors in life.
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What a refreshing perspective.
- By shawn wilson on 08-26-24
By: Shalinee Sharma
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The Man from the Future
- The Visionary Life of John von Neumann
- By: Ananyo Bhattacharya
- Narrated by: Nicholas Camm
- Length: 11 hrs and 56 mins
- Unabridged
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The smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Nuclear weapons and self-replicating spacecrafts. All bear the fingerprints of one remarkable, yet largely overlooked, man: John von Neumann.
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Good book, very odd narration
- By Ben Wiener on 04-10-22
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Humble Pi
- When Math Goes Wrong in the Real World
- By: Matt Parker
- Narrated by: Matt Parker
- Length: 9 hrs and 33 mins
- Unabridged
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Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.
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Fascinating & enlightening even for da mathphobic✏️
- By C. White on 01-23-20
By: Matt Parker
What listeners say about The Equation That Couldn't Be Solved
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- david malaguti
- 02-25-23
enjoyable..but all over the place
well worth the listen.A little bit undisciplined, though. The first two chapters are throwaways, imho. But the actual stories of the Italian algebraists, then of Abel and Galois, are compelling.
The last few chapters then wander off a bit..and a bit hard to follow by ear.
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- Dmitry Rubinstein
- 04-15-24
Wonderful book on a variety of topics
Allow me to start by expression frustration with Audible's arbitrary limitation of 50 characters for the review headline. Can't for all that is sacred express my intent in that many characters.
Ok, now to the book. It's a wonderful book, exploring the variety of topics. The 3 main themes of the book are the polynomic equations of a single variable and the history of attempts to solve them, the group theory, and symmetry. Those who are not familiar with these topics at least a superficial familiarity, or are not at least extremely curious about them, are likely not to enjoy the book very much, although it's full of entertaining anecdotes and creative metaphors. They are likely to get bogged down in the mathematical parts. Those who are somewhat familiar will enjoy learning in depth the history of the mathematical and physical ideas they are accustomed to, including the lives of people who gave names to all these tools and ideas. All the people whose names fly around during the calculus and algebra lectures come to life in this book.
That's as far as the content of the book is concerned. I do question the decision to release the book in the audio format, as is. First, it's pretty old - published in 2005, yet the audio version was released in 2018 with seemingly zero alterations. The Large Hadron Collider, launched in 2010, so 8 years before the audio version was published, is mentioned as a planned event. Second, the mathematical bits, when read aloud, are simply unintelligible. I do know some group theory, so I just phased out while the narrator read the various multiplication tables row after row, in a monotonous tone, but for those who are not familiar with these topics - good luck to you, you're going to need it. Clearly, a more imaginative approach to transferring the content into the audio format was called for, but it seems the author was not involved in the process, so it didn't happen. The narrator is doing as good a job as can be done, except mispronouncing some of the names (such as that of Henri Poincaré), but the result is useless. Which is a pity since the story parts are excellent.
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- John Coppolella
- 03-13-19
Enlightening geniuses found here
I am so excited inspired by your book. Thank you for introducing and enlightening me on these wonderful people buried in the sands of time.
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3 people found this helpful
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- Mo Rutherford
- 02-03-21
Does not translate over to audio very well
An excellent book. However this is one that should be red with a pencil paper in hand and therefore does not translate over to audio very well
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2 people found this helpful
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- Anonymous User
- 01-12-23
Riveting
Fascinating stories of some of the greatest minds to have ever lived. The book is written for everyone, not just for those who are mathematically inclined.
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- Michael Hanrahan
- 01-22-20
Historical Perspective Appreciated
I was very enrapt in the history and personal perspective of this book, as well as the detailed explanation of group theory and how it evolved. Thanks for a wonderful 12 hours of listening.
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6 people found this helpful
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- David
- 01-16-19
Sad stories, complex math, good read
I needed to get a copy of the book to see some of the patterns made by tables. but really neat book if you are comfortable with some hard ideas in math.
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4 people found this helpful
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- Michael
- 01-16-20
4/5
I enjoyed most of this, and struggled through some of the technical parts. I liked the stuff about symmetry, and the history. I still don't really understand what group theory actually is. Perhaps that's my fault, not the book's. The narrator was excellent.
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2 people found this helpful
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- JM Calmer
- 05-25-23
Great
This is an interesting historical story. It’s informative and entertaining. This is a book to learn and enjoy
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- James S.
- 10-13-21
One bad chapter, otherwise deeply worthwhile
If you've been searching for a somewhat mathematically rigorous book on the history and science of group theory, this is the best option I've come across so far.
The audible was almost ruined by the verbatim narration of permutation tables during a large part of one chapter. If the narrators of these types of books were to ever be allowed - or motivated - to avoid verbatim narrations like this, for sections that could otherwise be summarily explained in a way that got the point across to the listener, audiobooks could catch on in rigorous science and engineering disciplines.
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1 person found this helpful