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

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

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

4.85 56,993 ratings · 5,375 reviews
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Overview: 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.

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Published 2005
ISBN 233873
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Mario Livio
About the Author
Mario Livio
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Mario Livio is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Mario Livio enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Karen Allen
Karen Allen July 07, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Nicholas Jackson
Nicholas Jackson January 19, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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James Carter October 19, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Betty Smith
Betty Smith December 17, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Rebecca Williams
Rebecca Williams August 22, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Patricia Wright
Patricia Wright August 13, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Carol Sanchez December 11, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Deborah Hill
Deborah Hill December 09, 2025
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Stephanie Garcia July 25, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Charles Robinson September 05, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Jacob Gonzalez February 26, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Andrew Lopez July 03, 2025
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Carol Mitchell February 19, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Patricia Lewis December 28, 2024
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Christopher Nguyen July 07, 2025
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Joshua Davis November 19, 2025
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Steven Evans November 23, 2024
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Joseph  Davis
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Donna Lewis
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Paul Clark February 23, 2025
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Susan Gonzalez
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Michelle Hall February 24, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Patricia Wright March 06, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Rebecca Rodriguez
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Cynthia Gomez
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Donna Garcia
Donna Garcia December 19, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Betty Johnson
Betty Johnson January 22, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Eric Taylor
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Stephanie Reyes
Stephanie Reyes August 03, 2025
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Joshua Collins
Joshua Collins March 02, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Thomas Collins
Thomas Collins March 07, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Thomas Scott
Thomas Scott March 10, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Joshua Brown
Joshua Brown March 17, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Gary White
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Laura Robinson
Laura Robinson October 18, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Ashley Gonzalez
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Kimberly Lee
Kimberly Lee December 09, 2025
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Sarah Flores
Sarah Flores June 19, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Michael Mitchell
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Donna Reyes
Donna Reyes November 02, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Paul Garcia
Paul Garcia April 11, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Gary Harris
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Lisa Torres
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Jennifer  Davis
Jennifer Davis May 12, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Thomas Mitchell
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Robert Johnson
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Nancy Rivera
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Andrew Lopez
Andrew Lopez July 30, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Laura Lee
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Daniel Thompson
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Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Donna Martinez
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Robert Nelson
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Kevin Diaz
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Joshua Nelson
Joshua Nelson February 08, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Michael Nelson
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Edward Nelson
Edward Nelson June 03, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
James Jones
James Jones June 29, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Michelle Edwards
Michelle Edwards April 06, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Mary King
Mary King December 01, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Kevin Robinson
Kevin Robinson September 27, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Gary Mitchell
Gary Mitchell March 10, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Anthony Clark
Anthony Clark September 15, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Susan Flores
Susan Flores November 26, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Laura Ramirez
Laura Ramirez February 21, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Brian Collins
Brian Collins June 02, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Margaret Lee
Margaret Lee January 14, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Kimberly Garcia
Kimberly Garcia October 10, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Gary Campbell
Gary Campbell November 10, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Kimberly Phillips
Kimberly Phillips September 14, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Charles Robinson
Charles Robinson October 10, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Barbara Phillips
Barbara Phillips May 23, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Kenneth Williams
Kenneth Williams July 06, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Michelle Diaz
Michelle Diaz February 11, 2025
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Edward Sanchez
Edward Sanchez January 30, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Linda Phillips
Linda Phillips November 06, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
George Gonzalez
George Gonzalez December 15, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Carol Mitchell
Carol Mitchell March 27, 2025
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Nancy Cruz
Nancy Cruz February 16, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Robert Young
Robert Young April 30, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Linda Taylor
Linda Taylor May 13, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Emily Martin
Emily Martin April 13, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Brian Lopez
Brian Lopez September 09, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Nancy Evans
Nancy Evans January 02, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Jacob Adams
Jacob Adams June 17, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Jennifer Young
Jennifer Young October 12, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
George Nelson
George Nelson April 07, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Amanda Thomas
Amanda Thomas July 12, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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