The Equation That Couldn't Be Solved

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The Equation That Couldn't Be Solved

How Mathematical Genius Discovered the Language of Symmetry

Mario Livio, Tom Parks


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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.


Mario Livio:
Dr. Mario Livio is an internationally known astrophysicist, a bestselling author, and a popular speaker.

He is a Fellow of the American Association for the Advancement of Science, who worked for 24 years with the Hubble Space Telescope.

He has published more than 400 scientific papers on topics ranging from Dark Energy and cosmology to black holes and extrasolar planets.

Dr. Livio is also the author of six popular science books, including The Golden Ratio (an International Bestseller for which he received the Peano Prize and the International Pythagoras Prize) and Is God a Mathematician? (which was the basis for the 2016 Emmy-nominated TV NOVA program The Great Math Mystery).

Livio's book Brilliant Blunders was a national bestseller in the U.S., and was selected by The Washington Post as one of the "Best Books of the Year.”

The paperback edition of his new book, Why?: What Makes Us Curious, appeared on May 22, 2018.