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

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What do the music of J. S. Bach, the basic forces of nature, Rubik's Cube, and the selection of mates have in common? They are all characterized by certain symmetries. Symmetry is the concept that bridges the gap between science and art, between the world of theoretical physics and the everyday world we see around us. Yet the "language" of symmetry--group theory in mathematics--emerged from a most unlikely source: an equation that couldn't be solved. Over the millennia, mathematicians solved progressively more difficult algebraic equations until they came to what is known as the quintic equation. For several centuries it resisted solution, until two mathematical prodigies independently discovered that it could not be solved by the usual methods, thereby opening the door to group theory. These young geniuses, a Norwegian named Niels Henrik Abel and a Frenchman named Evariste Galois, both died tragically. Galois, in fact, spent the night before his fatal duel (at the age of twenty) scribbling another brief summary of his proof, at one point writing in the margin of his notebook "I have no time." The story of the equation that couldn't be solved is a story of brilliant mathematicians and a fascinating account of how mathematics illuminates a wide variety of disciplines. In this lively, engaging book, Mario Livio shows in an easily accessible way how group theory explains the symmetry and order of both the natural and the human-made worlds.

"Essential reading for anyone who wants to understand how the apparently remote concerns of pure mathematics can lead too deep and practical insights into the natural world." --Ian Stewart, author of DOES GOD PLAY DICE?

"A highly readable and illuminating book." --Sir Michael Atiyah, Abel Prize in Mathematics Laureate 2004

About the Author

Mario Livio is a Senior Astronomer and the former Head of the Science Division at the Space Telescope Science Institute (STScI), the institute that conducts the scientific program of the Hubble Space Telescope. He received his Ph.D. in theoretical astrophysics from Tel Aviv University in Israel and was a professor in the Physics Department at the Technion-Israel Institute of Technology from 1981 to 1991, when he joined STScI. Dr. Livio has published more than 400 scientific papers and has received numerous awards for research and for excellence in teaching. He is the author of The Golden Ratio, a highly acclaimed book about mathematics and art for which he received the International Pythagoras Prize and the Peano Prize, and The Accelerating Universe.

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