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The Equation That Couldn't Be Solved
Mario Livio
How Mathematical Genius Discovered the Language of Symmetry
Simon and Schuster
September 2005
368 pages ISBN: 0743258207 Hardcover
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Non-Fiction
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.
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