The Equation That Couldn't Be Solved:

Mario Livio, "The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry"
English | 2005-09-13 | ISBN: 0743258207 | 368 pages | EPUB

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."