“By now the reader is certainly convinced that group theory shows up in diverse situations. But it would be a great disservice to the history of mathematics if I did not mention one more application, the very reason that group theory was invented! In the nineteenth century, two young mathematical prodigies, Neils Abel and Evariste Galois, solved a mathematical problem that had stood unsolved for centuries. It has come to be called 'the unsolvability of the quintic.' It is one of the great discoveries in mathematics, and when you come to Chapter 10 of this book, you will be ready to read about it in some detail. It rests on the fact that the solutions to polynomial equations have a certain relationship to one another. They form a group.”