Understanding Symmetry

I have been reading a book over the past few weeks, whenever time would permit, called 'The Equation That Couldn't Be Solved', by mathematician Mario Livio. So far, I'm about halfway through it, but I thought I'd put up a word here anyway.

This book talks about the mathematical theory of symmetry developed by Niels Henrik Abel and Evariste Galois, two mathematicians separately tackling the solvability of the quintic equation (an algebraic equation in one variable, of degree 5), which mathematicians had struggled with for over 200 years at the time.* It tells the heart-rending tale of their lives (really, mathematicians aren't always a bunch of grey-haired, high-collared, pince-nez-wearing geezers. Both the protagonists of this book are very young, and live intense lives...but I'll let Livio do the telling) and gives, beautifully and accessibly, the concept of group theory.



Returning to the mathematicians' quest...sadly, they discovered not the general solution, but rather proved the lack of one (of course, this was just as exciting), at least one using the common algebraic operations. But then, unexpectedly, Galois came up with something altogether new...a group theory. In it, he used a new concept, that of mathematical symmetry, to determine whether an equation of a given degree was solvable using algebra. While this was a massive achievement in itself (even more for the fact that Galois was barely 20 years old at the time he came up with it), group theory went on to find application in a whole lot more of mathematics. It showed up wherever symmetry played a role...and symmetry is very popular in nature.

I wanted to provide a general idea about the working of group theory, but I think that should wait until I've finished the book...don't want to put some half-baked understanding out here. So I'll edit this entry in a few days, once I'm through.

Meanwhile, if you can, be sure to pick up the book. It's not just for students of mathematics...you don't even need to have done a whole lot of algebra in school. That's one of the great things about the book- without a lot of mathematical jargon or squiggly equations, Livio manages to bring out quite gracefully, one of the most deeply satisfying concepts in mathematics.

Or you can order it here: http://www.amazon.com/Equation-That-Couldnt-Solved-Mathematical/dp/0743258215/ref=pd_bbs_2?ie=UTF8&s=books&qid=1208546525&sr=1-2

Happy reading. Later.