Saturday, July 5, 2008

Group Theory for (non) Mathematicians

Group Theory - the study of symmetry

Have you ever stood at an airport curb wondering what pattern predicted the arrival of your shuttle? Have ever bought a lottery ticket or visited a casino wishing you knew the pattern to predict the winners? Did you know that men and women are attracted to potential mates exhibiting the most symmetry? The same is true for many animals. We seem genetically programmed to find symmetries and patterns whether they exist of not. However is wasn't until the nineteenth century that mathematicians invented the serious study of symmetry - Group Theory.

Now 200 years later two books have been published about this branch of Mathematics that is only studied in college and only be math majors. Symmetry by Marcus du Sautoy (2008) and The Equation That Couldn't Be Solved by Mario Livio (2005) both provide introductions to Group Theory for non-mathematicians.

By introduction, I do not mean primer. After reading either of these books, you'll be no more prepared to do your Group Theory homework problems than before you started. These book are more about the history and philosophy than Group Theory itself. Think about Sex. These books are like biology books, lots of interesting background, but nothing practical enough to let you know what to do in bed.

Symmetry (Marcus du Sautoy) is more like a memoir or journal and gives a fine insight into the mind of a mathematician with a running commentary on Group Theory. However, Mario Livio (The Equation That Couldn't Be Solved) very successfully places Group Theory into an interesting narrative structure focusing on the interesting lives of the various mathematicians who created this important theory.

As a recreational reader, I enjoyed Mario Livio because he spent more time on the lives of Niels Abel and Nicolas Galois, two very troubled young geniuses who suffered for love and died young while still changing the face of mathematics forever. These stories are so compelling that both books spend significant portions on their lives.

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