Most folks who have been through high school mathematics courses will have taken a class called algebra ' maybe even a sequence of classes called algebra I and algebra II that asked you to solve for x. The word 'algebra' may evoke memories of complicated-looking polynomial equations like ax' + bx + c = 0 or plots of polynomial functions like y = ax' + bx + c. Equations and plots like these are part of algebra, but they're not the whole story. What unifies algebra is the practice of studying things ' like the moves you can make on a Rubik's cube or the numbers on a clock face you use to tell time ' and the way they behave when you put them together in different ways. What happens when you string together the Rubik's cube moves or add up numbers on a clock' The short version of the story is that mathematicians found formulas that looked a lot like the quadratic formula for polynomial equations where the highest power of x was three or four. But they couldn't do it for five. It took...
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