Chapter 8

Our life is frittered away by detail….

Simplify, simplify.

—Henry David Thoreau, Walden (1854)

“Symbolic mathematics” is to numerical mathematics as algebra is to arithmetic: it deals with variables and expressions rather than just numbers. Computers were first developed primarily to solve arithmetic problems: to add up large columns of numbers, to multiply many-digit numbers, to solve systems of linear equations, and to calculate the trajectories of ballistics. Encouraged by success in these areas, people hoped that computers could also be used on more complex problems; to differentiate or integrate a mathematical expression and come up with another expression as the answer, rather than just ...

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