Journey Through Genius; William Dunham; 1990; Penguin; 300 pgs, index

If you appreciate the beauty of mathematics, but hate the actual math, you might enjoy this book. If not, skip it.

The history of math is the history of science. And vice versa. For centuries, people twiddled about with unmarked straight edges, and compasses (to draw circles). From this, Euclid and others were able to prove what you and I would consider the bleedin' obvious. But it made sense to do it that way. It removed guesswork entirely and turned math into a rigorous philosophy.

It starts with Hippocrates (the other one, not the doctor) and "quadratures". The idea was to take a complex shape and calculate it area by breaking it down into rectangles. This gave rise the "squaring the circle"… creating a square from a circle using a straight edge and compass with the same area as the circle.  As it turned out, it cannot be done.

From there, we pass through Euclid, who have us geometry, Pythagoras and his famous equation, Archimedes and areas, Newton and calculus, Euler, Cantor, Liebnitz, infinite series and other stuff. Along the way, Fermat proposed his much vaunted theorem. When the book was written, it had not been proved, but it has now. Time marches on.  

The math is not hard to follow, and some of the ideas are very deep. Such as an infinity of infinities, each one infinitely larger than the next. They actually do exist.

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