Infinite Powers

Calculus sits behind cell phones, TV, GPS and ultrasound, and behind the work that unraveled DNA and located Neptune. Steven Strogatz writes a history of the subject for readers who were put off by it in high school or college.

His argument is that calculus rests on simplicity. It brings in infinity, a number that is not real, to handle problems from the real world. Each hard problem is split into easier pieces, and the answers to those pieces are reassembled into a solution.

The account starts with the first glimmers of the idea in ancient Greece and runs up to the discovery of gravitational waves, a phenomenon calculus predicted. Along the way it shows how the mathematics met the demands of each era, and how its inventors were drawn in by it.

The questions it tackles are concrete ones. One is finding the area of a circle with only sand and a stick. Another is why Mars seems to move backwards at times. Others cover how magnets generate electricity and how a rocket avoids missing the moon. The final example is the fight against AIDS.

It is popular history of mathematics, written in a plain, down-to-earth voice for general readers. It shows what the language behind all of these discoveries looks like when its principles are laid out.