Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

For reasons nobody understands, the universe is deeply mathematical.

To put this awesome assertion another way, there seems to be something like a code to the universe, an operating system that animates everything from moment to moment and place to place.

The truly radical and distinctive move of calculus is that it takes this divide-and-conquer strategy to its utmost extreme—all the way out to infinity. Instead of cutting a big problem into a handful of bite-size pieces, it keeps cutting and cutting relentlessly until the problem has been chopped and pulverized into its tiniest conceivable parts, leaving infinitely many of them.

If you rotate a circle about its center, it looks unchanged.

That’s the big idea behind calculus. Everything becomes simpler at infinity.