The Joy Of X: A Guided Tour of Math, from One to Infinity

by Steven H. Strogatz

Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan—and so are its textbooks.

Roughly speaking, the derivative tells you how fast something is changing; the integral tells you how much it’s accumulating.

Change is most sluggish at the extremes precisely because the derivative is zero there. Things stand still, momentarily. This zero-derivative property

If 1 were allowed in, it would mess up a theorem that we’d like to be true. In other words, we’ve rigged the definition of prime numbers to give us the theorem we want.