Imagine, one day, that life shows up on another planet. Moreover, it’s intelligent life. Imagine, too, that we’ve a reasonably swift means of communication. We’d need a common language with which to talk. What might that language be? One candidate would be mathematics. ... It’s not just the universal nature of mathematics that’s striking; it’s that mathematics works at all. The natural world is a complex place. It’s packed with variations and permutations, random events and patterns so complex they are far from obvious to the eye. And yet, mathematics can capture so much of that intricacy.