What's the deal with Euler's identity? Basically, it's an equation about numbers—specifically, those elusive constants π and e. Both are "transcendental" quantities; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it's in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore's law. It's used to model everything that grows.
Enter Leonhard Euler, the one-eyed Swiss genius whom Frederick the Great lovingly called "our Cyclops." What Euler showed, in his 1748 book Introduction to Analysis of the Infinite, is that π and e are deeply related, but in a very weird way. They're connected in a dimension perpendicular to the world of real things—a place measured in units of i, the square root of –1, which of course doesn't … exist. Mathematicians call it an imaginary number.