Five Constants

In 1748, Leonhard Euler discovered Euler’s formula in his Introctio in analysis infinitorum:

eix = cos x + i sin x

Substituting x = π into the equation gives Euler’s identity — the most beautiful equation in mathematics.

e + 1 = 0

The name Five constants comes from the five fundamental constants in mathematics: e, the base of the natural logarithms; i, the square root of –1; π, the ratio of the circumference of a circle to its diameter; 1, the identity for multiplication; and 0, the identity for addition.

Five different constants, with different origins, each ubiquitous in its own field, addressing completely different problems. And yet, all come together as a whole to form something beautiful. In Einstein’s words — “Beauty is the radiance of truth.” Euler’s equation reaches down to the very essence of truth and presents it beautifully. It brings together five ideas from different domains, reminding us once again that the whole is greater than the sum of its parts.