Euler's identity

"One of the most frequently mentioned equations was Euler's equation, e^{i \pi} + 1 = 0. \,\! Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" The equation contains nine basic concepts of mathematics — once and only once — in a single expression. These are: e (the base of natural logarithms); the exponent operation; π; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero."

"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

"There is a famous formula, perhaps the most compact and famous of all formulas — developed by Euler from a discovery of de Moivre: e^{i \pi} + 1 = 0. \,\! It appeals equally to the mystic, the scientist, the philosopher, the mathematician."

"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."

"For any real number x, Euler’s formula is"

"This most extraordinary equation first emerged in Leonard Euler’s Introductio in 1748."

"Since high school I have been utterly fascinated by the “mystery” of i = \sqrt{-1} and by the beautiful calculations that flow, seemingly without end, from complex numbers and functions of complex variables."

"-1 = e^iπ, proves that Euler was a sly guy."