The special case of the formula with gives the beautiful identity

(3)

an equation connecting the fundamental numbers i, pi, e, 1, and 0 (zero),
the fundamental operations , ,
and exponentiation, the most important relation , and nothing else. Gauss is reported to have commented that
if this formula was not immediately obvious, the reader would never be a first-class
mathematician (Derbyshire 2004, p. 202).

The Euler formula can be demonstrated using a series expansion

(4)

(5)

(6)

It can also be demonstrated using a complex integral.
Let

(7)

(8)

(9)

(10)

(11)

(12)

so

(13)

(14)

A mathematical joke asks, "How many mathematicians does it take to change a light bulb?" and answers "" (which, of course, equals 1).