The most beautiful equation in mathematics.

In mathematics, Euler's identity^{[n 1]} (also known as Euler's equation) is the equality

${\displaystyle e^{i\pi }+1=0}$.    

where

e is Euler's number, the base of natural logarithms,

i is the imaginary unit, which by definition satisfies i² = −1, and

π is pi, the ratio of the circumference of a circle to its diameter.

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics.

PROOF:

We know that,

 Therefore,e^i(pi)=cos(pi)+isin(pi)

Implies,e^i(pi)=-1

      Or, e^i(pi)+1=0

                          ( Proved)