Math's most beautiful equation

A very clever 18th century guy named Euler discovered an interesting mathematical relation that others have since called the most beautiful equation in mathematics.

The equation says, somewhat less beautiful without superscript:
e^(i𝜋) + 1 = 0 (or e raised to the power of i times 𝜋, plus one equals 0).

To explain the terms:
e is the base of the natural logarithm. By definition, e is the limit (as x approaches infinity) of (1+(1/x))^x. A special property of e is that the value of the function e^x at any point, x, is equal to the slope of the function at that point. People who know maths a lot better than I do can do cool things with this.

i is the imaginary unit, equal to the square root of -1. Neither this number nor any number multiplied by it is in the set of real numbers, but it is very useful nonetheless, especially in electrical engineering where it changes name to j.

𝜋 is a geometric constant, the ratio of a circle's circumference to its diameter. It is an irrational number, inexpressible as a ratio of two integers, and is therefore an unending, non-repeating decimal roughly equal to 3.14. It plays an important role in trigonometry.

The number 1 itself is special, since any other number multiplied or divided by 1 or raised to the power of 1 equals itself. It is the unit of identity for these operations.

The number 0 is also special, in that any number plus or minus 0 equals itself. It is the unit of identity for addition and subtraction. It has other special properties as well: any number raised to the power of 0 equals 1, and any number multiplied by 0 equals 0.

Relating all of these special numbers in one equation, using the operations of addition, multiplication and exponentiation, gives us hope that reality (or our particular way of looking at it) has an elegant simplicity beneath its chaotic surface.

The proof of this relationship is well beyond me, but you can find out more about it by researching “Euler's Identity”.