Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in complex arithmetic called Euler’s Formula, which the late great physicist Richard Feynman called in his lectures "our jewel" and "the most remarkable formula in mathematics."
In an interview with the BBC, Prof David Percy of the Institute of Mathematics and its Applications said Euler's Identity was “a real classic and you can do no better than that … It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants.”
Euler's Identity is written simply as:
e^iπ + 1 = 0
The five constants are:
The number 0.
The number 1.
The number π, an irrational number (with unending digits) that is the ratio of the circumference of a circle to its diameter. It is approximately 3.14159…
The number e, also an irrational number. It is the base of natural logarithms that arises naturally through study of compound interest and calculus. The number e pervades math, appearing seemingly from nowhere in a vast number of important equations. It is approximately 2.71828….
The number i, defined as the square root of negative one: √(-1). The most fundamental of the imaginary numbers, so called because, in reality, no number can be multiplied by itself to produce a negative number (and, therefore, negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter i is therefore used as a sort of stand-in to mark places where this was done.