Euler’s identity

Day 59 / 366

Euler’s identity is known as one of the most beautiful equations in Mathematics. It is named after the mathematician Leonhard Euler who said that the formula is “proof that god exists”.

But what is so special about it?

The equation has 5 constants that come from 5 different areas of mathematics

The first one is e, an irrational number that is the base of natural logarithms. It arises naturally through the study of Compound Interest and calculus.

Next is i, which is an imaginary number used to denote the square root of -1. The concept of imaginary numbers was created because in reality no number can be squared to produce a negative number.

Then we have π (pi), which comes from geometry and is the ratio of the circumference of a circle to its diameter.

We then have the number 1, which was the most basic unit of arithmetics.

And of course, we have 0, invented by Aryabhatta. For us 0 might seem trivial, but it's a relatively new concept in mathematics. It denotes the concept of the absence of any quantity.

So the fact that so many different concepts, invented by different people in different centuries, can come together so elegantly in a formula is astounding.

There is an ongoing debate amongst Mathematicians about whether Maths was invented or discovered. Are these concepts a creation of the human mind, or do they already exist in the universe, waiting to be discovered? I think Euler’s Identity makes a good case for the latter.