I'm trying to generate an intuitive notion for eulers number and why it's important.
I understand it's definition as a limit, it's relation to the trigonometric functions and that the derivative of $e^x$ is $e^x$, but i feel there's some conceptual insight im absolutely missing that has to explain why it's everywhere in such a seemingly random way.
Can anyone explain me in an intuitive way why the number shows up so much?, preferably not using heavy math notation (if possible), i'm just trying to grasp the very high level concept.
Read this https://www.quora.com/What-is-math-pi-math
If you are in calculus
$e^x$ is the solution to this equation $y'=y$
And if that makes sense to you, then you will realize how powerful it is.
It also connects to the trigonometric functions in the complex plane. That it
$e^{i\theta} = \cos\theta + i \sin\theta$ which is also some pretty handy stuff.