Demystifying Euler’s number

Euler’s number $e := 2.71828\dots$ has, to me, always been a semi-mysterious number. While I understood many facts about $e$, I never felt I ever truly understood what it really was – it’s core essence so to speak. I believe that part of the reason for my confusion is that $e$ is often taught coming from two seemingly different perspectives: Either it is introduced in the context of compound…