Its a nicely written post, but I think its a bit misleading.
This type of exposition preys on peoples feeling that there must be something deeper going on, but ultimately just kicks a real grasp of math down the road. On the bright side maybe a few more people know of the complex exponential though?
The truth is that there is no royal road. No perfect explanation. Nobody can tell you what a mathematical concept really is. The only surefire route is through experience doing and using math.
If you want to know what these numbers "are"... then simply do more math. I encourage you to squeeze some philosophy in as well. Reading Wittgenstein's lectures on mathematics, after taking my first model theory course, really messed me up for awhile!
Yes, there is no royal road.
But there is a very harsh one. There you ignore that pi is about circles and instead think of it as the period of some solution to a differential equation.
The truth is that there is no royal road. No perfect explanation. Nobody can tell you what a mathematical concept really is. The only surefire route is through experience doing and using math.
If you want to know what these numbers "are"... then simply do more math. I encourage you to squeeze some philosophy in as well. Reading Wittgenstein's lectures on mathematics, after taking my first model theory course, really messed me up for awhile!