[chobytes]

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!

[constantcrying]

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.