In this follow-up video to his "e to the i pi for dummies" video the Mathologer sets out to properly explain the coolest features of the famous number e and the exponential function e^x. Find out WHY e is irrational, how you go about calculating the first 1,000,000 digits of e, WHY the exponential function e^x is its own derivative, etc.

Here are links to the videos that I refer to in this video:

e to the pi i for dummies:    • e to the pi i for dummies   (this is the video I summarise at the beginning)

Indeterminate: the hidden power of 0 divided by 0:    • Indeterminate: the hidden power of 0 ...   (about derivatives, among other things)

Math in the Simpsons: e to the i pi:    • Math in the Simpsons: e to the i pi   (this is the video that I refer to at the very end)

This week's t-shirt I made myself. Check out this wiki page about this pretty identity https://en.wikipedia.org/wiki/Proof_t...

Thank you very much to my friend Marty Ross for proofwatching drafts of this video and helping me to get the words "just right" and to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.

Enjoy!