The simplest explanations I have found for involute gears is from one of those old 50's training films[0]. Not sure if this is the same one, but the first few minutes give a very intuitive explanation of where the involute shape comes from.
This old training video is great too, it also mentions the idea touched upon in the article that gear teeth are levers:
Spinning Levers - How A Transmission Works (1936) https://www.youtube.com/watch?v=JOLtS4VUcvQ
The idea of shining polarized light through gears made of Lucite to view the stress lines at the point of tooth contact is genius!