> Something that I think anyone can take away from this lecture is a story of discovering new mathematical relationships. He starts with a function that correlates to a logical problem, changes the inputs in an new (strange) way, then studies the output to form a theory that connects to the original problem.

This type of mathematical exploration seems to be the story of his life. See Quarter-imaginary base for him doing the same thing in high school.

https://en.wikipedia.org/wiki/Quater-imaginary_base