One of my favorite quotes about mathematics is from John von Neumann:
“In mathematics you don’t understand things. You just get used to them.”
On one level, this runs against everything I believe as a teacher. Mathematics should not be an intimidating collection of inscrutable methods! It should be a timidating collection of scrutable methods! We should accept nothing on authority. Everything in mathematics is there to be understood.
And I do believe that.
But I also know that mathematics is full of startles and shocks. I know that even the simplest objects can bury deep secrets.
Take the number line.
Boring, right? Nothing could be more prosaic.
Well, that’s only because you’ve gotten used to it. To my mind, the number line merits only one possible reaction: