Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence.

The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.

Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.

I firmly believe that mathematics does not exist outside of humans. It is something we, as a species, invent.

For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture.

Some of the justifiable critiques has been by - been so successful in telling this story, you know, there's a danger of saying, oh, well, you know, we don't need to worry about this because that's absolutely not the case. What [Hans] Rosling is doing is showing us an overall global trend, which in a sense tells us how bad things were - doesn't mean to say the problems are gone, doesn't mean to say they're any less.

I've never met Hans Rosling, but I just knew him through his many YouTube videos, and they were absolute dynamite.