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

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.

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

Hans Rosling typically would go into the room, and he would ask the audience questions. Often they had to answer them with clickers or raising their hands or something. We get [data] wrong because 50 years ago that wasn't the case and because we haven't had these graphics we don't realize that over the last 30, 40, 50 years things have changed dramatically. And you see how the world has been getting a better, safer, more homogeneous place. It just has.

Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.

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.

Calculus works by making visible the infinitesimally small.