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

We mathematicians are used to the fact that our subject is widely misunderstood, perhaps more than any other subject (except perhaps linguistics).

Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience.

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.

In fact, we tend to think things have been getting much worse. In fact, over the last 50 years, almost everything in the world on a global scale has got better. And the way that Hans [ Rosling] did this - it was very good.

I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.

Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.