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.

There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.

A PhD in Mathematics is three years of guessing it wrong, plus one week of getting it right and writing a dissertation.

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.

Sure, some [teachers] could give the standard limit definitions, but they [the students] clearly did not understand the definitions - and it would be a remarkable student who did, since it took mathematicians a couple of thousand years to sort out the notion of a limit, and I think most of us who call ourselves professional mathematicians really only understand it when we start to teach the stuff, either in graduate school or beyond.

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