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.

The completion of a rigorous course in mathematics - it is not even necessary that the student does well in such a course - appears to be an excellent means of sharpening the mind and developing mental skills that are of general benefit.

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.

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

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.

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.

In fact, when you try to use [Hans Rosling] data to predict the future, all sorts of problems arise. But what it does do is say, hey, just catch your breath a minute and see what's really been going on. We do have reason to feel good about the fact we've made progress.