Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
Keith DevlinIn 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.
Keith DevlinIn 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.
Keith DevlinCardinal 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.
Keith DevlinSome 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.
Keith Devlin