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.
Keith DevlinThe 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.
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 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 DevlinI saw the first one [video with Hans Rosling ] when he did - I think it was his first one - in 2006, a TED Talk. And for the first time in my life, I thought here's someone who can take statistics that most people regard as dull and boring and bring it alive.
Keith Devlin