Cardinal 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 firmly believe that mathematics does not exist outside of humans. It is something we, as a species, invent.
Keith DevlinThe human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.
Keith DevlinThe whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.
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