DavidW wrote: > They don't have to be applicable to anything in the real world, but I would have > thought that, at the very least, their aim should be to make discoveries about > numbers. Perhaps you can explain what makes one formal system a branch of > mathematics and another a game of snakes and ladders.
Just "Numbers"? You don't, as they say, know much, do you? But you might find it interesting to read Hardy's "A mathemacician's apology", in which he opines that pure mathematics, and abstract algebra in particular, has no application to the "real world". It turns out that he was gloriously wrong about this, in the form of cryptography. But if mathematicians are only allowed to do stuff that the Really Important With All the Money can see an application for, we are doomed not to have future things like cryptography.