Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.

Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.

Perhaps the most surprising thing about mathematics is that it is so surprising.

Algebra goes to the heart of the matter at it ignores the casual nature of particular cases.

There are certainly people who regard √2 as something perfectly obvious but jib at √-1. This is because they think they can visualise the former as something in physical space but not the latter. Actually √-1 is a much simpler concept.

I met a man once who told me that far from believing in the square root of minus one, he didn't believe in minus one. This is at any rate a consistent attitude.

Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.