ABSTRACT
The goal of this chapter is to introduce you to proofs in mathematics. We start with what we mean by truth.
2.1 MATHEMATICAL TRUTH Humans can believe things for purely emotional reasons.1 An advance on this is believing something because somebody in authority told you. Most of what we take to be true, certainly as children, is based on such appeals to authority. Although this is not automatically a bad thing, after all we cannot be experts in everything, it has also been at the root of humanity’s darkest episodes. There must be a better way of getting at the truth. And there is. The scientific method with the appeal to experiment at its centre, combined with a culture of debate and criticism, is the only basis for any rational attempt to understand our world. This makes the following all the more surprising: in mathematics, the appeal to experiment, let alone the appeal to authority or the appeal to psychological well-being, plays no rôle whatsoever in deciding mathematical truth.
