ABSTRACT
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. Proofs are difficult because it is usually far from obvious how to reach the conclusions from the assumptions. In particular, the readers are allowed to assume anything that has previously been proved, which is daunting given the scale of the subject. Mathematics should be viewed as a collection of different mathematical domains each described by its own ‘rules of the game’ which in mathematics are termed axioms. These axioms are the basic assumptions on which the theory is built and are the building blocks of all proofs within that mathematical domain. One way of learning mathematics is to begin with a list of axioms for some mathematical domain and then start proving theorems.
