Although there have been suggestions that mathematics is becoming
more 'experimental,' and the notion of proof less salient, this
has provoked vigorous denials from the mathematical community
which continues to maintain that proof is one of the key concepts
which characterise the discipline. It is surprising therefore, that the
fundamentals of mathematical proof have rarely been taught in a
systematic way. Most students of mathematics are expected to develop
their understanding of proof and the associated theorem-proving
skills by a process of 'osmosis' through encounters with the various
techniques and methods. The result is that students frequently have
an inadequate appreciation of the underlying structure of proofs and
a consequent inability to distinguish a correct proof from a flawed
one. It is therefore no wonder that they have considerable difficulty
in constructing their own proofs, often not knowing how to start a
suitable line of reasoning.