Abstract

The aim of the paper is to show the complexity of problems concerning mathematical proof, and, in particular, the extramathematical aspects of the process of proving theorems in mathematics. The proof can be treated as a tool enabling the justification of a given theorem. In this sense the proof can be perceived as a tool persuading others to accept this proof as an element of mathematical knowledge. The justifying aspect of mathematical proof is most important for mathematics. It is a ‘certificate’ of the truthfulness of the considered theorem. However, apart from the persuasive aspect, the role that proofs play in mathematics is much more complex. Proofs can serve as a way of ‘making accessible’ a ‘fragment’ of mathematical reality to a mathematics adept person. By following attentively the proof progression, a beginning mathematician performs a ‘reconstruction of mathematical discovery’, thus participating – though ‘secondarily’– in discovering mathematical truth. In this way he can reach the essence of how mathematics functions as science. This participative character of mathematical proof – understood as a pass to participate in a mathematical experience – is definitely essential for the process of mathematical education. The third dimension of the functioning of mathematical proof in mathematical practice is its ritualistic character. Proving – once again – the already proven theorems, repeating once more the steps of the proving process accepted earlier, not only do we again get stronger in our conviction that the given theorem is true, but we also deepen our understanding of the performed reasoning. Such a conduct can be a component of ‘mathematical way of life’ of mathematicians. The process of carrying out a proof can be perceived as some celebration, ritual, ceremonial, present in life of mathematicians allowing them to appreciate beauty and elegance of conducted proofs, alongside allowing them to keep their brains ‘in aptitude’.