Classifying proofs

The current developments of computer assisted proof systems give rise to new considerations concerning the old question: What is a proof ? We will address this question taking into account that proofs may serve different purposes. First we propose to distinguish unveiling proofs—the first proof of a theorem, uncovering its truth—from consolidating proofs—new proofs of theorems already known to be true. Further distinctions should take into account whether a proof, for instance: – is methodologically “pure”, – allows for generalizations (Hilbert), – uses new concepts, capturing a productive unity (Poincare), – shows unexpected relations of “unrelated” areas, etc. ´ In addition to the analysis of examples, we will illustrate our classification with a discussion of how proofs are evaluated.