Passages of Proof

In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialise. We will argue that there is little ‘intrinsic’ difference between traditional and ‘unconventional’ types of proofs.