Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles And by opposing end them? Hamlet 3/1, by W. Shakespeare 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. Computer-assisted proofs will be give a special attention. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialize. We will argue that there is little ‘intrinsic ’ difference between traditional and ‘unconventional ’ types of proofs. 2 Mathematical Proofs: An Evolution in Eight Stages Theory is to practice as rigour is to vigour. D. E. Knuth Reason and experiment are two ways to acquire knowledge. For a long time mathematical

ABSTRACT: What are the limits of physics ’ explanatory power? Can physics explain everything? In this paper I discuss a somewhat broader question: can physics explain existence itself? I argue that genuinely ultimate explanations—those that really explain everything—involve the most basic and most general elements of logic. Such explanations cannot be done within physics unless physics undergoes a methodology shift more closely aligning itself with mathematics and logic. However, I give reasons for thinking that just such a shift might be in operation. Even a solipsist agrees there is at least one thing!

The object of mathematical rigour is to sanction and