Powstanie i perspektywy dowodu matematycznego

This paper is an attempt to review the historically existing types of demonstration of mathematical theorems. The author shows how the notion of mathematical proof has changed through the time from the moment when mathematicians realised (thanks to the philosophical method) the necessity to justify their theses until a precise notion of proof has appeared in the framework of the formal method. Next, the author considers the possibility of modifying the notion of mathematical proof under the influence of the development of computer sciences.