Contemporary computer technology is so advanced that it leads some mathematicians to suggestions that computers can enrich the already-known forms of mathematical theses proving. Some mathematicians openly speak about computer method of proving mathematical theorems. The paper is an attempt to consider notion of computer proof. The author describes various roles that computer can play in mathematics, compares the notion of experiment in the sciences and mathematics and then indicates possible conceptual difficulties with application of computers to proving mathematical theorems. Finally, the author formulates a key questions for the considered issue: Can computer prove mathematical theses in a different sense than a formalized proof does?; and: Can the application of computer in the procedure of proving the theorems undermine the dominating position of the mathematician?