The massive use of computers in mathematical proofs, which started in the end of the seventies trough the solution of one famous mathematical problem – the Four-Color Theorem – entailed philosophical disputes still in need of elucidation. The central aim of this thesis consists in elaborating some of these elucidations from a point of view motivated by Ludwig Wittgenstein’s philosophy of mathematics, mainly in what concerns the distinction between proofs and experiments, which was continuously used and elaborated by the philosopher in the course of the development of his thought. After the presentation of the main ideas involved in the proof of the Four-Color Theorem from a historical perspective, some methodological conceptual distinctions are elaborated. The thesis then shifts to an analysis of the introduction of experiment in mathematics argument, by Thomas Tymoczko, from the point of view of Arthur Pap’s conception of functional a priori. An interpretation of the controversies that followed that argument is developed trough the application of the conceptual distinctions previously elaborated. At last, some wittgensteinian ideas about the distinction between proofs and experiments are explored in connection with the notion of surveyability of proofs, concerned less with its specific roles in Wittgenstein’s philosophy of mathematics than with investigating the advantages of its possible applications in the elucidation of some critical points in the referred controversies.