Most of the professional mathematicians turn out to be mathematical platonists who admit that the mathematical structures exist independently of the human mind. Consequently, each mathematician is a discoverer of objective mathematical truths proper to the abstract world of ideas. The paper presented surveys an interesting discussion among famous mathematicians regarding their views on the philosophy of mathematics published in the “European Mathematical Society Newsletter” with the main question on whether mathematical platonism is a viable option in this regard. The discussion reveals a number of fundamental problems of both ontological and epistemological nature generated within the Platonist position. The main objection concerns the problem of mathematical intuition that is supposed to be responsible for the mind’s direct access to the mathematical truth. Inasmuch as several participants consider intuition to be a fully theistic position, they anticipate its scientific clarification in the area of contemporary cognitive sciences.