The problem of infinity has been one of the most important problems in the works of a theologian, philosopher and naturalist P. A. Florensky and a mathematician N. N. Luzin. The former was keenly interested in G. Cantor’s set-theoretic ideas he first became familiarized with when he was the first-year university student. However, even in his student years Florensky studied Cantor and his set theory from the standpoint of a philosophizing theologian: for him, Cantor’s idea of transfinite ordinals had been, first and foremost, the key to the problem of celestial hierarchy. Luzin joined the supporters of the viewpoint that set-theoretic concepts and principles needed to be revisited, that unlimited use of the notion of the infinite and the axiom of choice in mathematics could lead to conclusions devoid of epistemological meaning. Therefore, in their ponderings, Luzin and Florensky held opposite positions on this matter. Exploring the origin of this discrepancy is what this paper is devoted to.