Pavel Alexandrovich Florensky (1882-1937), philosopher, priest, scientist and mathematician, showed a unique cosmology in Imaginary points in geometry. He argues that from the viewpoint of the theory of general relativity the cosmos must be closed non-Euclidean space. His conclusion is that the Ptolemaic system, central to the cosmos of Dante's Divine Comedy, is valid. This study addresses the interpretation of Florensky's cosmology, focusing especially on his thought related to mathematics and space. The cosmos, for Florensky, consists of two spheres: the terrestrial sphere, which real number represents, and the celestial sphere, which imaginary number represents. These two spheres are united discontinuously and form the whole. The essential concepts in Florensky's mathematical thought are discontinuity and actual infinity. Under the influence of Nikolai Bugaev(1837-1903), a prominent mathematician in the 19th century, Florensky studied discontinuous function and then applied the concept of discontinuity to various studies beyond mathematics. Florensky argues that the concept of continuity is dominant in every field in the 19th century. However, not all phenomena are explained by continuity and furthermore, discontinuity precedes continuity. Non-Euclidean space is discontinuous on his view. Actual infinity, the concept of which was invented in the set theory of Georg Cantor, is related to discontinuity. While potential infinity is conceived as infinite process, actual infinity, which is larger than any other number, is regarded as a mathematical real existence. Florensky expands the concept of actual infinity into the theological thought and describes God as actual infinity. Florensky's cosmology, which is featured by non-Euclidean space and discontinuity, must be seen as an attempt to overcome the values of the 19th century and to visualize the whole relation between the earth and God, describing God as actual infinity.