This issue is devoted to the philosophical (metaphysical) analysis of the foundations of mathematics and its relationship with physics. The collection consists of four parts. The first part presents articles by domestic mathematicians in which fundamental problems of mathematics are considered. The second part includes articles by prominent scientists of the past on the foundations of mathematical science. The third part is composed of articles by theoretical physicists that discuss the relationship between physics and mathematics. Finally, the fourth part includes the work of philosophers on the foundations and key problems of mathematics.