Basic concepts of Foundations of Mathematics are analyzed. Short historical analysis of this problem of is represented. Short classification of main theories of foundation of mathematics is made. We have only structural and natural concepts. Necessary of creation more general natural system concept of foundation of mathematics is formulated. Polymet5ric analysis as example of natural concept of foundations of mathematics is represented. This theory may be represented as theory of everything in general sense. Six criteria of formation the other theories of everything are analyzed too.