The existing theory of space transformation in mathematics is a theory that will not be evolved. it is a basic task of this paper to turn the theory that can't be evolved into a theory that can be evolved. By introducing a concept of distribution density of geometry point, the paper changes it into the basic theory of space evolution in mathematics, thus, endows the theory of space transformation with vitality. Replacing the three-dimensional Euclidean space with vacuum and the distribution density of geometry point with distribution density of vacuum matter point, the basic theory of space evolution in mathematics has become the basic theory of space evolution in physics. Distribution density of vacuum matter point is a matter concept, so the basic theory of space evolution is in fact a basic theory of matter evolution. The basic theory of space evolution also accurately expresses the thought of "Gathering to form a shape and diffusing to form nothing". Moreover, through the application for the basic theory of space evolution to Lorentz transformation, this paper not only deduces out the conversion formula of moving and unmoving mass, but also clarifies the essence of mass, namely, the mass of an object is the distribution density of vacuum matter point. And then, there is a novel explanation of no shielding of gravitation and the cause of gravitation formation. It is a natural thing to explain the phenomenon of producing new vacuum while the gold core is colliding, which is so called that when conditions are ripe, success is achieved.