With the development of mathematics, the internal meaning is extended to replace scientific phenomena with group structure or various structures.
Algebraic number theory is a branch that extends the concept of integer to algebraic integer. Mathematicians extended the concept of integer to the general algebraic number field, and accordingly established the concepts of prime number and divisibility.
Geometric number theory was initiated and laid the foundation by German mathematician and physicist Minkowski and others. The basic object of geometric number theory research is "spatial grid". What is a spatial grid? In a given rectangular coordinate system, the point whose coordinates are all integers is called the whole point; A group of all integer points is called a spatial grid. Spatial grid is of great significance to geometry and crystallography. Because the problems involved in geometric number theory are complicated, it needs a considerable mathematical foundation to study it in depth.