It is our intention that this tour provide enough description of the terrain to help you select the heading of the Mathematics Subject Classification appropriate for a specific inquiry. Browse a list of subject headings. Help for using this site. We keep the broad definition here, that mathematics includes all the related areas which touch on quantitative, geometric, and logical themes. We draw the line only at experimental sciences, philosophy, and computer applications.
Personal perspectives vary widely, of course.
The latter often arise from analytical models in the empirical sciences, but may emerge from purely mathematical considerations. The study of well-defined things. The branch of science which you could continue to do if you woke up and the universe were gone. As we shall see there are branches of mathematics concerned with setting up equations, or analyzing their solutions, and there are parts of mathematics devoted to creating methods for doing computations. But there are also parts of mathematics which have nothing at all to do with numbers or equations.