The seven abilities of mathematics include: abstract generalization ability, spatial imagination ability, reasoning ability, operational solving ability, data processing ability, application consciousness and innovation consciousness. Mathematics is a subject that studies concepts such as quantity, structure, change, space and information.

Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.