Open classification: mathematics, geometry, algebra, elementary mathematics.

Before Newton and Leibniz founded calculus and strictly based on limit theory, there was no concept of limit in mathematical research methods. It can be vaguely said that elementary mathematics is mathematics with high learning skills and simple methods, excluding extreme thoughts. It is vague because it is impossible and unnecessary for us to give it a precise definition. It seems that there is no secondary mathematics, and the calculus content after Newton Bryan's time is all advanced mathematics.

Advanced mathematics is higher than elementary mathematics. In a broad sense, all mathematics except elementary mathematics are advanced mathematics, and some call algebra, geometry and simple set theory logic in middle school secondary mathematics, which is the transition between elementary mathematics in junior high school and advanced mathematics in undergraduate stage. Among them, Newton and Leibniz jointly established calculus, which brought great influence to later generations.

Higher mathematics pays more attention to the research and application of mathematical foundation.