Pure mathematics, also known as basic mathematics, is a kind of knowledge that specializes in mathematics itself and does not aim at practical application. Studying the internal relations of mathematical laws abstracted from the objective world can also be said to be studying the laws of mathematics itself. Compared with applied mathematics, it is closely related to other theoretical sciences (such as theoretical physics and theoretical chemistry) that do not aim at application.

Pure mathematics is famous for its preciseness, abstraction and beauty. Since18th century, pure mathematics has become a special mathematical research, which develops with the development of exploration, astronomy, physics and engineering. Pure mathematics is represented by number theory.

origin

The word "pure mathematics" officially appeared in mathematical literature at the beginning of19th century. At that time, there were three kinds of professional mathematics journals officially marked with the words "pure mathematics". They are: 18 10 Yearbook of Pure and Applied Mathematics, which was founded by French mathematician Gergona, and 1826 Journal of Pure and Applied Mathematics, which is often called "Pure and Applied Mathematics".

The Journal of Pure and Applied Mathematics, founded by French mathematician joseph liouville, competes with the magazine Crelle. These three mathematical journals have chosen the title of "pure mathematics" in unison, which shows that the concept of pure mathematics has matured; Pure mathematics is the opposite of applied mathematics; Pure mathematics has gained a certain legal status, laying the foundation for its continuous expansion.

These are inseparable from the revolutionary situation of the whole society at that time. Speaking of mathematics, mathematicians began to be professional and specialized. They not only want to teach, but also want to engage in scientific research. To engage in scientific research, it is necessary to publish the results in professional magazines. Without the result, it goes without saying that you will get a promotion, or even lose your job.

In the past 200 years, the banner of pure mathematics has provided opportunities for the innovation of many talented mathematicians. In this sense, the Norwegian Abel can be said to be the first pure mathematician. Today, pure mathematics has become the mainstream of the whole mathematics.

In the 20th century, influenced by Hilbert, mathematicians began to use axiomatic systems. Russell established the logical formula of "pure mathematics" in the form of quantitative proposition. With the axiomatization of mathematics, these formulas become more and more abstract, and "strict proof" becomes a simple standard. In fact, "strictness" is nothing new in "proof". According to bourbaki Group, pure mathematics has been proved.