1, the knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has continued to make small progress. But algebra and geometry at that time were still independent for a long time.
Mathematics is applied in many different fields, including science, engineering, medicine and economics. The application of mathematics in these fields is generally called applied mathematics, which sometimes arouses new mathematical discoveries and promotes the development of new mathematical disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although a lot of work started from the study of pure mathematics, it may find a suitable application later.
3. The early definition of mathematical logic is Benjamin Peirce's Science of Drawing Inevitable Conclusions (1870). In Principles of Mathematics, Bertrand Russell and alfred north whitehead put forward a philosophical program called logicism, trying to prove that all mathematical concepts, statements and principles can be defined and proved by symbolic logic. The logical definition of mathematics is Russell's "All mathematics is symbolic logic" (1903).
4. Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. As far as it is concerned, it is the origin of Godel's second incomplete theorem, which is perhaps the most widely circulated achievement in logic. Modern logic is divided into recursion theory, model theory and proof theory, which are closely related to theoretical computer science.
Math language is also difficult for beginners. How to make these words have more accurate meanings than everyday language also puzzles beginners. For example, the words "open" and "domain" have special meanings in mathematics. Mathematical terms also include proper nouns such as embryo and integrability. But these special symbols and terms are used for a reason: mathematics needs accuracy more than everyday language. Mathematicians call this requirement for linguistic and logical accuracy "rigor".