The origin of mathematical knowledge, what is the origin and development of mathematics?

Mathematics originated in the early production activities of human beings, and the ancient Babylonians had accumulated a certain amount of mathematical knowledge since ancient times and could apply practical problems. From the perspective of mathematics itself, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but it is also necessary to fully affirm their contributions to mathematics.

The knowledge and application of basic mathematics is an integral part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical texts in ancient Egypt, Mesopotamia, and ancient India. Since then, there has been a steady stream of development.

But algebra and geometry at that time remained independent for a long time.

Algebra is arguably the most widely accepted form of "mathematics". It can be said that since everyone started learning to count when they were young, the first mathematics they came into contact with was algebra. As a discipline that studies "numbers", algebra is also one of the most important components of mathematics.

Geometry was the first branch of mathematics to be studied.

It was not until the Renaissance in the 16th century that Descartes created analytic geometry, linking algebra and geometry, which were completely separate at the time. Since then, we can finally prove the theorems of geometry with calculations; At the same time, it can also be used to visualize abstract algebraic equations and trigonometric functions. Later, calculus was developed into more subtle forms.

The Bourbaki School of France, founded in the thirties of the twentieth century, held that mathematics, at least pure mathematics, is the study of abstract structures. Structure is a deductive system based on initial concepts and axioms.

According to them, there are three basic parent structures in mathematics: algebraic structures (groups, rings, fields, lattices,......Order structure (partial order, full order,......Topology (neighborhood, limit, connectivity, dimensionality, ,......).

Mathematics is used in many different fields, including science, engineering, medicine, and economics. The application of mathematics in these areas is often referred to as applied mathematics and sometimes provokes new mathematical discoveries and the development of entirely new mathematical disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without aiming for any practical application.

While much of the work begins with the study of pure mathematics, it may be possible to find suitable applications later.

Specifically, there are sub-fields that explore the connections between the core of mathematics and other fields: from logic and set theory (the foundations of mathematics) to empirical mathematics from different sciences (applied mathematics), to more recent studies of uncertainty (chaos and fuzzy mathematics). In terms of verticality, the exploration of their respective fields of mathematics has also become more and more in-depth.

1. As far back as 15,000 years ago, human beings began to germinate graphic consciousness and counting consciousness. Graphic consciousness and counting consciousness have developed to a certain extent, and the consciousness of measurement has been produced. This series of developments gradually formed a complete discipline of mathematics, including arithmetic, geometry, algebra, trigonometry, calculus, statistics, and probability, and continues to develop.

2. Mathematics [English: mathematics, derived from the ancient Greek máthēma); Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space, and information. Shanpin.

3. Mathematics is a kind of general hand-to-hand paragraph that human beings strictly describe the abstract structure and pattern of things, which can be applied to any problem in the real world, and all mathematical objects are essentially artificially defined. In this sense, mathematics belongs to the formal sciences, not the natural sciences. Different mathematicians and philosophers have a series of opinions about the exact scope and definition of mathematics noisy.

4. Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for learning and researching modern science and technology.