But actually, mathematics is definitely not such a boring thing.
Every branch of mathematics is related to application.
For example, in order to find out the time of farming, people in ancient times had to judge when a year began according to the position of the stars (otherwise they could not farm). The ancient Egyptians observed that Sirius and the sun rose together every 360 days, so the length of a year was fixed. Observational astronomy is a sign of the development of a civilization. Greece, Egypt, India and China are all civilizations with advanced astronomy.
But it goes without saying that astronomical observation cannot be separated from mathematics. For example, after knowing the star, people want to know how it moves, which leads to the problem of orbit calculation. The calculation of orbit is a mathematical problem.
From Aristotle to Galileo, Kepler and Newton, the motions of celestial bodies have been clarified one by one, including mathematical work. It can be said that without the corresponding development of mathematics, it is impossible to understand the motion of celestial bodies. Newton relied on the knowledge of calculus to prove that celestial bodies move in elliptical orbits.
For another example, in physics, we should thoroughly study wave propagation, heat transfer and fluid motion (for example, wave propagation is limited by speed, but heat propagation is not limited by speed, and so on). ), a partial differential equation is required. When it comes to partial differential equations, it is a pure mathematical problem. Starting from the needs of partial differential equations, there are many basic theories of mathematical analysis, the basis of contemporary mathematics.
Furthermore, there will be mathematical problems from production needs.
For example, the ancient Egyptians measured land and produced geometry; Building a house should be beautiful and firm, which involves mechanics and ultimately comes down to mathematics (Pythagorean theorem and differential equation used in mechanics); The production of market economy should consider the maximization of production profit, which leads to the planning theory; Why does the motion of an object have a certain trajectory? This is calculus.
From the perspective of some historical inheritance, ancient mathematical problems often use the conclusions of modern mathematics.
The ancient Greeks knew three main drawing problems: bisecting an angle, turning a circle into a square and folding a cube in half. But no one can solve it in a thousand years. When was it finally solved? After the emergence of group theory. What is group theory? What only students in the department of mathematics learn.
Did the ancients solve equations once, twice and three times? In a thousand years, someone will understand. What about four times? It will be solved later. What about five times? It didn't work. Can it be solved? I don't know how it was finally solved. Group theory. It's over.
Another example is the study of the motion and spin of elementary particles in quantum mechanics, which is closely related to Lie groups and Lie algebras. Lie groups and lie algebras are super abstract things in mathematics, which no one can understand except mathematicians.
People are interested in integers, so it is necessary to study prime numbers and composite numbers. This is number theory. But some problems can't be worked out with a pen, such as Goldbach's conjecture and Fermat's last theorem (also derived from Pythagorean theorem), but they are just problems that people are suddenly interested in. In order to solve all kinds of conjectures, people have developed tools to solve problems. Algebraic number theory, analytic number theory and finally these theories are basically incomprehensible, but only these theories can solve the problems raised by people.
People are always interested in nature and always want to improve the life around them; But every progress must be accompanied by the use of mathematical tools. Without the satisfactory tool of mathematics, people's research will be very difficult. Although mathematicians study things that few people can understand, the results of their research will always be the theoretical basis for others' work. Without the work of mathematicians, people would make many irreparable mistakes.