The history of mathematical development is also the history of scientific development. At first, babbling created a colorful counting system, and then more and more detailed mathematical branches were established in the rainy season. Today, it has demonstrated its dazzling mathematical achievements in In the Mood for Love. Every step contains hardships and infinite thinking. During this period, how many people devoted their lives to mathematics, which endowed the subject with infinite charm.

The book Selected Lectures on the History of Mathematics first tells a variety of notation, including the tedious notation in hieroglyphics, the unique notation in cuneiform, the simple notation in ancient China, the strange notation that Maya used the head of God as numbers, and the Indo-Arabic numerals that are still in use today. It is not difficult to see from the evolution of the early counting system that even the creation of numbers is arduous. At that time, how to invent a convenient and durable counting method was a crucial foundation for establishing mathematics discipline. It can be said that if there is no initial research and exploration of numbers and counting systems by human beings and efforts are made to create the simplest and most convenient counting methods, the future research on mathematics will be doubly tortuous and difficult.

In the long history of mathematics development, the most important thing is countless mathematicians who have struggled for it all their lives. Because of their bitterness and tears, their rigorous attitude and persistent spirit of exploration, they laid a solid mathematical foundation, thus creating opportunities for the birth of mathematical branches such as plane analytic geometry, calculus and infinite set theory. However, the development history of mathematics is tortuous and arduous, especially the research mileage of mathematicians. Most of the innovative thinking and super-era theory they have bought in their lifetime will not be recognized by the world in their lifetime. When hippasus announced his discovery of incommensurability to other members of the Pythagorean school, the frightened members threw him into the sea; The strong group theory put forward by Galois has been submitted to the Academy of Sciences many times, but the final result is "completely incomprehensible" comments; Cantor, who created amazing infinite set theory, finally passed away with many regrets and infinite anguish. Abel, a middle school mathematician, is the most talented person. Through countless efforts, he finally proved this eternal puzzle-algebraic equations with five or more degrees have no general formula for finding roots, but they have been met with a series of cold shoulder. Even the "prince of mathematics" Gauss only said, "It's terrible to write such things!" He threw the paper into the pile of books without even reading the text. Although Berlin University had recognized his talent and appointed him as a professor of mathematics at that time, Abel had already died in the devastation of the disease.

Although their theory is praised by the world today, it was ridiculed and reviled at the beginning. Unlike mathematicians who were famous all over the world at that time, as soon as new theories came into being, they were paid attention to by the whole world, and then they continued to study under the light of admiration and glory. Nevertheless, they still believe in themselves, strive independently for their own mathematics career, explore deeply, and further develop and improve their theories. Just like Cantor's confident words: "My theory is as firm as a rock. Anyone who wants to shake it will shoot himself in the foot." This confidence and determination are admirable.

And many mathematicians have one thing in common, that is, their knowledge level includes many other fields besides mathematics. For example, Thales was the earliest mathematician and philosopher in ancient Greece, and he dabbled in almost all fields of human thought and activity at that time; Fermat has rich legal knowledge and is proficient in many languages. Leibniz studied Latin, Greek, rhetoric, arithmetic, logic and music, and also extensively read and studied a large number of philosophical and scientific works. In Euler's works, mathematics is closely related to the application of other sciences, various technical applications and public life. It often provides mathematical methods for solving problems such as mechanics, astronomy, physics, navigation, geography, geodesy, fluid mechanics, ballistics, insurance and demography. It can be seen that if you want to succeed in a subject, you need to master not only the knowledge of the subject, but also the knowledge of other disciplines and fields, and make comprehensive use of it to make this knowledge better serve your own research.

Confidence, determination and knowledge in many fields are important, but teachers are also very helpful to them. Newton was inspired to study the number of streams in Professor Barrow's course, and Euler inherited the mantle of johann bernoulli, the authority of calculus, and became the "incarnation of analysis". With the encouragement and guidance of his teacher Holmbo, Abel solved the unsolved mystery of algebraic equations five or more times. As a swift horse, Galois was discovered by Professor Richard and became the founder of group theory. Cantor studied under famous mathematicians such as Kummer, Wilstrass and Kroneck, and founded infinite set theory, especially Hua. A great mathematician often has a diligent teacher behind him. Perhaps their teacher is unknown now, but their efforts and teaching are no less than these mathematicians. It is precisely because of their patient teaching, great support and encouragement that they are given the opportunity to show their edge. The spirit of these mathematicians learning from them modestly is worth learning and emulating.

In addition, from the efforts of mathematicians, we can find the necessary process of mathematical research. First of all, we should explore the truth of mathematics from subtle things, discover the existence of problems, or have great interest and research spirit in a certain problem. Many people can do this, just like Newton thought of a falling apple and created the law of gravity. In our daily life, we can all ask questions about some common things, and when we encounter some problems, we have an impulse to break them. Then, we must make unremitting and in-depth exploration. This step is often only a few people can do, but it is the most important step. Without it, all the previous efforts will be in vain. In the face of difficulties, it is often the key to a great start and success to still have the initial impulse and courage to conquer it. But only this kind of impulse and courage is not enough. A great mathematician must also have the spirit of innovation, question the spirit of people's deep-rooted thoughts, break the cult of personality and dogmatism, and have the courage to create his own new ideas, just like Descartes established the coordinate system, Newton and Leibniz established calculus, Gauss established non-Euclidean geometry, Galois established the new concept of group theory, and Cantor firmly believed in infinite set theory.

Generally speaking, the successful experience of these mathematicians has taught us how to prepare for future challenges at this stage. Ideologically, we should cultivate innovative thinking, self-confidence, firm self-belief and fearless spirit in the face of difficulties. In action, we should learn from teachers with an open mind, not shy about asking questions, and actively learn all kinds of knowledge, so as to master and apply it to daily life.

"Liu Hui's tangent circle method is hundreds of years later than the exhaustive method in ancient Greece", "Descartes and Fermat established analytic geometry in the same way", "Newton and Leibniz, two founders, worked hard to establish calculus as an independent discipline" ... In the development of the history of mathematics, many identical research results were repeatedly discovered by human beings, which undoubtedly delayed the development of mathematics. Repeated efforts for the same problem, but I don't know that others have actually solved it. If the world can integrate earlier, exchange mathematical culture with each other better, conduct research and make progress, then it won't take hundreds of years or even longer to take the same detour repeatedly, but it can promote the development of mathematics faster, and perhaps the development speed of mathematics in the world will exceed the current pace.

The book also mentions a condition for the emergence of mathematics: "After practical technological inventions, there will be sciences that are not directly for the needs or satisfaction of life. It first appeared in places where people had leisure, and mathematical science first rose in Egypt because priests there enjoyed enough leisure. " This shows the importance of leisure for the rise of science. Indeed, people have no time to invent science when the problem of food and clothing has not been solved, and when mental labor and physical labor have not been separated. Only by enjoying leisure can people have enough time and energy to spend on scientific creation. Only by playing with numbers at the beginning will they gradually explore deeply, find mathematical problems from trivial matters in life, create puzzles and then solve them, and then step by step go to today's mathematics discipline. If there is no leisure, there will probably be nothing behind. Similarly, as students, we also need to take time out to study math seriously. If it is difficult to finish our daily homework on time, how can we solve this math problem?

The development of mathematics is still very long, and there are still many ways to go. As Newton said, we are just children playing by the sea. There is an ocean of unknown truth before us, and the infinite charm of mathematics is buried in it, waiting for us to explore and explore.