History

A Brief History of Western Mathematics

The evolution of mathematics can be seen as a continuous development of abstraction, or an extension of subject matter, and Eastern and Western cultures have adopted different perspectives, with European civilization developing geometry and China developing arithmetic. The first abstracted concept was probably the number (Chinese arithmetic), and its recognition of something similar between two apples and two oranges was a major breakthrough in human thought, and in addition to knowing how to count the number of actual objects, prehistoric humans also knew how to count the number of abstract concepts, such as time - days, seasons, and years. Arithmetic (addition, subtraction, multiplication, and division) also comes naturally.

Further, writing or other systems that could record numbers, such as rune wood or the Chip used by the Incas. There have been many different notation systems throughout history.

In ancient times, the main principles of mathematics were formed in order to study the rational distribution of land, food, crops, taxation and trade, and other related computational mathematics in order to understand the relationship between numbers, to measure land, and to predict cultural events. These needs can be summarized simply as the mathematical study of quantity, structure, space, and time.

In Western Europe, from ancient Greece to the 16th century, through the Renaissance, elementary mathematics such as elementary algebra and trigonometry were largely complete, but the concept of limits had not yet appeared.

In the 17th century, the concept of variables in Europe was born, so that people began to study the relationship between quantities and quantities in change and the mutual transformation between figures. With the further development of natural science and technology, the fields of set theory and mathematical logic began to develop slowly for the study of mathematical foundations. [3]

A Brief History of Chinese Mathematics

Main article: History of Chinese mathematics

Mathematics, known as arithmetic in ancient times, is an important discipline in ancient Chinese science, which can be divided into five periods according to the characteristics of the development of ancient Chinese mathematics: germination; the formation of the system; Develop; Prosperity and the fusion of Chinese and Western mathematics.

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Many of the research results of ancient Chinese arithmetic have already given birth to the ideas and methods that were later involved in Western mathematics, and many of the world's leading mathematical research results in modern times are named after Chinese mathematicians:

【Li Shanlan Identity】Mathematician Li Shanlan's research results in series summation have been named "Li Shanlan Identity" (or Li Identity) in the world.

【Fahrenheit's theorem】Mathematician Hua Luogeng's research results on complete trigonometric sums are known as "Fahrenheit's theorem" by the international mathematical community; In addition, he and mathematician Wang Yuan proposed a method for approximating multiple integrals, which is internationally known as the "Hua-Wang method".

Mathematician Su Buqing's research results in affine differential geometry have been named "Su's cone" in the world.

Mathematician Xiong Qinglai's research results on integer functions and infinite-level metapure functions have been praised by the international mathematical community as "Xiong's infinite level".

Mathematician Chern Shiingshen's research results on demonstrative classes are internationally known as "demonstrative classes".

Mathematician Zhou Weiliang's research achievements in algebraic geometry are known as "Zhou's coordinates" by the international mathematical community. In addition, there are "Zhou's theorem" and "Zhou's ring" named after him.

【Wu Method】Mathematician Wu Wenjun's method of machine proving geometric theorems is internationally known as the "Wu method"; There is also the "Wu formula" named after him.

【Wang's Paradox】A proposition of mathematician Wang Hao on mathematical logic has been internationally designated as "Wang's paradox".

【Kok's theorem】Mathematician Ke Zhao's research results on the Cattelan problem are known as "Kortle's theorem" by the international mathematical community; In addition, his research results in number theory with mathematician Sun Qi are internationally known as the "Ke-Sun guess".

【Chen's theorem】The proposition proposed by mathematician Chen Jingrun in the study of Goldbach's conjecture is known as "Chen's theorem" by the international mathematical community.

【Yang-Zhang theorem】The research results of mathematicians Yang Le and Zhang Guanghou in function theory are internationally known as the "Yang-Zhang theorem"

【Lu's Conjecture】Mathematician Lu Qihang's research results on the manifold of constant curvature are internationally known as the "Lu's Conjecture".

【Xia's inequality】The research results of mathematician Xia Daoxing in the field of functional integration and invariant measure theory are known as "Xia's inequality" by the international mathematical community.

Mathematician Jiang Boju's research results on Nelson number calculation have been named "Jiang's space" internationally; In addition, there is the "Jiang subgroup" named after him.

【Hou's theorem】Mathematician Hou Zhenting's research results on Markov process have been named "Hou's theorem" internationally.

Mathematician Zhou Haizhong's research results on the distribution of Mersenne prime numbers have been named "Zhou's guess" internationally.

【Wang's theorem】The research results of mathematician Wang Xutang on point set topology have been praised as "Wang's theorem" by the international mathematical community.

【Yuan's Lemma】Mathematician Yuan Yaxiang's research results in nonlinear programming have been internationally named "Yuan's Lemma".

Mathematician Jing Naihuan's research results in symmetry functions have been named "Jing's operator" internationally.

Mathematician Chen Yongchuan's research achievements in combinatorial mathematics have been internationally named "Chen's Grammar".

Foreign figures

Everything counts. —Pythagoras

There is no king in geometry. —Euclid

Mathematics is the word that God uses to write the universe. - Galileo

I was determined to abandon the mere abstract geometry. That is, I do this in order to study a different kind of geometry, that is, a geometry that is intended to explain natural phenomena. - Rene Descartes (1596-1650)

Mathematicians have tried to discover some order in this sequence of prime numbers, and we have reason to believe that this is a mystery that the human mind can never penetrate. - Euler

Some beautiful theorems in mathematics have the property that they are so easy to generalize from the facts, but the proofs are very hidden. Mathematics is the king of science. - Gauss

This is the benefit of a well-structured language, whose simplified notation is often a source of esoteric theory. —Pierre Simon Laplace (1749-1827)

It would be a grave mistake to think that necessity is only in geometric proofs or in sensory proofs. - Augustin Louis Cauchy (1789-1857)

The essence of mathematics lies in its freedom. —Georg FerdinandLudigPhilippCantor (1845-1918)

Music can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can move the heartstrings, philosophy can make people gain wisdom, science can improve material life, but mathematics can give a touch of the above - Christian Felix Klein (1849-1925)

As long as a branch of science can ask a large number of questions, it is full of vitality, and the lack of problems heralds the end or demise of independent development. - David Hilbert (1862-1943)

Problems are the heart of mathematics – Paul Halmos (1916-2006)

Time is a constant, but for those who are diligent, it is a "variable". People who use "minutes" to calculate time have 59 times more time than those who use "hours" to calculate time. - Rybakov

Chinese characters

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Zu Chongzhi

Things are pushed to each other, each has its own return, so although the branches are divided and the same stem knows, one end of the hair has been analyzed and reasoned, dismantled with the diagram, Shu is also about and can be Zhou, through but not reckless, the person who reads it thinks more than half - Liu Hui

The rate of delay is not out of the gods, it is tangible and detectable, and there are several that can be deduced - Zu Chongzhi (429-500)

New mathematical methods and concepts are often more important than solving mathematical problems themselves

Accurate and concise in mathematical expression, abstract and universal in logic, and flexible in form, it is an ideal tool for cosmic communication——Zhou Haizhong [4]

Science needs experiments, but experiments cannot be absolutely precise, and if there is a mathematical theory, it is all by inference, which is completely correct, and the reason why this science cannot be separated from mathematics

Many of the basic concepts of science often need mathematical concepts to represent that mathematicians have something to eat, but they can't win the Nobel Prize, because there is no Nobel Prize in natural mathematics, which is perhaps a good thing, and the Nobel Prize is too eye-catching, so that mathematicians can't focus on their own research

After modern high-energy physics has reached quantum physics, there are many experiments that cannot be done at all, and they can be calculated with paper and pen at home, which is not far from what mathematicians think, so mathematics has an incredible power in physics - Yau Chengtong

We should pay attention to the order of reading books and writing homework, and try to review the knowledge we have learned when we go home, especially the notes we take should be focused on, and then write homework, so that the effect is better