Yang Wuzhi

Yang Wuzhi

Yang Wuzhi (April 14, 1896 - May 12, 1973), originally named kechun, was born in Fengyang, Anhui Province. He was born in Hefei, Anhui Province on April 14, 1896. He is a mathematician and mathematical educator. Long term in Tsinghua University and southwest United University Mathematics Department as head or acting director. He is the father of Nobel laureate Yang Zhenning, an early scholar engaged in the teaching and research of modern number theory and algebra in China. Yang Wuzhi's main academic contribution is the study of number theory, especially his work on Waring problem. Yang Wuzhi devoted his whole life to mathematics education, especially when he taught and presided over the Department of Tsinghua University and southwest United University. He cultivated and brought up two generations of mathematics talents and made great contributions to modern mathematics in China.

Life of the characters

Chronology of Events

Yang Wuzhi is from Fengyang, Anhui Province.

He was born on April 14, 1896 in Hefei, Anhui Province (now belongs to Feixi County).

He graduated from Anhui Provincial No.2 Middle School in 1914.

He graduated from Beijing Normal University from 1914 to 1918.

From 1918 to 1922, he was a teacher of Anhui Provincial No.2 Middle School and Anhui Anqing middle school.

From 1923 to 1928, he went to the United States to study and obtained master's and doctor's degrees at the University of Chicago.

He was a professor of Xiamen University from 1928 to 1929.

He was a professor of Tsinghua University from 1929 to 1937.

He was a professor of southwest United University from 1937 to 1946.

He was a professor of Tsinghua University from 1946 to 1949.

He was a professor of Tongji University from 1950 to 1952.

He was a professor of Fudan University from 1950 to 1973.

He died in Shanghai on May 12, 1973.

teenagers

Yang Bangsheng, Yang Wuzhi's father, was a scholar in the late Qing Dynasty. In his early years, he had been teaching in private schools. Later, he went to Tianjin, where he took charge of "writing letters" in Duan Zhigui's shogunate, doing similar things. In 1907, due to Duan Zhigui's loss of power, he went home to work. The next year, I wanted to seek a job in Shenyang. Unfortunately, I caught the plague in the hotel and died. Yang Wuzhi's mother, Wang, died when he was 9 years old (1905). Therefore, Yang Bangsheng and his wife did not take care of Yang Wuzhi much, and their life was mostly arranged by their uncle Yang bangrui.

In 1914, Yang Wuzhi graduated from Anhui Provincial No.2 Middle School. This is a good school, which has laid a good cultural foundation for Yang Wuzhi. In the autumn of this year, he was admitted to the preparatory course of Beijing Normal University for a period of one year. He was required to study for three years and graduated in 1918. This degree was the highest level in the normal education at that time, and all over the country competed for employment. Finally, Yang Wuzhi decided to return to his alma mater, No.2 Middle School of Anhui Province, as a teacher and supervisor. Yang Wuzhi, a young and vigorous man, had strict discipline in his school and had strict control over a group of dandies. According to the school's regulations, the school gate will be closed at 10 pm, so that a group of students who have been out for fun and come back late will not be allowed to enter. As a result, some students who didn't want to make progress were very dissatisfied with Yang Wuzhi, the warden of the house. They even started to make trouble and prepare to use force to retaliate. After the disturbance, the parents of the students tried to let it go because they were protecting the students. Yang Wuzhi resigned angrily and transferred to Anqing middle school to teach. This incident deeply stimulated him. He felt that it was difficult for a scholar to deal with the corrupt government and local tyrants and evil gentry. Therefore, Yang Wuzhi came up with the idea of "saving the country by science", hoping to change the dark reality of China by studying abroad, revitalizing Chinese science and carrying forward Chinese civilization. During the period of teaching in Anqing, I actively prepared for the examination of studying abroad. Yang Wuzhi was decided by his parents. When he was young, he was engaged to Luo Menghua, the daughter of fellow countryman Luo Zhuquan, and married him in 1919. Luo Menghua's culture is not high, has been running the housework. They have a strong relationship with each other and will never change. In 1922, the eldest son Yang Zhenning was born. Yang Wuzhi's preparation for the exam has also reached a tense stage.

Academic success

In the spring of 1923, Yang Wuzhi successfully passed the examination of studying abroad at public expense in Anhui Province. Then he left his wife and son under one year old and went to the United States to study alone. He first went to Stanford University in the west of the United States to study for three seasons and obtain a bachelor's degree. He then transferred to the University of Chicago in the fall of 1924. Yang Wuzhi studied algebra and number theory under the guidance of L.E. Dickson. In 1926, he got his master's degree in the paper invariants of bilinear forms. Two years later, Yang Wuzhi became the first doctor in the study of factor theory in China with his book various promotion of Hualin problem.

In the autumn of 1928, Yang Wuzhi returned home from his studies. He first taught in Xiamen University for one year. The next year, he was employed by Tsinghua University as a professor of mathematics. Since then, Yang Wuzhi has been teaching at Tsinghua University (including southwest United University during the Anti Japanese War) until liberation. After 1950, he stayed in Shanghai Fudan University as a professor of mathematics. At the end of 1948, Yang Wuzhi flew back to Nanjing from Peiping, and then transferred to Kunming to meet his family members in Shanghai to welcome the liberation. In 1950, Tsinghua University did not re employ Yang Wuzhi, so he stayed in Shanghai and became a professor of mathematics at Tongji University. He began to teach in Fudan University in 1952. In the 1950s, he taught several courses in Fudan University. Later, he recuperated at home because of diabetes.

In 1957, Yang Zhenning, Yang Wuzhi's eldest son, won the Nobel Prize in physics, which excited him very much. In 1957, 1960 and 1964, he went to live in Geneva for three times. He got together with Yang Zhenning and met with his old friends and students abroad, such as Chen Shengshen. These gatherings made Yang Zhenning know more about new China and directly influenced his decision to return to the mainland to visit his relatives in the summer of 1971. Yang Zhenning became one of the first overseas famous scholars to visit the people's Republic of China.

old age

In his later years, Yang Wuzhi was in poor health and seldom went out. He loves traditional culture, especially go.

On May 12, 1973, Yang Wuzhi died in Shanghai.

Research on number theory

Doctoral dissertation: promoting the "warringian problem of pyramid numbers"

The study of number theory in China has a long history. Sun Tzu's theorem, Chinese Remainder Theorem and Qin Jiushao's theory of Diophantine equation are all famous works in the world. However, by the time of Ming and Qing Dynasties, the study of number theory had lagged far behind that of Europe. By the 1920s, Yang Wuzhi should be the first Chinese who could study modern number theory and publish creative papers.

The so-called warringian problem refers to the following conjecture: every positive integer is the sum of four square numbers, the sum of nine cubic numbers, and generally, the sum of G (k) k-th power numbers. In 1770, J. - L. Lagrange proved that every positive integer is indeed the sum of four squares, that is, G (2) = 4. In 1909, the great mathematician D. Hilbert proved that G (k) must be a finite number. In 1928, Dixon, Yang Wuzhi's tutor, proved that G (3) = 9. In addition, Baer proved that an integer greater than 23 × 1014 is the sum of eight cubic numbers. So Dixon asked Yang Wuzhi to consider the warringian problem with coefficients, that is, whether every positive integer f can be expressed as F = RX3 + C7, where C7 = X31 + X32 + C7 X 37, r = 0, 1, 2 The following results were obtained by Yang Wuzhi

1. All positive integers larger than 14.1 × 4016 can be expressed as RX3 + C7, where r = 5,7.

2. Any positive integer greater than (30.1) × 4196 can be expressed as 3x3 + C7.

3. All positive integers greater than 23 × 1014 can be expressed as 8 × C3 + C7.

4. All odd positive integers larger than 23 × 1014 can be expressed as RX3 + C7, where r = 2,4,6.

5. Any double of odd positive integer greater than 23 × 1014 can be expressed as 2x3 + 7.

In his doctoral dissertation, Yang Wuzhi also discussed the representation of 7th power numbers with coefficients.

Yang Wuzhi's best work is on the warringian problem of pyramid numbers. The pyramid number P (n) = 1 / 6 (n3-n) is a generalization of the triangle number f (n) = n / 2 (n + 1). In 1640, Fermat conjectured that every positive integer is the sum of no more than three triangles. It turned out to be right. As for the fact that each positive integer can be expressed as the sum of several pyramid numbers, it has been studied one after another. In 1896, W.J. Maillet first obtained that every sufficiently large positive integer is the sum of 12 pyramid numbers. In 1928, Yang Wuzhi proved in his doctoral dissertation that:

Every positive integer can be written as the sum of nine pyramid numbers. This result did not improve in more than 20 years, until G.N. Watson reduced "9" to "8" in 1952. Up to 1991, this is still the best result that has been proved.

After the advent of the computer, many people have made practical calculations and thought that except for 241 exceptions, all positive integers less than 106 are the sum of five pyramid numbers. In 1991, Yang Zhenning and Deng Yuefan calculated that all positive integers less than 109 except 17, 27 In addition to 241 exceptions, they are all the sum of four pyramid numbers. They conjectured that except for these 241 numbers, four pyramid numbers are enough to represent any positive integer.

Yang Wuzhi's doctoral thesis was first introduced at the meeting of American Mathematical Society (April 6, 1928). In the same year, it was reported in the bulletin of the American Mathematical Society, Vol. 34, P. 412. The full text will be published later

Chinese PinYin : Yang Wu Zhi