# Yuan Wang

### Quick Info

Lanxi, Zhejiang province, China

**Wang Yuan**is a Chinese mathematician best known for his contributions to the Goldbach conjecture.

### Biography

**Wang Yuan**was born in Lanhsi, a town on the Lan River. It is in Chekiang province (also called Che-chiang or Zhejiang province), a coastal province bordering the East China Sea. His father, Wang Maoqing, was a county magistrate. Wang Yuan spent the first seven years of his childhood in Lanhsi which at that time was in an area benefiting from modernization programs, but things changed in 1937 when war broke out between China and Japan. Chekiang province was in the front line for Japanese attacks and many people left the province and moved to safer areas further west such as to Szechwan province (also called Ssu-ch'uan or Sichuan province). This is where Wang Yuan's family moved in 1937, leaving Chekiang province before the Japanese occupied much of it which they did by 1938. The family moved to Jiangbei which is now known as Yubei. It lies close to Chungking (also called Ch'ung-ch'ing, or Chongqing) the largest city of Szechwan province. There Wang Yuan completed his primary schooling in a modest school since at this stage his family were rather poor.

In 1942 Wang Yuan's father became the chief secretary in the Academia Sinica, the Chinese national research organization. Wang Yuan enrolled in the National Second Middle School in Ho-ch'uan (also called Ho-yang, Hechuan, or Heyang), still in Szechwan province, However, in 1946 his family moved to Nanking (also called Nan-ching or Nanjing) the capital of Kiangsu province where he attended the middle school attached to the Social Education College. He graduated in 1948 and entered Yingshi University to study mathematics. After one year of study Yingshi University became part of Chekiang University (founded in 1897) in Hangchow. This was fortunate since Chekiang University had a strong mathematics department with an excellent seminar organised for graduate students. Wang Yuan fell in love with analytic number theory and gave a series of lectures to the graduate seminar based on Ingham's book

*The distribution of prime numbers*.

Wang Yuan graduated in 1952 and was assigned a position by the government in the Institute of Mathematics at the Academia Sinica in Nanking. Chern had acted as director there from 1946 to 1949 but had returned to the United States three years before Wang Yuan started to work there. Wang Yuan was assigned to the number theory section where he worked under Professor Hua Loo Keng, the director of the Institute.

Most of Wang Yuan's research has been in the area of number theory. He looked at sieve methods and applied them to the Goldbach Conjecture. He also applied circle methods to the Goldbach Conjecture. In 1956 he published (in Chinese)

*On the representation of large even integer as a sum of a prime and a product of at most 4 primes*in which he assumed the truth of the Riemann hypothesis and with that assumption proved that every large even integer is the sum of a prime and of a product of at most 4 primes. He also proved that there are infinitely many primes $p$ such that $p + 2$ is a product of at most 4 primes. In 1957 Wang Yuan published four papers:

*On sieve methods and some of their applications; On some properties of integral valued polynomials; On the representation of large even number as a sum of two almost-primes*; and

*On sieve methods and some of the related problems*. In the first of these he proved, among other results, that for infinitely many integers $n, n^{3} + 2$ has at most 4 prime factors. In the third paper he proved that every even integer is the sum of two integers each of which has at most 5 prime factors. The last of the four 1957 papers proved, this time assuming the Riemann hypothesis, that every sufficiently large even integer is the sum of a prime and a product of at most 3 primes, and there are infinitely many primes $p$ such that $p + 2$ is the product of at most 3 primes.

Wang Yuan continued to improve his results on the Goldbach conjecture. In 1958

*On sieve methods and some of their applications. I*showed that every even integer is the sum of two integers, one of which has at most 2 prime factors, the other having at most 3 prime factors. He also attacked other questions in number theory in papers such as

*On the least primitive root of a prime*(1959) and

*On Diophantine approximations and numerical integrations. I, II*(1964). Also in 1964 he published two papers on orthogonal Latin squares:

*A note on the maximal number of pairwise orthogonal Latin squares of a given order*; and

*On the maximal number of pairwise orthogonal latin squares of order s, an application of the sieve method*.

Political changes in China meant that his research stopped in 1966. The Chinese Communist Party chairman Mao Zedong launched the Cultural Revolution in August 1966. Schools were shut, there was widespread disorder, and many intellectuals were not only verbally attacked but were physically abused. Higher education was greatly curtailed, for example education at Peking University ceased from 1966 to 1970. Wang Yuan was harassed and put through critical interrogation. From 1966 to 1972 he did no mathematical research but after 1972 he resumed his research activities, although never as vigorously as before the start of the Cultural Revolution. However he did write a number of books such as: (with Hua Loo Keng)

*Applications of number theory to numerical analysis*(1978);

*Goldbach Conjecture*(1984); (with Hua Loo Keng)

*Popularising mathematical methods in the People's Republic of China*(1989);

*Diophantine equations and inequalities in algebraic number fields*(1991); (with Fang Kai-Tai)

*Number theoretic methods in statistics*(1994);

*Hua Loo Keng*(1995); and (with Fong Yuen)

*Calculus*(1997).

In 1978 Wang Yuan was promoted to professor at the Institute of Mathematics at the Academia Sinica and elected to membership of the Academia Sinica in 1980. In 1984 he became director of the Institute of Mathematics at the Academia Sinica. He was elected as president of the Chinese Mathematical Society during 1988-92. He was also honoured with many prizes for his books promoting mathematical learning.

Finally let us note that he became interested in the history of mathematics and published

*Analytic number theory in China*in 2001.

### References (show)

- Y Wang (ed.),
*Selected papers of Wang Yuan*(World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005). - W Li and X Yuan, Wang Yuan: a brief outline of his life and works, in
*Y Wang (ed.), Selected papers of Wang Yuan*(World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005), xi-xxii. - Y Wang, Analytic number theory in China (Chinese),
*Adv. Math. (China)***30**(4) (2001), 289-292.

### Additional Resources (show)

Other websites about Wang Yuan:

Written by J J O'Connor and E F Robertson

Last Update November 2006

Last Update November 2006