# Chen Jingrun

### Quick Info

Fuzhou, Fujian province, China

Beijing, China

**Chen Jingrun**was a Chinese mathematician who made outstanding advances in the study of Goldbach's Conjecture, proving that every sufficiently large integer can be represented as the sum of a prime and the product of at most two primes.

### Biography

**Chen Jingrun**was the son of Chen Yuanjun, a clerk in the post office. Chen Yuanjun and his wife had twelve children, with Chen Jingrun being the third. The family were poor but the children were looked after as well as the parents could in difficult circumstances. When Chen Yuanjun was four years old, in July 1937, the Second Chino-Japanese War broke out. Fujian province was a particularly bad place to be at this time since the Island of Taiwan was already controlled by Japan and the Japanese army invaded by crossing the Strait of Taiwan into Fujian province. Many fled to the mountains to avoid the fighting and Chen Jingrun's family went to Sanyuan County in the central part of Shaanxi province where Chen Yuanjun became the director of the post office which had been set up in an old temple.

For some time Chen Yuanjun's family were able to live in comparative peace in the mountains but in 1941 the war intensified and Japan began bombing Fujian province. Civilians fled to the mountains as refugees but Japanese troops followed them and took over control of the area where Chen Yuanjun's family were living. During the next few years the family lived in horrific circumstances which only ended in September 1945 when hostilities came to an end. The family were then able to return to Fuzhou in Fujian province where Chen Jingrun entered Sanyi Middle School. Although the terrors of the war were over, Chen Jingrun's life was still far from easy since he was a fragile child and was bullied at school. Things became far worse in 1947 when his mother died of tuberculosis.

In February 1948, he was admitted to the Fuzhou Yinghua Senior High School, the predecessor of the Middle School affiliated to Fujian Normal University. There he was taught mathematics by Shen Yuan (1916-2004) who became an important influence on his life. Shen Yuan had, like Chen Jingrun, been born in Fuzhou, Fujian province and had studied at Fuzhou Yinghua Senior High School. He studied at the Department of Mechanical Engineering of Tsinghua University but, after the outbreak of the Second Chino-Japanese War in 1937 transferred to Tsinghua University in Kunming where he studied Aeronautical Engineering. He studied for a Ph.D. at the University of London, England and was awarded the degree for his thesis on the compressible flow around a cylinder at high Mach number. Back in China in 1946 he taught mathematics at the Fuzhou Yinghua Senior High School, and taught in the Department of Aeronautical Engineering of Tsinghua University. One day he was teaching the class which Chen Jingrun attended and told them about Goldbach's Conjecture. He said:-

Mathematics is the queen of the sciences, number theory is the queen's crown, and the Goldbach's conjecture is the pearl on the crown.Shen Yuan jokingly said to the class that perhaps one day one of them would solve Goldbach's Conjecture and all the pupils laughed except Chen Jingrun. Xu Chi reported in [20] that many years later Chen Jingrun said:-

I did not laugh, I did not dare to laugh. I was worried my classmates would know my vision. But I never forgot this lesson to always remember the pearl on the crown and to never forget my aspirations or ideals.Chen Jingrun graduated from the Fuzhou Yinghua Senior High School in 1949 and later that year entered the Mathematics and Physics Department of Xiamen University. He enjoyed his undergraduate studies and was totally obsessed by mathematics [18]:-

Acquaintances remember Chen appearing on the Xiamen University campus in a black student uniform with a black cap, rubber shoes, carrying a small rattan box and bedroll; his brother, a Xiamen law student, gave Chen his coat to keep warm. Xiamen Professor of Mathematics Ha Fang Zhi related that Chen's study and life in the university was one of poverty "but [he was] obsessed with school."In September 1953 Chen Jingrun graduated from Xiamen University and became a mathematics teacher in Beijing No. 4 Middle School. It was quickly decided, however, that his teaching was not good enough since the pupils could not understand his accent, and he was told that he could only correct the pupils homework. In February 1954 he was dismissed from the school and he returned to his home town. When Wang Yanan, the president of Xiamen University, learnt what had happened to Chen Jingrun he was surprised given his outstanding undergraduate performance. Realising that Chen Jingrun might not be good at explaining simple mathematics to young children, Wang Yanan invited him to return to Xiamen University in 1955 as a librarian.

When the Chinese Civil War ended in 1949 with the mainland becoming the Communist People's Republic of China, many of the anti-Communist Chinese fled to the island of Taiwan and the Kinmen Islands close to Xiamen on mainland China. In late 1954 the People's Republic of China began shelling the Kinmen Islands in an attempt to take control and this continued to 1955. In Xiamen [15]:-

... air raid alarms were often sounded and the people hid in the air raid shelter. Chen brought several pages of Hua Loogeng's book "Additive Prime Number Theory" and studied it even in the shelter. The Chapter 4 "Mean value theorems of certain trigonometric sums II" in Hua's book discusses the mean value theorems of trigonometric sums of polynomials with lower degrees treated by Hua's method, and Chapter 5 "Vinogradov's mean value theorem and its applications" is devoted to the mean value theorems of trigonometric sums of polynomials with higher degrees by Vinogradov's method. Chen succeeded in using the method in Chapter 5 to improve some results in Chapter 4 of Hua's book. He wrote a paper "On Tarry's problem" and mailed to Hua Loogeng. Hua was confident in that Chen has high talent in mathematics after Chen's paper was approved by some mathematicians in the number theory section of the Institute of Mathematics, Academia Sinica.Hua Loogeng asked Chen Jingrun to present his results on Tarry's problem to the meeting of the Chinese Mathematical Society in Xiamen University in August 1956. At this meeting Hua Loogeng and Chen Jingrun met in person for the first time and, recognising his remarkable talents, Hua recommended Chen Jingrun for the position of assistant at the Institute of Mathematics at the Chinese Academy of Sciences. He took up the post in 1957 and began a period in which he produced some outstanding number theory results. His first paper

*On Waring's problem for n-th powers*(Chinese) appeared in

*Acta Mathematica Sinica*in 1958.

Waring's Problem concerns $g(k)$ and $G(k)$. The number $g(k)$ is the least integer such that every number is the sum of $g(k)$ or less $k$-th powers. The number $G(k)$ is the least integer such that every integer from a certain point onwards is the sum of $G(k)$ or less $k$-th powers. In the paper by Chen Jingrun quoted above, he shows that $G(k) ≤ k(3\log k + 5.2)$, improving on Ivan Matveevich Vinogradov result $G(k) ≤ k(3\log k + 11)$. In his next paper

*Waring's problem for g(5)*(1959), he shows that $37 ≤ g(5) ≤ 40$, improving on L E Dickson's result $37 ≤ g(5) ≤ 54$ published in 1933. Chen Jingrun finally achieved the result he sought for $g(5)$ in 1964 when he proved $g(5) = 37$. He had, however, produced a series of paper between 1959 and 1964 improving on several number theory results. These include:

*On the representation of a natural number as a sum of terms of the form*$\large\frac{1}{k!}\normalsize x(x+1) ... (x+k-1)$ (1959);

*The number of lattice points in a given region*(1962);

*Improvement of asymptotic formulas for the number of lattice points in a region of three dimensions*(1963);

*The lattice-points in a circle*(1963); and

*On the divisor problem for*$d_{3}(n)$.

For a list of Chen Jingrun's papers, see THIS LINK.

Chen Jingrun's output now became quite remarkable and he had eleven papers published in the two years 1964-1965. It is even more remarkable when we realise that his main work during these two years was on the Goldbach conjecture. He made a major breakthrough and proved that a large even integer can be represented as the sum of a prime and the product of at most two primes. He showed the proof to a colleague Min Shie who suggested that, as the result was an important breakthrough in attacking the Goldbach conjecture, Chen Jingrun should announce the result and then tidy up the proof before publishing the details. An announcement and brief sketch of the proof was published in the paper

*On the representation of a larger even integer as the sum of a prime and the product of at most two primes*(1966).

The timing proved extremely unfortunate since the announcement of Chen Jingrun's theorem coincided with the Cultural Revolution which was launched by Mao Zedong, Chairman of the Chinese Communist Party, in May 1966 with the aim of ending any opposition to Communism. Academics were particularly targeted with schools and universities being closed and teachers and professors persecuted. Members of the Chinese Academy of Sciences were badly affected, and research stopped. Many academics were sent to work in rural farming communities. Chen Jingrun was forced to do manual labour, and lived in a room converted from a boiler room [18]:-

Chen was constantly harassed by the newly formed young militant political activist regimen, the "Red Guards," who vigorously sought out pockets of dissent, especially among those they labelled "intellectuals" or anyone who held traditional Chinese beliefs. Chen was frequently insulted, spat on, and beaten. The attacks were often so severe that Chen would lose consciousness. Amazingly, even under these horrible conditions, Chen kept working on his mathematical interests. ... As more obvious and expedient targets for the Red Guards emerged, Chen was fortunately left alone and was able to secretly resume his studies, working by kerosene lamp because he was provided no electricity. Chen subsequently became chronically sick; the horrors of his life were having severe physical effects on him ...While in the Institute in 1966 it is thought that Chen Jingrun was beaten and he [18]:-

... may have attempted suicide by jumping out of a third-floor window at the institute, where he landed on a balcony of the second floor and sustained a leg injury.Conditions for academics greatly improved in 1971 after the First Vice Premier Lin Biao died in a plane crash. He was replaced by Zhou Enlai who was better disposed towards science and academics, and the Chinese Academy of Sciences began operating again. Chen Jingrun returned to working on publishing the proof of his major contribution to the Goldbach Conjecture which he had announced in 1966. When it was completed in 1973 he was unsure what to do. One day he met Luo Shengxiong who headed a department at the Mathematical Institute of the Chinese Academy of Sciences. Chen Jingrun told him that he had completed the proof and wanted to publish it but was afraid of being criticised. Luo Shengxiong said that provided the proof was correct, Chen Jingrun should not be afraid. Luo Shengxiong asked a military representative to persuade Chen Jingrun to publish and told him he had nothing to fear. First Vice Premier Zhou Enlai had told the Chinese Academy of Sciences to strengthen research and a meeting of the Academy took place at which the head of the Academy spoke of the importance of Chen Jingrun's theorem. Some members objected to Chen Jingrun's work, saying it was not in line with the aims of the Cultural Revolution. It was also criticised as having no practical significance. Despite opposition, the Chinese Academy of Sciences supported publication of Chen Jingrun's paper proving that every large even integer can be represented as the sum of a prime and the product of at most two primes. It was published in April 1973 was quickly recognised as a major step forward in attacking the Goldbach Conjecture.

Heine Halberstam and Hans Egon Richert were in the process of having their book

*Sieve Methods*printed when they became aware of Chen Jingrun theorem. They added the chapter "Chen's Theorem" to their book

*Sieve Methods*beginning this new chapter as follows:-

Our object in this chapter will be to prove the following remarkable result of Jin-run Chen, which came to our attention only after Chapters 1-10 had gone to press; it constitutes a splendid climax to any account of sieve theory.After reading Chen Jingrun's paper, André Weil said:-

Chen Jingrun's work is like walking on the top of the Himalayas, every step is very difficult.There was still questions about Chen Jingrun's political views, particularly since he tried hard to avoid being involved in politics in any way. He had, however, brought fame to China and it was quickly realised that his health was in a very poor way. Reports on his health were transmitted to Chairman Mao and to Jiang Qing who required that he get immediate medical attention. He received treatment in hospital for a few months, then returned to the Institute of Mathematics at the Chinese Academy of Sciences and went back to working on the Goldbach Conjecture.

In 1976 the Cultural Revolution ended following the death of Mao Zedong and the development of science became a major aim. Chen Jingrun received much recognition and fame in China and abroad [18]:-

Chen became a "science hero" in China, and his work on Goldbach's conjecture even became a topic of public interest. His images and stories of his life constantly appeared in various newspapers, books, television programs, and even movies. In addition to achieving fame, Chen inspired many students to study science.He received many honours [3]:-

In January 1975, he was elected as a deputy to the Fourth National People's Congress, and later served as a deputy to the Fifth and Sixth National People's Congress. Exceptionally he was promoted to researcher in 1977. In 1979, he was invited by the Institute for Advanced Study in Princeton to visit and give lectures, and he received extensive praise from the international community. In 1980, he was elected as a member of the Department of Physics and Mathematics of the Chinese Academy of Sciences. In March 1981, he was elected as a full member of the Chinese Academy of Sciences. In 1988, he was designated as a first-class researcher. In 1992, he served as the editor-in-chief of "Acta Mathematica" and won the first Hua Loo-Keng Mathematics Award.The International Congress of Mathematicians was to be held in Helsinki, Finland, in August 1978. The scientific programme was the responsibility of the International Mathematical Union through their Consultative Committee, whose chairman was Armand Borel. The Consultative Committee took advice from panels of the various sections on who should be invited and the Number Theory Section panel recommended Chen Jingrun be invited. He was invited by the International Mathematical Union to give a 45-minute talk and, after receiving the invitation gave it serious consideration. He did not accept, however, sending the following reply to the International Mathematical Union:-

First, my country has always attached great importance to the development of academic exchanges and friendly relations with scientists from all over the world. Therefore, I would like to thank the President of the International Mathematical Union. Second, there is only one China in the world, the People's Republic of China, Taiwan is an inalienable province of China, and Taiwan currently occupies the seat of our country in the International Mathematical Union, therefore, I cannot participate. Third, if the Taiwan representative is expelled, I can consider attending.At the 1978 Congress, Henryk Iwaniec, a Polish mathematician at the Institute of Mathematics of the Polish Academy of Sciences, addressed the Number Theory Section with his talk

*Sieve Methods*. He said:-

Recently Chen [On the representation of a larger even integer as the sum of a prime and the product of at most two primes (1973)] caused a sensation by his proof of the following result, the last but one approximation to the solution of the Goldbach problem:As we have seen, Chen Jingrun's health was poor even before he was hospitalised in 1973. Certainly despite the steady stream of outstanding research he produced, he struggled with illness. In November 1977 his admission to the No. 309 Liberation Army Hospital was arranged by Vice Premier Deng Xiaoping [6]:-

THEOREM 1. Every sufficiently large even number N is a sum of a prime and the product of at most two primes.

...

In the speaker's opinion, a real revolution in the sieve theory has been initiated by another achievement of Chen [On the distribution of almost primes in an interval (1975)]:

THEOREM 2. If x is sufficiently large then there must be the product of at most two primes in the interval (x, x + √x).

The news that the great mathematician Chen Jingrun was recuperating in the 309 hospital quickly spread, causing a sensation in the whole hospital. To be honest, everyone really wanted to see this genius mathematician, but they were too embarrassed to disturb him, so they always hid at the door. Looking around quietly, Chen Jingrun didn't say anything, but smiled at everyone.You Kun was a 22-year old doctor studying at the hospital, and after she had met Chen Jingrun and they had got on well together, she was assigned to Chen Jingrun's ward as the doctor on duty. They became close friends and after Chen Jingrun left the hospital the two continued to communicate. Eventually Chen Jingrun, who had previously found talking to women difficult, asked her to marry him. They were married in Beijing on 25 August 1980 and their only child, a son Chen Youwei, was born in 1981.

In April 1984 Chen Jingrun, who was working at the Mathematical Institute of the Chinese Academy of Sciences in Beijing, cycled from his home to the Xinhua Bookshop. He was hit by a fast moving cyclist, was knocked unconscious, and was taken to hospital. When treating him for head injuries, the doctors realised that he had problems which were not a consequence of the accident and he was diagnosed with Parkinson's disease. A few months later, when getting off a bus, he was pushed by a crowd and again fell causing concussion. Although he made some slow progress, he was hospitalised for a long time and received many treatments, both Western and traditional Chinese. He returned to mathematics although his mental powers were seriously affected by his illness. All his papers after 1986 were joint ones and, because of Parkinson's disease, he probably was unable to make much of a contribution to them, although his students greatly appreciated working with such a famous mathematician. He died of pneumonia at the age of 63 years.

Following his death in 1996, his achievements continued to be honoured. In 1999 China issued a commemorative 80-yuan stamp "The Best Result of Goldbach Conjecture" with a silhouette of Chen Jingrun. On 19 September 2020 China issued a "Chen Jingrun, Mathematician" 1.20 renminbi yuan stamp with his portrait. See THIS LINK.

The Minor Planet Center, part of the Smithsonian Astrophysical Observatory, named asteroid 7681 Chenjingrun after him. In 2006, Xiamen University erected a seated bronze statue of Chen Jingrun near its School of Mathematical Sciences. The Chinese Academy of Sciences presents the Chen Jingrun Award for Young Talents.

### References (show)

- About Chen Jingrun (Chinese),
*Department of the Central Committee of the Communist Party of China*(2019).

http://zmfdz.news.cn/188/index.html - Biography of the mathematician Chen Jingrun, known as "the first person in Goldbach's conjecture" (Chinese),
*new.qq.com*(2 February 2021).

https://new.qq.com/omn/20210202/20210202A00M8L00.html - Chen Jingrun, Academician of Chinese Academy of Sciences, Mathematician (Chinese),
*baike.baidu.com*.

https://baike.baidu.com/item/陈景润/18067 - Chen Jingrun (Chinese),
*baike.sogou.com*.

https://baike.sogou.com/m/fullLemma?lid=238171 - Chen Jingrun: Famous Chinese mathematician (Chinese),
*Kuaike Encyclopedia*.

https://www.baike.com/wikiid/3061343922713330643?prd=mobile&view_id=364rvv265qrhmo - Chen Jingrun's wife, You Kun: She is still alive, living alone in an old house of 60 square metres and living on pensions (Chinese),
*163.com*(9 January 2021).

https://www.163.com/dy/article/FVSOMI3005373W4L.html - Chen Jingrun had a son at the age of 48 and died of illness at the age of 62. How is the achievement of his only son now?,
*MINNEWS*.

https://min.news/en/tech/5c5cdc03b5b947a5f1eb68fb9bfc3706.html - Chen Jingrun: A world-famous mathematician who married a female military doctor who was 18 years old at the age of 47,
*DayDayNews*(18 June 2020).

https://daydaynews.cc/en/science/624194.html - D E Falbo, Almost Goldbach theorems,
*The Mathematical Gazette***105**(562) (2021), 111-116. - Genius mathematician Chen Jingrun, 47-year-old married a 29-year-old female military doctor (Chinese),
*sohu.com*(21 October 2020).

http://www.sohu.com/a/426238597_572660 - Liaocheng University, Xu Chi's reporting breakthrough, Experience and Warning Significance (Chinese),
*chinawriter.com.cn*.

http://www.chinawriter.com.cn/n1/2017/1218/c405173-29711930.html - Li Wen Zhu, The legacy of Jing Run Chen (Chinese),
*J. Math. Study***30**(1) (1997), 110-112. - March 19: Chen Jingrun passed away (Chinese),
*The Central People's Government of the People's Republic of China*(1996).

https://baike.baidu.com/reference/18067/c3e5jw5SEo7BZhxlcw9_63zJxXmr8dgRrGQi4zg1F5FF7Qdn9xjEijVSh5adVkpA3oTNZYqmqhmQ1f9T7N60y2y2kaQT_15HzA - Model of the times - Chen Jingrun (Chinese),
*China News Service*.

https://baike.baidu.com/reference/18067/fd1duVy-py0ZUyjfXkGfZtLOUcQ2ukCjnpRYtR6yNw39kSuci50OzsS4yDxGcu6QWcDIpDJuY94hFbSXVpsnyd8rVEBxyhu3-qa-DU_MacxLcMHfVgjtuBpFNds - Pan Chengtong and Wang Yuan, Chen Jingrun: A brief outline of his life and works,
*Acta Mathematica Sinica, New Series***12**(3) (1996), 225-233. - Professor Chen-Jing-Run (22-05-1933 to 19-03-1996),
*Hardy-Ramanujan J.***23**(2000), 21-23. - Shen Shihao, Chen Jingrun (Chinese),
*99csw.com*.

https://99csw.com/book/40/index.htm - Ting Lei, Evgenii Belykh, Alexander B Dru, Kaan Yagmurlu, Ali M Elhadi, Peter Nakaji, and Mark C Preul, Chen Jingrun, China's famous mathematician: devastated by brain injuries on the doorstep to solving a fundamental mathematical puzzle
- Wu Biwen, The real Chen Jingrun who tried to commit suicide by jumping off the building in despair (Chinese),
*Centre for Chinese Studies, Chinese University of Hong Kong*.

http://mjlsh.usc.cuhk.edu.hk/Book.aspx?cid=4&tid=3656 - Xu Chi,
*Goldbach's Conjecture*(Chinese) (People's Literature, 1978). - Yuan Wang and Cheng Dong Pan, A brief outline of the life and work of Jing RunChen (Chinese),
*Acta Math. Sinica (Chin. Ser.)***39**(4) (1996), 433-441. - Yuan Wang (ed.),
*Goldbach Conjecture*(World Scientific, Singapore, 1984). - Yuwu Song, Chen Jingrun (1933-1996), in
*Biographical Dictionary of the People's Republic of China*(McFarland, 2014), 35. - Zhang Shouren, Uncovering the Mystery of the Poet Xu Chi's Jumping from a Building (Chinese),
*Centre for Chinese Studies, Chinese University of Hong Kong*(2016).

http://mjlsh.usc.cuhk.edu.hk/Book.aspx?cid=4&tid=3821

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Written by J J O'Connor and E F Robertson

Last Update March 2022

Last Update March 2022