Early years (1910–1936) Hua Luogeng was born in
Jintan, Jiangsu on 12 November 1910. Hua's father was a small businessman. Hua met a capable math teacher in middle school who recognized his talent early and encouraged him to read advanced texts. After middle school, Hua enrolled in Chinese Vocational College in
Shanghai, and there he distinguished himself by winning a national abacus competition. Although tuition fees at the college were low, living costs proved too high for his means, and Hua was forced to leave a term before graduating. After failing to find a job in Shanghai, Hua returned home in 1927 to help in his father's store. In 1929, Hua contracted
typhoid fever and was in bed for half a year. The culmination of Hua's illness resulted in the partial paralysis of his left leg, which impeded his movement quite severely for the rest of his life. After middle school, Hua continued to study mathematics independently with the few books he had, and studied the entire high school and early undergraduate math curriculum. By the time Hua returned to Jintan, he was already engaged in independent mathematics research, and his first publication
Some Researches on the Theorem of Sturm, appeared in the December 1929 issue of the Shanghai periodical
Science. In the following year Hua showed in a short note in the same journal that a certain 1926 paper claiming to have solved the
quintic was fundamentally flawed. Hua's lucid analysis caught the eye of Prof.
Xiong Qinglai at
Tsinghua University in
Beijing, and in 1931 Hua was invited, despite his lack of formal qualification and not without some reservations on the part of several faculty members, to join the mathematics department there. At Tsinghua, Hua began as a clerk in the library, and then moved to become an assistant in mathematics. By September 1932, he was an instructor, and two years later, after having published another dozen papers, he was promoted to the rank of lecturer. During 1935–36
Jacques Hadamard and
Norbert Wiener visited Tsinghua, and Hua eagerly attended the lectures of both and created a good impression. Wiener visited England soon afterward and spoke of Hua to
G. H. Hardy. In this way Hua received an invitation to Cambridge, England, where he stayed for two years.
Early middle years (1936–1950) At
Cambridge University, Hua worked on applying the
Hardy–Littlewood circle method to problems in number theory. He produced seminal work on
Waring's problem, which established his reputation in the international math community. In 1938, after the full outbreak of the
Second Sino-Japanese War, Hua returned to China to Tsinghua, where he was appointed full professor despite having no degree. At the time, with vast areas of China under Japanese occupation,
Tsinghua University,
Peking University, and
Nankai University had merged into the
Southwest Associated University in
Kunming, capital of the southern province
Yunnan. In spite of the hardships of poverty, enemy bombings, and relative academic isolation from the rest of the world, Hua continued to produce first-rate mathematics. During his eight years there, Hua studied
Vinogradov's seminal method of estimating trigonometric sums and reformulated it in sharper form, in what is now known universally as Vinogradov's mean value theorem. This result is central to improved versions of the
Hilbert–Waring theorem, and has important applications to the study of the
Riemann zeta function. Hua wrote up this work in his booklet
Additive Theory of Prime Numbers, which was accepted for publication in Russia as early as 1940, but, owing to the war, did not appear in expanded form until 1947 as a monograph of the
Steklov Institute. In the closing years of the Kunming period, Hua turned to
algebra and
analysis, to which he soon began to make original contributions. After the war, Hua spent three months in the Soviet Union in the spring of 1946, at
Ivan Vinogradov's invitation, after which he departed for the
Institute for Advanced Study in
Princeton, New Jersey. There, Hua worked on
matrix theory, functions of
several complex variables, and
group theory. At this time civil war was raging in China and it was not easy to travel, and for "convenience of travel," the Chinese authorities assigned Hua the rank of general in his passport. In the spring of 1948, Hua accepted appointment as full professor at the
University of Illinois Urbana–Champaign, but his stay in Illinois was brief. In October 1949, the
People's Republic of China was established, and Hua, wanting to be part of a new epoch, returned to China with his wife and children, despite having comfortably settled in the United States.
Later career in China (1950–1985) Back in China, Hua threw himself into educational reform and the organization of mathematical activity at the graduate level, in the schools, and among workers in the burgeoning industry. In July 1952 the Mathematical Institute of the
Chinese Academy of Sciences (CAS) came into being, with Hua as its first director. In 1953, he was one of a 26-member delegation from CAS to visit the Soviet Union to establish links with Russian science. Later, he was the first chair of the Department of Mathematics and Vice President of
University of Science & Technology of China (USTC), a new type of Chinese university established by CAS in 1958, aimed at fostering skilled researchers necessary for the economic development, defense and education in science and technology. Despite his many teaching and administrative duties, Hua remained active in research and continued to write, not only on topics that had engaged him before but also in areas that were new to him or had been only lightly touched on before. In 1956, his voluminous text
Introduction to Number Theory appeared. It was later published in English by
Springer.
Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains came out in 1958 and was translated into Russian in the same year, followed by an English translation by the
American Mathematical Society in 1963. Outside of pure math, Hua first proposed in 1952 the development of China's
electronic computer, and in early 1953, an initial research team for this project was formed under Hua's leadership by the Mathematical Institute of the Chinese Academy of Sciences. The start of the
Great Leap Forward in 1958 came with a vehement attack on pure mathematics and intellectuals, prompting Hua to shift to
applied mathematics. He and
Wang Yuan developed a broad interest in
linear programming,
operations research, and
multidimensional numerical integration. In connection with the last of these, the study of the
Monte Carlo method and the role of
uniform distribution led them to invent an alternative deterministic method based on ideas from
algebraic number theory. Their theory was set out in
Applications of Number Theory to Numerical Analysis, which was published in 1978, and by Springer in English translation in 1981. The newfound interest in
applicable mathematics took him in the 1960s, accompanied by a team of assistants, all over China to show workers of all kinds how to apply their reasoning to shop-floor and everyday problems. Whether in ad hoc problem-solving sessions in factories or open-air teachings, he touched his audiences with the spirit of mathematics to such an extent that he became a national hero and even earned an unsolicited letter of commendation from
Mao Zedong, a valuable protection in uncertain times. Hua had a commanding presence, a genial personality, and a talent for putting things simply, and his travels spread his fame and the popularity of mathematics across the land. After the
Cultural Revolution, Hua resumed contact with Western mathematicians. In 1980 Hua became a cultural ambassador of China charged with re-establishing links with Western academics, and over the next five years he traveled extensively in Europe, the United States, and Japan. In 1979 he was a visiting research fellow of the then Science Research Council of the United Kingdom at the
University of Birmingham and during 1983–84 he was Sherman Fairchild Distinguished Scholar at the
California Institute of Technology. He died of a heart attack at the end of a lecture he gave in Tokyo on 12 June 1985.
Hua Luogeng Park in Jintan, Jiangsu, is named after him. ==Works==