**Hau Loo-Keng** was a Chinese mathematician and politician famous for his important contributions to number theory.

- If many Chinese mathematicians nowadays are making distinguished contributions at the frontiers of science and if mathematics in China enjoys high popularity in public esteem, that is due in large measure to the leadership Hua gave his country, as scholar and teacher, for 50 years.
- Hua was born in 1910 in Jintan in the southern Jiangsu Province of China.
- Fortunately Hua was blessed from the start with a cheerful and optimistic disposition, which stood him in good stead then and during the many trials ahead.
- Hua's formal education was brief and, on the face of it, hardly a preparation for an academic career - the first degree he would receive was an honorary doctorate from the University of Nancy in France in 1980; nevertheless, it was of a quality that did help his intellectual development.
- The Jintan Middle School that opened in 1922 just when he had completed elementary school had a well-qualified and demanding mathematics teacher who recognized Hua's talent and nurtured it.
- In addition, Hua learned early on to make up for the lack of books, and later of scientific literature, by tackling problems directly from first principles, an attitude that he maintained enthusiastically throughout his life and encouraged his students in later years to adopt.
- Next, Hua gained admission to the 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.
- By the time Hua returned to Jintan he was already engaged in mathematics 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 Xiong Qinglai at Quing Hua 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.
- By that time he had published another dozen papers and in some of these one could begin to find intimations of his future interests; thanks to his natural talent and dedication, Hua was now, at the age of 24, a professional mathematician.
- At this time Quing Hua University was the leading Chinese institution of higher education, and its faculty was in the forefront of the endeavour to bring the country's mathematics and science abreast of knowledge in the West, a formidable task after several hundred years of stagnation.
- During 1935-36 Hadamard and Norbert Wiener visited the university; 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 come to Cambridge, England, and he arrived in 1936 to spend two fruitful years there.
- Hua lived on a $1,250 per annum scholarship awarded by the Culture and Education Foundation of China; it is interesting to recall that this foundation derived its funds from reparations paid by China to the United States following wars waged in China by the United States and several other nations in the previous century.
- Hardy assured Hua that he could gain a PhD in two years with ease, but Hua could not afford the registration fee and declined; of course, he gave quite different reasons for his decision.
- During the Cambridge period Hua became friendly with Harold Davenport and Hans Heilbronn, then two young research fellows of Trinity College - one a former student of Littlewood and the other Landau's last assistant in Göttingen - with whom he shared a deep interest in the Hardy-Littlewood approach to additive problems akin to Waring's.
- They helped to polish the English in several of Hua's papers, which now flowed from his pen at a remarkable rate; more than 10 of his papers date from this time, and many of these appeared in due course in the publications of the London Mathematical Society.
- This is the background against which Hua set to work as a young man, and it is probably fair to say that it is for his contributions in this area that Hua's name will remain best remembered: notably for his seminal work on the estimation of trigonometric sums, singly or on average.
- Hua might well have remained in England longer, but home was never far from his thoughts and the Japanese invasion of China in 1937 caused him much anxiety.
- However, Quing Hua University was no longer in Beijing; with vast portions of China under Japanese occupation, it had migrated to Kunming, the capital of the southern province of Yunan, where it combined with several other institutions to form the temporary Associated University of the South West.
- Despite these hardships Hua maintained the level of intensity of his Cambridge period and even exceeded it; by the end of 1945 he had more than 70 publications to his name.
- Hua wrote up this work in a booklet that 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.
- Hua spent three months in Russia in the spring of 1946 at Vinogradov's invitation.
- In the years ahead, even though Hua's scientific activities branched out in other directions, Hua was always ready to return to Waring's problem, to number theory in general and especially to questions involving exponential sums; thus as late as 1959 he published an important monograph on Exponential Sums and Their Applications in Number Theory for the Enzyklopädie der Matematischen Wissenschaften.
- In the closing years of the Kunming period Hua turned his interests to algebra and to analysis, as much as anything for the benefit of his students in the first instance, and soon began to make original contributions in these subjects too.
- Thus Hua became interested in matrix algebra and wrote several substantial papers on the geometry of matrices.
- He had been invited to visit the Institute for Advanced Study in Princeton, but because C L Siegel was working there along somewhat similar lines, Hua declined, at first in order to develop his ideas independently.
- In September 1946, shortly after returning from Russia, Hua did depart for Princeton, bringing with him projects not only in matrix theory but also in functions of several complex variables and in group theory.
- Much of his algebraic work later provided the basis for the monograph Classical Groups by Wan Zhe Xian and Hua (published by the Shanghai Scientific Press in Chinese in 1963).
- In the spring of 1948 Hua accepted appointment as a full professor at the University of Illinois in Urbana-Champaign.
- His stay in Illinois was all too brief, exciting developments were taking place in China, and Hua watched them eagerly, wanting to be part of the new epoch.
- 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 Academia Sinica came into being, with Hua as its first director.
- At this time Hua entertained doubts whether the Communist Party at home trusted him, and it came as an agreeable surprise to him to learn in Moscow that the Chinese government had agreed to a proposal by the Soviet government to award Hua a Stalin Prize.
- (The preface to the 1975 Chinese edition was excised by government order because Hua was out of favour during much of the Cultural Revolution); later this was published by Springer in English translation and is still in print.
- Despite his eminence and some protection in high places, Hua had to suffer harassment, public abuse, and constant surveillance.
- Nevertheless, during this troubled period Hua developed, with Wang Yuan, a broad interest in linear programming, operations research, and multidimensional numerical integration.
- Hua had a commanding presence, a genial personality, and a wonderful way of putting things simply, and the impact of his travels spread his fame and the popularity of mathematics across the land.
- Hua spent many of these years under virtual house arrest.
- (In 1978 the Chinese ambassador to the United Kingdom described one such occasion to me; Chen Jing-run, then probably the best known Chinese mathematician of the next generation, was made to stand in a public place for several hours, surrounded by a mob, and exhorted to bear witness against Hua.
- Chen, present at this conversation, chimed in to say that, actually, he had quite enjoyed the occasion, since no student could trouble him with silly questions and he had had time, uninterrupted, to think about mathematics!) It is surely no accident that the flow of Hua's publications came to an untimely end in 1965.
- With the end of the Cultural Revolution in 1976 Hua entered upon the last period of his life.
- In addition, Chinese Television (CCTV) produced a mini-series telling the story of Hua's life, which has been shown at least twice since then.
- Hua received honorary doctorates from the University of Nancy (1980), the Chinese University of Hong-Kong (1983), and the University of Illinois (1984).

Born 12 November 1910, Jintan, Jiangsu Province, China. Died 12 June 1985, Tokyo, Japan.

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Origin China

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive