Hua Luogeng or Hua Loo-Keng (; 12 November 1910 – 12 June 1985) was a Chinese mathematician and politician famous for his important contributions to
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
and for his role as the leader of mathematics research and education in the
People's Republic of China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
. He was largely responsible for identifying and nurturing the renowned mathematician
Chen Jingrun
Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime.
Life and career
Chen was the third son in ...
who proved
Chen's theorem
In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes).
History
The theorem wa ...
, the best known result on the
Goldbach conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
The conjecture has been shown to hold ...
. In addition, Hua's later work on
mathematical optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
and operations research made an enormous impact on China's economy. He was elected a foreign associate of the US
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
in 1982.
He was elected a member of the
standing Committee of the first to sixth National people's Congress, Vice-Chairman of the sixth National Committee of the
Chinese People's Political Consultative Conference
The Chinese People's Political Consultative Conference (CPPCC, zh, 中国人民政治协商会议), also known as the People's PCC (, ) or simply the PCC (), is a political advisory body in the People's Republic of China and a central part of ...
(April 1985) and Vice-Chairman of the
China Democratic League
The China Democratic League (CDL) is one of the eight legally recognized minor political parties in the People's Republic of China under the Chinese Communist Party's United Front. The CDL was originally founded in 1941 as an umbrella coalition ...
(1979). He joined the Communist Party of China in 1979.
Hua did not receive a formal university education. Although awarded several honorary PhDs, he never got a formal degree from any university. In fact, his formal education only consisted of six years of primary school and three years of middle school. For that reason,
Xiong Qinglai
Xiong Qinglai, or Hiong King-Lai (, October 20, 1893 – February 3, 1969), courtesy name Dizhi (), was a Chinese mathematician from Yunnan. He was the first person to introduce modern mathematics into China, and served as an influential preside ...
, after reading one of Hua's early papers, was amazed by Hua's mathematical talent, and in 1931 Xiong invited him to study mathematics at
Tsinghua University
Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...
.
Biography
Early years (1910–1936)
Hua Luogeng was born in
Jintan
Jintan District is a district under the administration of Changzhou in the Jiangsu province of the People's Republic of China.
History
Jintan, known as Jinshan () in ancient times, was a township of Yanling commandery since the reign of the ...
, 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
Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flow ...
, 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
Typhoid fever, also known as typhoid, is a disease caused by '' Salmonella'' serotype Typhi bacteria. Symptoms vary from mild to severe, and usually begin six to 30 days after exposure. Often there is a gradual onset of a high fever over several ...
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
In algebra, a quintic function is a function of the form
:g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\,
where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a q ...
was fundamentally flawed. Hua's lucid analysis caught the eye of Prof.
Xiong Qinglai
Xiong Qinglai, or Hiong King-Lai (, October 20, 1893 – February 3, 1969), courtesy name Dizhi (), was a Chinese mathematician from Yunnan. He was the first person to introduce modern mathematics into China, and served as an influential preside ...
at
Tsinghua University
Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...
in
Beijing
}
Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...
, 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
Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations.
Biography
The son of a teac ...
and
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...
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
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
. In this way Hua received an invitation to come to Cambridge, England, where he stayed for two years.
Early middle years (1936–1950)
While at
Cambridge University
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
, Hua worked on applying the
Hardy–Littlewood circle method
In mathematics, the Hardy–Littlewood circle method is a technique of analytic number theory. It is named for G. H. Hardy and J. E. Littlewood, who developed it in a series of papers on Waring's problem.
History
The initial idea is usually at ...
towards problems in number theory. He produced seminal work on
Waring's problem
In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural num ...
, which would establish his reputation within the international math community. In 1938, after the full outbreak of the
Second Sino-Japanese War
The Second Sino-Japanese War (1937–1945) or War of Resistance (Chinese term) was a military conflict that was primarily waged between the Republic of China and the Empire of Japan. The war made up the Chinese theater of the wider Pacific Th ...
, Hua chose to return to China to Tsinghua, where he was appointed full professor despite not having any degree. At the time, with vast areas of China under Japanese occupation,
Tsinghua University
Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...
,
Peking University
Peking University (PKU; ) is a public research university in Beijing, China. The university is funded by the Ministry of Education.
Peking University was established as the Imperial University of Peking in 1898 when it received its royal charter ...
, and
Nankai University
Nankai University (NKU or Nankai; ) is a national public research university located in Tianjin, China. It is a prestigious Chinese state Class A Double First Class University approved by the central government of China, and a member of the fo ...
had merged into the
Southwest Associated University
When the Second Sino-Japanese War broke out between China and Japan in 1937, Peking University, Tsinghua University and Nankai University merged to form Changsha Temporary University in Changsha and later National Southwestern Associated Universi ...
in
Kunming
Kunming (; ), also known as Yunnan-Fu, is the capital and largest city of Yunnan province, China. It is the political, economic, communications and cultural centre of the province as well as the seat of the provincial government. The headquar ...
, capital of the southern province
Yunnan
Yunnan , () is a landlocked Provinces of China, province in Southwest China, the southwest of the People's Republic of China. The province spans approximately and has a population of 48.3 million (as of 2018). The capital of the province is ...
. 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
Vinogradov or Vinogradoff (russian: Виногра́дов) is a common Russian last name derived from the Russian word виноград (''vinograd'', meaning "grape" and виноградник ''vinogradnik'', meaning "vineyard"). Vinogradova (ru ...
'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 famous result is central to improved versions of the
Hilbert–Waring theorem
In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural numb ...
, and has important applications to the study of the
Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...
. Hua wrote up this work in a booklet titled ''Additive Theory of Prime Numbers'' 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
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...
. In the closing years of the Kunming period, Hua turned his interests to
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
and
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
towards which he soon began to make original contributions.
![Shoes HuaL](https://upload.wikimedia.org/wikipedia/commons/4/45/Shoes_HuaL.jpg)
After the war, Hua spent three months in the Soviet Union in the spring of 1946, at
Ivan Vinogradov
Ivan Matveevich Vinogradov ( rus, Ива́н Матве́евич Виногра́дов, p=ɪˈvan mɐtˈvʲejɪvʲɪtɕ vʲɪnɐˈɡradəf, a=Ru-Ivan_Matveyevich_Vinogradov.ogg; 14 September 1891 – 20 March 1983) was a Soviet mathematician, ...
's invitation, following which Hua departed for
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
. At Princeton, Hua worked on
matrix theory
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
For example,
\begi ...
, functions of
several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variable ...
, and
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
. At this time civil war was raging in China and it was not easy to travel, and for "convenience of travel," the Chinese authorities had 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
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...
. However, his stay in Illinois was far too brief. In October 1949, the
People's Republic of China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
was established, and Hua, wanting to be part of a new epoch, decided to return to China with his wife and kids, despite having settled comfortably 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
The Chinese Academy of Sciences (CAS); ), known by Academia Sinica in English until the 1980s, is the national academy of the People's Republic of China for natural sciences. It has historical origins in the Academia Sinica during the Republ ...
(CAS) came into being, with Hua as its first director. The following year he was one of a 26-member delegation from CAS to visit the Soviet Union in order 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, which was 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, and later it was published in English by
Springer
Springer or springers may refer to:
Publishers
* Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag.
** Springer Nature, a multinationa ...
. ''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
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
in 1963.
Outside of pure math, Hua first proposed in 1952 the development of China's
electronic computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These progra ...
, 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
The Great Leap Forward (Second Five Year Plan) of the People's Republic of China (PRC) was an economic and social campaign led by the Chinese Communist Party (CCP) from 1958 to 1962. CCP Chairman Mao Zedong launched the campaign to reconstruc ...
in 1958 came with a vehement attack on pure mathematics and intellectuals, which prompted Hua to shift towards
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
. Hua developed, with
Wang Yuan, a broad interest in
linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...
,
operations research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...
, and
multidimensional numerical integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
. In connection with the last of these, the study of the
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...
and the role of
uniform distribution
Uniform distribution may refer to:
* Continuous uniform distribution
* Discrete uniform distribution
* Uniform distribution (ecology)
* Equidistributed sequence In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be ...
led them to invent an alternative deterministic method based on ideas from
algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
. Their theory was set out in ''Applications of Number Theory to Numerical Analysis'', which was published much later, 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 faculty to the solution of 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
Mao Zedong pronounced ; also romanised traditionally as Mao Tse-tung. (26 December 1893 – 9 September 1976), also known as Chairman Mao, was a Chinese communist revolutionary who was the founder of the People's Republic of China (PRC) ...
, this last a valuable protection in uncertain times. 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.
Following the
Cultural Revolution
The Cultural Revolution, formally known as the Great Proletarian Cultural Revolution, was a sociopolitical movement in the People's Republic of China (PRC) launched by Mao Zedong in 1966, and lasting until his death in 1976. Its stated goal ...
, Hua resumed contact with Western mathematicians. In 1980 Hua became a cultural ambassador of China charged with re-establishing links with Western academics, and during the next five years he travelled 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
, mottoeng = Through efforts to heights
, established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...
and during 1983–84 he was Sherman Fairchild Distinguished Scholar at the
California Institute of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
. 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 has been named after him.
Works
*
*
*
*
References
External links
*
*
Biographical memoir– by ''Heini Halberstam''
– fro
MacTutor History of Mathematics from University of St Andrews* Hua Loo-Keng : a biography by
Wang Yuan
Heini Halberstam, "Loo-Keng Hua", Biographical Memoirs of the National Academy of Sciences (2002)
{{DEFAULTSORT:Hua, Luogeng
1910 births
1985 deaths
20th-century Chinese mathematicians
Boxer Indemnity Scholarship recipients
Chinese Communist Party politicians from Jiangsu
Educators from Changzhou
Foreign associates of the National Academy of Sciences
Mathematicians from Jiangsu
Members of the Chinese Academy of Sciences
National Southwestern Associated University faculty
Number theorists
People from Jintan District
Scientists from Changzhou
Tsinghua University faculty
TWAS fellows
University of Science and Technology of China faculty
Victims of the Cultural Revolution
Vice Chairpersons of the National Committee of the Chinese People's Political Consultative Conference
Burials at Babaoshan Revolutionary Cemetery