Ky Fan (樊𰋀, , September 19, 1914 – March 22, 2010) was a Chinese-American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

widely regarded as one of the most influential mathematicians from

China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...

and one of the greatest mathematicians of the 20th century. Fan's mathematical achievements were unusually versatile and covered numerous areas of mathematics, including both linear and nonlinear analysis, from finite to infinite dimensions, and extends from pure to applied mathematics. He made fundamental contributions in nonlinear analysis, convex analysis and inequalities, fixed point theory, operator and matrix theory, linear and nonlinear programming,

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, and

topological groups In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures t ...

. Fan's mathematical research is usually concerned with the foundation and central issues of a field or direction where many of his achievements and results have become classics and found wide applications in many fields, in particular in

mathematical economics Mathematical economics is the application of Mathematics, mathematical methods to represent theories and analyze problems in economics. Often, these Applied mathematics#Economics, applied methods are beyond simple geometry, and may include diff ...

. For instance, Fan's work in fixed point theory, in addition to influencing

nonlinear functional analysis Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear Map (mathematics), mappings. Topics Its subject matter includes: * generalizations of calculus to Banach spaces * implicit function theorems * fixed-p ...

, has found wide applications in mathematical economics and

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely g ...

calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

, and differential equations. The basic

theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...

of the mathematical economics theory of

Gérard Debreu Gérard Debreu (; 4 July 1921 – 31 December 2004) was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize ...

, winner of the 1983

Nobel Memorial Prize in Economic Sciences The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (), commonly referred to as the Nobel Prize in Economics(), is an award in the field of economic sciences adminis ...

, directly derives from a minimax principle of Fan. Fan was a doctoral student and collaborator of René Maurice Fréchet at the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

. He was also influenced by

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

and

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

. From 1945 to 1947, Fan was a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the Unit ...

New Jersey New Jersey is a U.S. state, state located in both the Mid-Atlantic States, Mid-Atlantic and Northeastern United States, Northeastern regions of the United States. Located at the geographic hub of the urban area, heavily urbanized Northeas ...

. Fan was elected to the

Academia Sinica Academia Sinica (AS, ; zh, t=中央研究院) is the national academy of the Taiwan, Republic of China. It is headquartered in Nangang District, Taipei, Nangang, Taipei. Founded in Nanjing, the academy supports research activities in mathemat ...

in 1964 and served as the director of the Institute of Mathematics of

Taiwan Taiwan, officially the Republic of China (ROC), is a country in East Asia. The main geography of Taiwan, island of Taiwan, also known as ''Formosa'', lies between the East China Sea, East and South China Seas in the northwestern Pacific Ocea ...

from 1978 to 1984. In 1985, an international mathematical conference was held at

UC Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a public land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an independent teachers college, UCSB joined ...

to celebrate the retirement of Fan. Many mathematicians from all over the world traveled to Santa Barbara to participate. Mathematical papers presented at the conference were later published in "Nonlinear and Convex Analysis: Proceedings in Honor of Ky Fan". An entire volume of the mathematical journal "Topological Methods in Nonlinear Analysis" was dedicated to Dr. Fan on the occasion of his 80th birthday.

Biography

Fan was born in

Hangzhou Hangzhou, , Standard Mandarin pronunciation: ; formerly romanized as Hangchow is a sub-provincial city in East China and the capital of Zhejiang province. With a population of 13 million, the municipality comprises ten districts, two counti ...

, the

capital Capital and its variations may refer to: Common uses * Capital city, a municipality of primary status ** Capital region, a metropolitan region containing the capital ** List of national capitals * Capital letter, an upper-case letter Econom ...

Zhejiang Province ) , translit_lang1_type2 = , translit_lang1_info2 = ( Hangzhounese) ( Ningbonese) (Wenzhounese) , image_skyline = 玉甑峰全貌 - panoramio.jpg , image_caption = View of the Yandang Mountains , image_map = Zhejiang i ...

. His father, named Fan Qi (樊琦, 1879—1947), served in the district courts of

Jinhua Jinhua is a prefecture-level city in central Zhejiang province in eastern China. It borders the provincial capital of Hangzhou to the northwest, Quzhou to the southwest, Lishui to the south, Taizhou, Zhejiang, Taizhou to the east, and Shaoxin ...

and

Wenzhou Wenzhou; Chinese postal romanization, historically known as Wenchow is a prefecture-level city in China's Zhejiang province. Wenzhou is located at the extreme southeast of Zhejiang, bordering Lishui, Zhejiang, Lishui to the west, Taizhou, Zheji ...

. Ky Fan went to Jinhua with his father when he was eight years old and studied at several middle schools in Zhejiang, including the Jinhua High School (currently

Jinhua No.1 Middle School Jinhua is a prefecture-level city in central Zhejiang province in eastern China. It borders the provincial capital of Hangzhou to the northwest, Quzhou to the southwest, Lishui to the south, Taizhou to the east, and Shaoxing to the northeast ...

), Hangzhou Zongwen High School (currently Hangzhou No.10 Middle School), and Wenzhou High School. Fan obtained his secondary diploma from the Jinhua High School. Fan enrolled into

Peking University Peking University (PKU) is a Public university, public Types of universities and colleges in China#By designated academic emphasis, university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of the Peop ...

Department of Mathematics in 1932, and received his B.S. degree from Peking University in 1936. Initially Fan wanted to study

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

, but eventually shifted to mathematics, largely because of the influence of his uncle Feng Zuxun ( 冯祖荀, 1880–1940; b. Hangzhou, d. Beijing), who was a mathematician in China and the then Chair of the Department of Mathematics of Peking University. After graduation, Fan became a

teaching assistant A teaching assistant (TA) or education assistant (EA) is an individual who assists a professor or teacher with instructional responsibilities. TAs include ''graduate teaching assistants'' (GTAs), who are graduate students; ''undergraduate teach ...

in the department. Fan went to

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

in 1939 and received his D.Sc. degree from the

in 1941. Fan's doctoral advisor was M.R.Fréchet. Fan was a

research fellow A research fellow is an academic research position at a university or a similar research institution, usually for academic staff or faculty members. A research fellow may act either as an independent investigator or under the supervision of a p ...

at the

French National Centre for Scientific Research The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engi ...

(CNRS). During his secondary school and college time, Fan said he "hated English". That was an important reason for him to choose

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, with less English but full of

equation In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for ...

s, and go to Paris. Fan was a member of the

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

from 1945 to 1947. In 1947, Fan joined the mathematical faculty of the

University of Notre Dame The University of Notre Dame du Lac (known simply as Notre Dame; ; ND) is a Private university, private Catholic research university in Notre Dame, Indiana, United States. Founded in 1842 by members of the Congregation of Holy Cross, a Cathol ...

, where he was an

assistant professor Assistant professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States, Canada, Japan, and South Korea. Overview This position is generally taken after earning a doct ...

at the beginning, and later promoted to

associate professor Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''. In the ''North American system'', used in the United States and many other countries, it is a position ...

and full

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

. In 1960, Fan also held a position at

Wayne State University Wayne State University (WSU) is a public university, public research university in Detroit, Michigan, United States. Founded in 1868, Wayne State consists of 13 schools and colleges offering approximately 375 programs. It is Michigan's third-l ...

Detroit Detroit ( , ) is the List of municipalities in Michigan, most populous city in the U.S. state of Michigan. It is situated on the bank of the Detroit River across from Windsor, Ontario. It had a population of 639,111 at the 2020 United State ...

for about one year, but immediately went to

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

near

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

. In 1965, Fan became a professor of mathematics at UCSB. Fan was known for being an extremely strict professor.Memory of my teacher -- Ky Fan
by Chuan-Kuan Yuan (袁传宽, American computer scientist) In 1999, Fan and his wife Yan Youfen (燕又芬) donated one million

US dollars The United States dollar (symbol: $; currency code: USD) is the official currency of the United States and several other countries. The Coinage Act of 1792 introduced the U.S. dollar at par with the Spanish silver dollar, divided it int ...

to 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, ...

, to set up the ''Ky and Yu-Fen Fan Endowment''. Fan had 23 graduate students. He died in Santa Barbara in March 2010. His given name 𰋀 ( Zh cj-gviw

) is a rare variant of the character 畿.

Academic career

Fan was the author of approximately 130 papers, Fan made fundamental contributions to operator and matrix theory, convex analysis and inequalities, linear and nonlinear programming, topology and fixed point theory, and topological groups. His work in fixed point theory, in addition to influencing nonlinear functional analysis, has found wide application in mathematical economics and game theory, potential theory, calculus of variations, and differential equations. The following are named after him: * Ky Fan norms * Ky Fan inequality * Ky Fan inequality (game theory) * Ky Fan lemma * Ky Fan metric

Publications

*''Sur quelques notions fondamentales de l'analyse générale'', 1941 *''Introduction à la topologie combinatoire'', co-author with M.R.Fréchet, first published in 1946, later translated into English and

Spanish Spanish might refer to: * Items from or related to Spain: **Spaniards are a nation and ethnic group indigenous to Spain **Spanish language, spoken in Spain and many countries in the Americas **Spanish cuisine **Spanish history **Spanish culture ...

.
Invitation to combinatorial topology
2003 *''Fonctions définies-positives et les fonctions complètement monotones; leurs applications au calcul des probabilités et à la théorie des espaces distanciés'', 1950

References

External links

*
Obituary of Ky Fan
by Bor-Luh Lin in the

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...

.
Tales of Dr. Fan
by Dennis Wildfogel. {{DEFAULTSORT:Fan, Ky 1914 births 2010 deaths 20th-century American mathematicians Chinese emigrants to the United States Educators from Hangzhou Institute for Advanced Study visiting scholars Mathematicians from Zhejiang Members of Academia Sinica Northwestern University faculty National University of Peking alumni Academic staff of Peking University Scientists from Hangzhou University of California, Santa Barbara faculty University of Notre Dame faculty University of Paris alumni Wayne State University faculty Chinese expatriates in France