Nathan Jacob Fine (22 October 1916 in

Philadelphia Philadelphia, often called Philly, is the List of municipalities in Pennsylvania#Municipalities, largest city in the Commonwealth (U.S. state), Commonwealth of Pennsylvania, the List of United States cities by population, sixth-largest city i ...

– 18 November 1994 in

Deerfield Beach Deerfield Beach is a city in Broward County, Florida, United States, just south of the Palm Beach County line. The city is named for the numerous deer that once roamed the area. As of the 2020 census, the population was 86,859. It is a principal ...

Florida Florida is a state located in the Southeastern region of the United States. Florida is bordered to the west by the Gulf of Mexico, to the northwest by Alabama, to the north by Georgia, to the east by the Bahamas and Atlantic Ocean, and to ...

) was an 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, structure, space, models, and change. History On ...

who worked on

basic hypergeometric series In mathematics, basic hypergeometric series, or ''q''-hypergeometric series, are ''q''-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series ''x'n'' is called ...

. He is best known for his lecture notes on the subject which for four decades served as an inspiration to experts in the field until they were finally published as a book. He solved the Jeep problem in 1946. Nathan Fine retired in 1978 as a professor at Pennsylvania State University. Prior to that he had been on the faculties of the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

and

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

. For a brief period (1946–1947) he also worked at the Operations Evaluation Group, affiliated with the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

. Beside the book he published about 40 papers in several fields of mathematics. He is known for the Rogers-Fine identity. Nathan Fine received his Ph.D. in 1946 from

, where he was a student of

Antoni Zygmund Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...

. Fine was at the Institute for Advanced Study for the three academic years 1953–1954, 1958–1959, and 1959–1960. Fine's doctoral students include J. J. Price. He wrote the book ''Basic Hypergeometric Series and Applications'' .

Selected publications

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References

External links

"Nathan Fine 1916–1994"
– biography article by George Andrews
Fine's Equation
– in

MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Di ...

"On Fine's Partition Theorems, Dyson, Andrews and Missed Opportunities"
– popular article by

Igor Pak Igor Pak (russian: link=no, Игорь Пак) (born 1971, Moscow, Soviet Union) is a professor of mathematics at the University of California, Los Angeles, working in combinatorics and discrete probability. He formerly taught at the Massachusetts ...

* * 1916 births 1994 deaths 20th-century American mathematicians Mathematical analysts University of Pennsylvania alumni University of Pennsylvania faculty Mathematicians at the University of Pennsylvania Pennsylvania State University faculty {{US-mathematician-stub