John Charles Fields

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John Charles Fields
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John Charles Fields
Born(1863-05-14)May 14, 1863
DiedAugust 9, 1932(1932-08-09) (aged 69)
Toronto, Ontario
Resting place Hamilton Cemetery
Nationality Canadian
Known for Fields Medal, Fields Institute
Scientific career
Fields Mathematics
Thesis Symbolic Finite Solutions and Solutions by Definite Integrals of the Equation dny/dxn = xmy (1886)
Doctoral students Samuel Beatty

John Charles Fields, FRS, [1] FRSC (May 14, 1863 – August 9, 1932) was a Canadian mathematician and the founder of the Fields Medal for outstanding achievement in mathematics.

Royal Society English learned society for science

The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge, commonly known as the Royal Society, is a learned society. Founded on 28 November 1660, it was granted a royal charter by King Charles II as "The Royal Society". It is the oldest national scientific institution in the world. The society is the United Kingdom's and Commonwealth of Nations' Academy of Sciences and fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, fostering international and global co-operation, education and public engagement.

Royal Society of Canada academy in Canada

The Royal Society of Canada, also known as the Academies of Arts, Humanities and Sciences of Canada, is the senior national, bilingual council of distinguished Canadian scholars, humanists, scientists and artists. The primary objective of the RSC is to promote learning and research in the arts, the humanities and the sciences. The RSC is Canada’s National Academy and exists to promote Canadian research and scholarly accomplishment in both official languages, to recognize academic and artistic excellence, and to advise governments, non-governmental organizations and Canadians on matters of public interest.

Canadians citizens of Canada

Canadians are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, several of these connections exist and are collectively the source of their being Canadian.


Life and career

Born in Hamilton, Ontario, to a leather shop owner, Fields graduated from Hamilton Collegiate Institute in 1880 and the University of Toronto in 1884 before leaving for the United States to study at Johns Hopkins University in Baltimore, Maryland. Fields received his Ph.D. in 1887. His thesis, entitled Symbolic Finite Solutions and Solutions by Definite Integrals of the Equation dny/dxn = xmy, was published in the American Journal of Mathematics in 1886.

Hamilton, Ontario City in Ontario, Canada

Hamilton is a port city in the Canadian province of Ontario. An industrialized city in the Golden Horseshoe at the west end of Lake Ontario, Hamilton has a population of 536,917, and a metropolitan population of 747,545. The city is located about 60 km southwest of Toronto, with which the Greater Toronto and Hamilton Area (GTHA) is formed.

Ontario Province of Canada

Ontario is one of the 13 provinces and territories of Canada and is located in east-central Canada. It is Canada's most populous province accounting for 38.3 percent of the country's population, and is the second-largest province in total area. Ontario is fourth-largest jurisdiction in total area when the territories of the Northwest Territories and Nunavut are included. It is home to the nation's capital city, Ottawa, and the nation's most populous city, Toronto, which is also Ontario's provincial capital.

University of Toronto university in Toronto, Ontario, Canada

The University of Toronto is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in the colony of Upper Canada. Originally controlled by the Church of England, the university assumed the present name in 1850 upon becoming a secular institution. As a collegiate university, it comprises eleven colleges, which differ in character and history, each with substantial autonomy on financial and institutional affairs. It has two satellite campuses in Scarborough and Mississauga.

Fields taught for two years at Johns Hopkins before joining the faculty of Allegheny College in Meadville, Pennsylvania. Disillusioned with the state of mathematical research in North America at the time, he left for Europe in 1891, locating primarily in Berlin, Göttingen and Paris, where he associated with some of the greatest mathematical minds of the time, including Karl Weierstrass, Felix Klein, Ferdinand Georg Frobenius and Max Planck. Fields also began a friendship with Gösta Mittag-Leffler, which would endure their lifetimes. He began publishing papers on a new topic, algebraic functions, which would prove to be the most fruitful research field of his career.

Allegheny College Pennsylvania liberal arts college

Allegheny College is a private, coeducational liberal arts college in northwestern Pennsylvania in the town of Meadville, approximately 35 miles (56 km) south of Erie. Founded in 1815, Allegheny is the oldest college in continuous existence under the same name west of the Allegheny Mountains. Allegheny is a member of the Great Lakes Colleges Association and the North Coast Athletic Conference and it is regionally accredited by the Middle States Commission on Higher Education.

Meadville, Pennsylvania City in Pennsylvania, United States

Meadville is a city in and the county seat of Crawford County, Pennsylvania, United States. The city is within 40 miles of Erie and within 90 miles of Pittsburgh. It was the first permanent settlement in northwest Pennsylvania. The population was 13,388 at the 2010 census. The city of Meadville is the principal city of the Meadville, PA Micropolitan Statistical Area. As well as one of two cities, the other being Erie, that make up the larger Erie-Meadville, PA Combined Statistical Area.

Pennsylvania State of the United States of America

Pennsylvania, officially the Commonwealth of Pennsylvania, is a state located in the northeastern and Mid-Atlantic regions of the United States. The Appalachian Mountains run through its middle. The Commonwealth is bordered by Delaware to the southeast, Maryland to the south, West Virginia to the southwest, Ohio to the west, Lake Erie and the Canadian province of Ontario to the northwest, New York to the north, and New Jersey to the east.

Fields returned to Canada in 1902 to lecture at the University of Toronto. Back in the country of his birth, he worked tirelessly to raise the status of mathematics within academic and public circles. He successfully lobbied the Ontario Legislature for an annual research grant of $75,000 for the university and helped establish the National Research Council of Canada, and the Ontario Research Foundation. Fields served as president of the Royal Canadian Institute from 1919 until 1925, during which time he aspired to mold the institute into a leading centre of scientific research, although with mixed success. His efforts, however, were pivotal in making Toronto the location of the 1924 International Congress of Mathematicians (ICM). [2] He was an Invited Speaker of the ICM in 1912 at Cambridge, [3] in 1924 at Toronto, and in 1928 at Bologna.

Legislative Assembly of Ontario single house of Legislature of Ontario

The Legislative Assembly of Ontario is one of two components of the Legislature of Ontario, the other being the Lieutenant Governor of Ontario. The Legislative Assembly is the second largest Canadian provincial deliberative assembly by number of members after the National Assembly of Quebec. The Assembly meets at the Ontario Legislative Building at Queen's Park in the provincial capital of Toronto.

The Royal Canadian Institute for Science (RCIS), known also as the Royal Canadian Institute, is a Canadian nonprofit organization dedicated to the advancement of science.

Toronto Provincial capital city in Ontario, Canada

Toronto is the provincial capital of Ontario and the most populous city in Canada, with a population of 2,731,571 in 2016. Current to 2016, the Toronto census metropolitan area (CMA), of which the majority is within the Greater Toronto Area (GTA), held a population of 5,928,040, making it Canada's most populous CMA. Toronto is the anchor of an urban agglomeration, known as the Golden Horseshoe in Southern Ontario, located on the northwestern shore of Lake Ontario. A global city, Toronto is a centre of business, finance, arts, and culture, and is recognized as one of the most multicultural and cosmopolitan cities in the world.

Fields is best known for his development of the Fields Medal, which is considered by some to be the Nobel Prize in Mathematics, although there are differences between the awards. First awarded in 1936, the medal was reintroduced in 1950 and has been awarded every four years since. It is awarded to two to four mathematicians, under the age of 40, who have made important contributions to the field.

Fields Medal prize for mathematicians

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

Nobel Prize Set of annual international awards, primarily 5 established in 1895 by Alfred Nobel

The Nobel Prize is a set of annual international awards bestowed in several categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances.

Fields began planning the award in the late 1920s but, due to deteriorating health, never saw the implementation of the medal in his lifetime. He died on August 9, 1932 after a three-month illness; in his will, he left $47,000 for the Fields Medal fund.

Fields was elected fellow of the Royal Society of Canada in 1907 and fellow of the Royal Society of London in 1913.

The Fields Institute at the University of Toronto was named in his honour.

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  1. Synge, J. L. (1933). "John Charles Fields. 1863–1932". Obituary Notices of Fellows of the Royal Society . 1 (2): 131. doi:10.1098/rsbm.1933.0010.
  2. Van Brummelen, Glen; Kinyon, Michael, eds. (2005). Mathematics and the historian's craft: the Kenneth O. May lectures. Springer. p. 173.
  3. Fields, J. C. "Direct derivation of the complementary theorem from elementary properties of the rational functions" (PDF). In: Proceedings of the Fifth International Congress of Mathematicians (Cambridge, 22–28 August 1912). vol. 1. pp. 312–326.

Further reading