John Charles Fields, FRS, FRSC (May 14, 1863 – August 9, 1932) was a

Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...

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 ...

and the founder of the

Fields Medal 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. The name of the award h ...

for outstanding achievement in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Career

Born in

Hamilton Hamilton may refer to: People * Hamilton (name), a common British surname and occasional given name, usually of Scottish origin, including a list of persons with the surname ** The Duke of Hamilton, the premier peer of Scotland ** Lord Hamilto ...

Ontario Ontario ( ; ) is one of the thirteen provinces and territories of Canada.Ontario is located in the geographic eastern half of Canada, but it has historically and politically been considered to be part of Central Canada. Located in Central Ca ...

, to a leather shop owner, Fields graduated from Hamilton

Collegiate Institute A collegiate institute is an institution that provides either secondary or post-secondary education, dependent on where the term is used. In Canada, the term is used to describe an institutions that provide secondary education, while the word is use ...

in 1880 and the

University of Toronto The University of Toronto (UToronto or U of T) 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 ...

in 1884 before leaving for the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

to study at

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...

Baltimore Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was ...

Maryland Maryland ( ) is a state in the Mid-Atlantic region of the United States. It shares borders with Virginia, West Virginia, and the District of Columbia to its south and west; Pennsylvania to its north; and Delaware and the Atlantic Ocean t ...

. Fields received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1887. His

thesis A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144 ...

, entitled ''Symbolic Finite Solutions and Solutions by Definite Integrals of the Equation dⁿy/dxⁿ = x^my'', was published in the ''

American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United S ...

'' in 1886. Fields taught for two years at Johns Hopkins before joining the faculty of

Allegheny College he, תגל ערבה ותפרח כחבצלת , mottoeng = "Add to your faith, virtue and to your faith, knowledge" (2 Peter 1:5)"The desert shall rejoice and the blossom as the rose" (Isaiah 35:1) , faculty = 193 ...

in Meadville,

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

. Disillusioned with the state of mathematical research in

North America North America is a continent in the Northern Hemisphere and almost entirely within the Western Hemisphere. It is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South America and th ...

at the time, he left for

Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...

in 1891, locating primarily in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitu ...

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

and

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...

, where he associated with some of the greatest mathematical minds of the time, including

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...

Ferdinand Georg Frobenius Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famou ...

and

Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...

. Fields also began a lifelong friendship with

Gösta Mittag-Leffler Magnus Gustaf "Gösta" Mittag-Leffler (16 March 1846 – 7 July 1927) was a Swedish mathematician. His mathematical contributions are connected chiefly with the theory of functions, which today is called complex analysis. Biography Mittag-Leffl ...

. He began publishing papers on a new topic,

algebraic functions In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations additi ...

, which would prove to be the most fruitful research field of his career. Fields returned to Canada in 1902 to lecture at the

. 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 The Legislative Assembly of Ontario (OLA, french: Assemblée législative de l'Ontario) is the legislative chamber of the Canadian province of Ontario. Its elected members are known as Members of Provincial Parliament (MPPs). Bills passed by ...

for an annual research grant of $75,000 for the university and helped establish the

National Research Council of Canada The National Research Council Canada (NRC; french: Conseil national de recherches Canada) is the primary national agency of the Government of Canada dedicated to science and technology research & development. It is the largest federal research ...

, and the Ontario Research Foundation. Fields served as president of the

Royal Canadian Institute The Royal Canadian Institute for Science (RCIScience), known also as the Royal Canadian Institute, is a Canadian nonprofit organization dedicated to connecting the public with Canadian science. History The organization was formed in Toronto as t ...

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 Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anch ...

the location of the 1924

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

(ICM). He was an Invited Speaker of the ICM in 1912 at Cambridge, in 1924 at Toronto, and in 1928 at Bologna. Fields is best known for his development of the

, which is considered by some to be the

Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

of 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, three or four mathematicians under the age of 40 who have made important contributions to the field. 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. His plan for the Fields medal was completed by J. L. Synge.

Honours

Fields was elected a fellow of the

Royal Society of Canada The Royal Society of Canada (RSC; french: Société royale du Canada, SRC), also known as the Academies of Arts, Humanities and Sciences of Canada (French: ''Académies des arts, des lettres et des sciences du Canada''), is the senior national, bil ...

in 1907 and of the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...

in 1913. The Fields Institute at the

was named in his honour.

References

External links

Fields Institute Biography
* *
John Charles Fields archival papers
held at th
University of Toronto Archives and Records Management Services
{{DEFAULTSORT:Fields, John Charles 1863 births 1932 deaths Canadian mathematicians Corresponding Members of the Russian Academy of Sciences (1917–1925) Corresponding Members of the USSR Academy of Sciences Fellows of the Royal Society of Canada Fellows of the Royal Society Johns Hopkins University alumni People from Hamilton, Ontario Scientists from Ontario University of Toronto alumni University of Toronto faculty

Career

Honours

References

Further reading

External links