John Charles Fields | |
---|---|

John Charles Fields | |

Born | |

Died | August 9, 1932 69) Toronto, Ontario | (aged

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 d (1886)^{n}y/dx^{n} = x^{m}y |

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.

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 d ^{n}y/dx^{n} = x^{m}y*, was published in the

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.

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.

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, 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.

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.

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.

**Stephen Arthur Cook**, is an American-Canadian computer scientist and mathematician who has made major contributions to the fields of complexity theory and proof complexity. He is a university professor at the University of Toronto, Department of Computer Science and Department of Mathematics.

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).

**Michael Hartley Freedman** is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic ℝ^{4} manifold exists.

**Curtis Tracy McMullen** is an American mathematician who is the Cabot Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory.

**Sydney Chapman** was a British mathematician and geophysicist. His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer has inspired a broad range of research over many decades.

**Albert William Tucker** was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming.

**John Lighton Synge** was an Irish mathematician and physicist, whose seven decade career included significant periods in Ireland, Canada, and the USA. He was a prolific author and influential mentor, and is credited with the introduction of a new geometrical approach to the theory of relativity.

**James Fraser Mustard**, was a Canadian doctor and renowned researcher in early childhood development. Born, raised and educated in Toronto, Ontario, Mustard began his career as a research fellow at the University of Toronto where he studied the effects of blood lipids, their relation to heart disease and how Aspirin could mitigate those effects. He published the first clinical trial showing that aspirin could prevent heart attacks and strokes. In 1966, he was one of the founding faculty members at McMaster University's newly established medical school. He was the Dean of the Faculty of Health Sciences and the medical school at McMaster University from 1972-1982. In 1982, he helped found the Canadian Institute for Advanced Research and served as its founding president, serving until 1996. He wrote several papers and studies on early childhood development, including a report used by the Ontario Government that helped create a province-wide full-day kindergarten program. He won many awards including being made a companion of the Order of Canada – the order's highest level – and was inducted into the Canadian Medical Hall of Fame. He died November 16, 2011.

The **Fields Institute for Research in Mathematical Sciences**, commonly known simply as **Fields Institute**, is an international centre for scientific research in mathematical sciences at the University of Toronto, in Toronto, Ontario, Canada. The institute is named for University of Toronto mathematician John Charles Fields, after whom the Fields Medal is also named. It was established in 1992, and was briefly based at the University of Waterloo before relocating to Toronto in 1995.

**Arthur William Conway** FRS was a distinguished Irish mathematician and mathematical physicist who wrote one of the first books on relativity and co-edited two volumes of William Rowan Hamilton's collected works. He also served as President of University College Dublin between 1940 and 1947.

**James Greig Arthur** is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor at the University of Toronto Department of Mathematics.

**John Francis Toland** FRS FRSE is an Irish mathematician based in the UK. From 2011 to 2016 he served as Director of the Isaac Newton Institute for Mathematical Sciences and N M Rothschild & Sons Professor of Mathematical Sciences at the University of Cambridge.

The **University of Toronto Department of Mathematics** is an academic department within the Faculty of Arts and Science at the University of Toronto. It is located at the University's main campus at the Bahen Centre for Information Technology.

**George Arthur Elliott** is a Canadian mathematician specializing in operator algebras, K-theory, and non-commutative geometry. He is a professor at the University of Toronto Department of Mathematics, and holds a Canada Research Chair.

**Donald Andrew Dawson** is a Canadian mathematician, specializing in probability.

**William Henry Metzler** (1863–1943) was a Canadian mathematician.

**Ilijas Farah** is a Canadian-Serbian set theorist and logician and a professor in mathematics at York University and at Mathematical Institute, Belgrade, Serbia. His research is in applications of logic to operator algebras and set theory. He writes about operator algebras that apply various concepts, tools, and ideas from logic and set theory to classification problems in operator algebras.

- ↑ 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. - ↑ Van Brummelen, Glen; Kinyon, Michael, eds. (2005).
*Mathematics and the historian's craft: the Kenneth O. May lectures*. Springer. p. 173. - ↑ 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.

- Riehm, Elaine (2011).
*Turbulent Times in Mathematics: The Life of J. C. Fields and the History of the Fields Medal*. Providence, RI: American Mathematical Society. ISBN 0-8218-6914-0.

- Fields Institute Biography
- O'Connor, John J.; Robertson, Edmund F., "John Charles Fields",
*MacTutor History of Mathematics archive*, University of St Andrews . - John Charles Fields at the Mathematics Genealogy Project
- John Charles Fields archival papers held at the University of Toronto Archives and Records Management Services

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