John Charles Fields was born in Hamilton, Ontario, then Upper Canada, in 1863. His father operated a leather shop at 32 King St. West, and the family lived nearby at 150 King St. East. (Both of these buildings have long since disappeared–the site of the shop is now occupied by Jackson Square, a shopping complex, and that of the house by a Ramada Inn).

Fields graduated from the University of Toronto in 1884, and then left to study at Johns Hopkins University, probably attracted by the fact that Johns Hopkins apparently was the North American University that stressed research most strongly at that time. Its mathematics program had been set up by J.J.Sylvester during the years 1876–83 that he spent there. Fields was awarded a Ph.D. in 1887. His thesis was entitled Symbolic Finite Solutions and Solutions by Definite Integrals of the Equation dⁿy/dxⁿ = x^my , and was published in the American Journal of Mathematics in 1886.After teaching at Johns Hopkins for two years, he joined the faculty of Allegheny College in Meadville, Pennsylvania, north of Pittsburgh. Fields was understandably dissatisfied with the state of mathematics in North America at that time, and in 1891 he left for Europe to spend the next 10 years there, combining a modest inheritance from his parents with economical living habits.

Fields’s years in Europe, mainly in Berlin but also in Göttingen and Paris, influenced him deeply and reinforced his convictions about the importance of mathematical research. He mingled with many of the greatest mathematicians of that time–Klein, Frobenius, Weierstrass, Fuchs, Hensel–and changed his mathematical interests to algebraic functions in which he published many papers during the rest of his mathematical career. He also developed there a life-long friendship with the Swedish mathematician Gösta Mittag-Leffler. Fields returned to Canada in 1902 as a special lecturer at the University of Toronto. He remained at the University of Toronto for the rest of his life, and became a Fellow of the Royal Society of Canada in 1909 and of the Royal Society of London in 1913. He spent much of his leisure time in Europe, and it is claimed that he was a personal acquaintance of several reigning monarchs. He attended a dinner party in 1912 given by the King of Sweden, and had a personal audience with Mussolini during the International Congress of 1928 in Bologna. Fields worked tirelessly to promote mathematical research.

Soon after his return from Europe, he lobbied the Ontario Legislature for support for research. He persuaded the government to provide the University of Toronto with a special annual research grant of $75,000, a significant sum at a time when professors earned less than $1,000 per year. He also devoted his efforts to the establishment of the National Research Council (from which the National Science and Engineering Research Council of Canada later developed) and the Ontario Research Foundation. It is possible that his strong promotion of research was also related to his friendship with Mittag-Leffler. The latter was the head of a faction at the Stockholm Högskola which was of “the view that the Högskola should be devoted to free learning and research at the highest level and not concern itself with exam or degree requirements”.

The Royal Canadian Institute, founded in 1849 by Sandford Fleming, was another of Fields’s endeavors. He served as its President between 1919 and 1925, and attempted to transform it into an instrument for the promulgation of scientific thought as well as a center for actual research. To that end, he spent much time and money in persuading distinguished scientists to lecture to the membership of the Institute and the public–its Saturday evening lectures became very popular during his tenure of office. Fields’s vision of the Royal Canadian Institute as a center of research did not materialize, but we would like to think that the Fields Institute is a worthy realization of his dreams.

The RCI is still active in its mission to enhance public awareness of science in several ways, and continues to be known best for its public lectures, now held on Sunday afternoons. Recently the Fields Institute joined forces with the RCI to present a Sunday afternoon lecture by Stu Whittington (Dept of Chemistry, U of T) on Random Knotting, describing the applications of the mathematical theory of knots to linear polymer molecules, especially very long molecules like DNA which can be highly self-entangled causing interference with cellular processes such as replication and transcription.

Through Fields’s efforts, Toronto was chosen in 1922 as the venue of the 1924 International Congress of Mathematicians. The nascent International Mathematical Union had decreed that mathematicians from the “Central Powers” be excluded from the meeting, but Fields, although he evidently had mixed feelings about holding the meeting under those circumstances, decided that it was important to hold the Congress in any case. He almost single-handedly organized it and worked tirelessly during the next two years to ensure its success, far from assured at the time because of the political controversy.

The 1924 Toronto Congress was in fact very successful, with 444 mathematicians in attendance, more than twice the number at Strasbourg, though fewer than at prewar Congresses. The meeting was followed by an organized rail excursion to British Columbia accompanied by Fields. For many nights he got no sleep, and on his return to Toronto his health broke down. From that time on, he never regained the vigor of his former years. With the help of his colleague J.Chapelon, he nevertheless managed to complete the proceedings of the Congress which appeared in two large volumes in 1928.

Fields is of course best known for establishing what is now known as the “Fields Medal”–the premier award in Mathematics, often called the “Nobel Prize in Mathematics”. After completing the proceedings of the 1928 Congress, he proceeded with the planning of the award of the first medals, but fell ill in May of 1932 and died in August.
Just before his death, with his friend and colleague J.L.Synge at his bedside, he made his will.It included an amount of $47,000 to be added to the funds for the medal.

Fields is buried in the Hamilton Cemetery overlooking the western end of Lake Ontario (“Cootes Paradise,” where McMaster University is also located). His gravestone could not be more modest short of not being there at all. It is set into the ground flat, is about 22 inches by 16 inches and simply says "J.C.Fields, born May 14, 1863, died August 9, 1932."

Marcus Emmanueal Barnes recently published a thesis entitled, "John Charles Fields: A Sketch of His Life and Mathematical Work." To access the paper in its entirety please click here.