June 26, 2016

The Fields Medal

After 1928: Fields Considers a Medal

Although the Bologna Congress of 1928 was truly international, the IMU remained divided, and German mathematicians were outside the organization. In Fields' words, "the rift was still wide." In a letter to University of Toronto President, Robert Falconer, Fields wrote that for some reason he was "persona grata" to both the French and the Germans. With this in mind, he travelled to Europe in the summers of 1929, 1930, and 1931 to see if there was something he could do to "bring the Germans in." Fields' approach was characteristic—quiet and personal, but determined. He now drew upon his wide circle of long time acquaintances and colleagues: Gabriel Koenigs in France, Salvatore Pincherle in Italy, Oskar Perron and Ludwig Bieberbach in Germany, Henri Fehr and Rudolph Fueter in Switzerland, among many others. He travelled over 8,000 miles in the summer 1930, tracking down mathematicians on their summer vacations. But in the end he was forced to recognize that the rift among mathematicians could not be bridged within the IMU. Sometime, around 1929, he also began to explore another idea, a small personal gesture-the gift of an international medal for outstanding research in mathematics.

He devoted the remaining three years of his life, in increasingly poor health, to the medal he wanted to establish. He did not live to see either its final design or its acceptance by the International Mathematics Union in Zurich in September 1932. Fields died August 9, 1932. Many friends and colleagues of long standing attended his funeral in Convocation Hall at University of Toronto, where he had opened the 1924 Congress exactly eight years earlier. A friend, University Bursar and Organist Ferdinand Mouré, played the organ. Colleagues from around the university accompanied his casket to the cemetery in Hamilton where he was buried alongside his parents.

The Fields Medal

While Fields was touring Europe in the summers of 1929 and 1930, he asked his scientific colleagues if, despite the rift in the IMU, they might individually support an international medal for research in mathematics. Their reactions ranged from lukewarm to enthusiastic. But support was widespread enough for Fields to proceed. In December 1930, he won the endorsement of the council of the American Mathematical Society (AMS). With the AMS letter in hand, he returned to Europe in the summer of 1931 and received endorsement for the medal from the Société mathématique de France, the Circolo Matematico di Palermo, the Société mathématique Suisse, and the Deutsche Mathematiker Vereinigung. Fields created the medal to do what he could to bring mathematicians back to a common understanding.

While he was planning the terms of the medal, Fields was also considering its design. One idea he had was to put the coastlines of the Atlantic on one side of the medal and the coastlines of the Pacific on the other. He discussed the matter with a number of people including R.G.D. Richardson, Secretary of the AMS, and D.E. Smith of Columbia University, who had a strong interest in the history of mathematics. Fields visited sculptors in Europe in 1931 in Europe, but was not satisfied. In the spring of 1932, he began a correspondence with R. Tait McKenzie (1867-1938), a Canadian sculptor who taught for many years at the University of Pennsylvania. Fields died in August 1932, however, before McKenzie had completed his design. It is possible, however, that Fields saw a preliminary sketch. A prototype of the medal was cast in bronze for McKenzie by the Medallic Art Company of New York and sent to Synge for approval in early 1933. Synge sent photographs of it to various mathematics societies and to the IMU. The original bronze prototype was recently discovered still in the original box addressed to Synge. Found in the archives at University of Toronto among the ephemera of the Bursar, it is now on display at the Fields Institute. It is on loan by the generosity of Cathleen Morawetz (Courant Institute), Synge's daughter.

The Fields Medal is nine centimetres in diameter. On one side is the head of Archimedes in profile with his name in Greek and the signature of Tait McKenzie along the border: "RTM" and the date, "MCMXXXIII". An inscription in Latin reads "Transire suum pectus mundoque potiri," which may be translated as "To pass beyond your understanding and make yourself master of the universe," from a longer passage by Manilius, first-century Roman poet: "The object of your quest is God; you are seeking to pass beyond your understanding and make yourself master of the universe. The toil involved matches the rewards to be won, nor are such high attainments secured without a price." The name of the recipient of the medal is engraved around the edge, and does not interfere with either face.

Fields' plans for the medal were meticulously carried out after his death by Synge, who obtained IMU support for it at the Zurich Congress (1932). Synge's description of the meeting of the IMU executive at which the medal was accepted is amusing. There was some discussion of the notion of a medal. Some members felt that mathematics should be its own reward (Synge privately felt that way), while others supported it as a positive international gesture at a time when such actions were needed. There was confusion at the meeting on the part of the chair, IMU President W.H. Young, over who was who, and in this slightly absent-minded, comedic atmosphere, Fields' medal was accepted by the Council of the IMU and the following day by delegates.

Fields' instructions about the medal were explicit: it was to be struck in gold; it was to be free of the name of any country or person; the inscription was to be in Latin or ancient Greek; it was to be awarded not only in recognition of distinguished research but also to encourage further effort. Fields did not stipulate any age limit. This was done in subsequent years by the IMU in a series of decisions culminating in the one taken at the Moscow Congress (1960) where an upper age limit of 40 was taken. The initial seed money for the medal came from funds left over from the 1924 Toronto Congress. But when Fields died, he left his estate to sustain it. In spite of his written instructions that the medal should bear the name of no person, from the beginning it has been known as the "Fields Medal." It was first awarded at the Oslo Congress (1936) to Jesse Douglas (USA) and Lars Ahlfors (Finland) and then, after World War II, at the Harvard Congress (1950), and has been given at all Congresses since.

When the medal was established in 1932, there was little publicity about it and surprisingly few articles in mathematics bulletins or elsewhere. It has grown in importance, however, with the passing of time, and has now become an international symbol of mathematics. This is likely because over the past eighty years, the "Fields Medallists" and their work have added lustre to the modest medal J.C. Fields founded.

For an appraisal of the Fields Medal and mathematics, see Michael Monastrysky, Modern Mathematics in the Light of the Fields Medal (Natick, Mass.: A.K. Peters, 1998). On the Fields medal, see Henry S. Tropp, "The Origins and History of the Fields Medal," Historia Mathematica 3 (1976); and Carl Riehm, "The Early History of the Fields Medal," Notices of the AMS 49:9 (2002). For a history of the International Congress of Mathematicians, see Guillermo P. Curbera, Mathematicians of the World, Unite! The International Congress of Mathematicians-A Human Endeavor (2009). For Fields' life, see Frances Hoffman and Elaine McKinnon Riehm, J.C. Fields, Turbulence in Mathematics, and the Medal (forthcoming).