The Fields, Nevanlinna and Abel Awards: Chasing the Mathematical Prize Jonathan M. Borwein, FRSC Prepared for Simon Fraser Lecture Series Recognizing Excellence: The Nobels and Other Prizes March 13, 2003 Canada Research Chair & Founding Director C E C M Centre for Experimental & Constructive Mathematics Simon Fraser University, Burnaby, BC Canada URL: www.cecm.sfu.ca/˜ jborwein/talks.html Revised: February 10, 2003 1 Mathematical Prizes • There is no Nobel Prize in Mathematics. • But we have our equivalents — the Fields Medals, the Nevanlinna Prize, and this year the new Abel Prize. • I shall describe a little of the History of the prizes, and say something about the cer- emony, the recent winners and their work — with very few formulae! • A Tom Lehrer Song makes the case that Mathematics is ubiquitous: the language of modern science, high technology, and everyday life. 2 THE FIELDS MEDAL • The highest honour in mathematics is a Canadian bequest (1932). • Two to four are awarded at quadrennial International Congress of Mathemati- · · · cians along with the Nevanlinna Prize. • In 2003, the first annual $500,000 (US) Abel Prize will be awarded, endowed by Norway in honour of: Abel Niels, Hendrik (1802–1829) Nor- wegian mathematician who made signifi- cant contributions to both algebra and anal- ysis, especially to the study of GROUPS and INFINITE SERIES. He proved the in- solubility of the quintic at the age of nine- teen. [From the Collins Dictionary.] 3 The transparencies, and other resources, for this presentation are available at www.cecm.sfu.ca/personal/jborwein/fields03.html · · · And now the players 4 A. John Charles Fields Born in Hamilton: 14 May 1863 Died in Toronto: 9 Aug 1932 5 “John Fields received his B.A. in math- ematics from the University of Toronto in 1884. After a Ph.D. at Johns Hop- kins University, Fields was appointed Professor of Mathematics at Allegheny College in 1889. However from 1892 Fields studied in Europe with Fuchs, Frobenius, Hensel, Schwarz and Planck. In 1902 Fields was appointed to the position of lecturer at the University of Toronto where he remained until his death. In 1923 he was promoted to research professor at the University of Toronto. His main research topic was on algebraic functions.” 6 “Fields received several important hon- ours. He was elected a fellow of the Royal Society of Canada in 1907 and, in 1913, he was elected fellow of the Royal Society of London. In 1924 the International Congress of Mathemati- cians was held at Toronto and Fields was honoured by being President of the Congress.” 7 • There is a world class Fields Institute for Research in Mathematical Sciences (Toronto 1992). • The ICM was held in Vancouver in 1974. • In 2010 we hope it will be in Montreal. • The IMU has more than 55 members. In ‘Group V’ are: Canada, China, France, Germany, Israel, Italy, Japan, Russia, UK, USA. • The prize is poorly funded — the CMS and Fields Institute are trying to improve this (so far without result). 8 B. The Legacy of John Charles Fields “However Fields is best remembered for conceiving the idea of, and for pro- viding funds for, an international medal for mathematical distinction. Adopted at the International Congress of Math- ematicians at Zurich in 1932, the first medals were awarded at the Oslo Congress of 1936. Field’s Medals are awarded to no fewer than two and no more than four math- ematicians under 40 years of age every four years at the International Congress of Mathematicians. These conditions were set down to recognise Fields’ wish, set out in his Will, that the awards recognise both work com- pleted and point to the potential for future achievement.” 9 C. The Fields Medal Itself Obverse: Archimedes facing right The inscription is: TRANSIRE SUUM PECTUS MUNDOQUE POTION “To transcend one’s spirit and to take hold of (to master) the world.” (cid:1) In the field is “of Archimedes” in Greek, the artist’s monogram and date RTM, MC- NXXXIII. R(obert) T(ait) M(cKenzie), the Canadian sculptor/designer. The correct date is “MCMXXXIII” (1933). 10