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Fields Medal





The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded by the International Mathematical Union. The uniqueness of the Fields Medal is that it  is awarded with the aim of providing encouragement to the young mathematicians so that they can carry out their research works further unlike the Nobel prize which is more of a recognition of a scientist's achievement. The Fields Medal is the highest scientific award for mathematicians, and is presented every four years at the International Congress of Mathematicians, together with a prize of 15000 Canadian dollars. The first Fields Medal was awarded in 1936 at the World Congress in Oslo. The Fields Medal is made of gold, and shows the head of Archimedes (287-212 BC) together with a quotation attributed to him: "Transire suum pectus mundoque potiri" ("Rise above oneself and grasp the world"). The reverse side bears the inscription: "Congregati ex toto orbe mathematici ob scripta insignia tribuere" ("The mathematicians assembled here from all over the world pay tribute for outstanding work").

The Fields Medal originated from surplus funds raised by John Charles Fields (1863–1932), a professor of mathematics at the University of Toronto, as organizer and president of the 1924 International Congress of Mathematicians in Toronto. The Committee of the International Congress had $2,700 left after printing the conference proceedings and voted to set aside $2,500 for the establishment of two medals to be awarded at later congresses. Following an endowment from Fields’s estate, the proposed awards—contrary to his explicit request—became known as the Fields Medals. The first two Fields Medals were awarded in 1936. An anonymous donation allowed the number of prize medals to increase starting in 1966. Medalists also receive a small (currently $1,500) cash award. A related award, the Rolf Nevanlinna Prize, has also been presented at each International Congress of Mathematicians since 1982. It is awarded to one young mathematician for work dealing with the mathematical aspects of information science.

The Fields Medal is a good indicator of current fertile areas of mathematical research, as the winners have generally made contributions that opened up whole fields or integrated technical ideas and tools from a wide variety of disciplines. A preponderance of winners worked in highly abstract and integrative fields such as algebraic geometry and algebraic topology. This is to some extent a reflection of the influence and power of the French consortium of mathematicians, writing since 1939 under the name of Nicolas Bourbaki, which in its multivolume Éléments de mathématiques has sought a modern, rigorous, and comprehensive treatment of all of mathematics and mathematical foundations. However, medals have also been awarded for work in more classical fields of mathematics and for mathematical physics, including a number for solutions to problems that David Hilbert enunciated at the International Congress of Mathematicians in Paris in 1900.



The Fields Medal


Obverse :

The head represents Archimedes facing right.
(1) In the field is the word  in Greek capitals and
(2) the artist's monogram and date RTM, MCNXXXIII.

The inscriptions mean:
(1) "of Archimedes", namely the face of Archimedes.
(2) R(obert) T(ait) M(cKenzie), that is the name of the Canadian sculptor who designed the medal. The correct date would read: "MCMXXXIII" or 1933. The second letter M has to be substituted for the false N.
(3) "To transcend one's spirit and to take hold of (to master) the world".



Reverse :


The inscription on the tablet reads:


It means: "The mathematicians having congregated from the whole world awarded (this medal) because of outstanding writings". The verb form "tribuere" (the first "e" is a long vowel) is a short form of "tribuerunt". In the background there is a representation of Archimedes' sphere being inscribed in a cylinder.


 Fields Medalists


Year Name Birthplace Primary Research
1936 Ahlfors, Lars Helsinki, Finland Riemann surfaces
1936 Douglas, Jesse New York, New York, U.S. Plateau problem
1950 Schwartz, Laurent Paris, France functional analysis
1950 Selberg, Atle Langesund, Norway number theory
1954 Kodaira Kunihiko Tokyo, Japan algebraic geometry
1954 Serre, Jean-Pierre Bages, France algebraic topology
1958 Roth, Klaus Breslau, Germany number theory
1958 Thom, René Montbéliard, France topology
1962 Hörmander, Lars Mjällby, Sweden partial differential equations
1962 Milnor, John Orange, New Jersey, U.S. differential topology
1966 Atiyah, Michael London, England topology
1966 Cohen, Paul Long Branch, New Jersey, U.S. set theory
1966 Grothendieck, Alexandre Berlin, Germany algebraic geometry
1966 Smale, Stephen Flint, Michigan, U.S. topology
1970 Baker, Alan London, England number theory
1970 Hironaka Heisuke Yamaguchi prefecture, Japan algebraic geometry
1970 Novikov, Sergey Gorky, Russia, U.S.S.R. topology
1970 Thompson, John Ottawa, Kansas, U.S. group theory
1974 Bombieri, Enrico Milan, Italy number theory
1974 Mumford, David Worth, Sussex, England algebraic geometry
1978 Deligne, Pierre Brussels, Belgium algebraic geometry
1978 Fefferman, Charles Washington, D.C., U.S. classical analysis
1978 Margulis, Gregori Moscow, Russia, U.S.S.R. Lie groups
1978 Quillen, Daniel Orange, New Jersey, U.S. algebraic K-theory
1983* Connes, Alain Darguignan, France operator theory
1983* Thurston, William Washington, D.C., U.S. topology
1983* Yau, Shing-Tung Shantou, China differential geometry
1986 Donaldson, Simon Cambridge, Cambridgeshire, England topology
1986 Faltings, Gerd Gelsenkirchen, West Germany Mordell conjecture
1986 Freedman, Michael Los Angeles, California, U.S. Poincaré conjecture
1990 Drinfeld, Vladimir Kharkov, Ukraine, U.S.S.R. algebraic geometry
1990 Jones, Vaughan Gisborne, New Zealand knot theory
1990 Mori Shigefumi Nagoya, Japan algebraic geometry
1990 Witten, Edward Baltimore, Maryland, U.S. superstring theory
1994 Bourgain, Jean Ostend, Belgium analysis
1994 Lions, Pierre-Louis Grasse, France partial differential equations
1994 Yoccoz, Jean-Christophe Paris, France dynamical systems
1994 Zelmanov, Efim Khabarovsk, Russia, U.S.S.R. group theory
1998 Borcherds, Richard Cape Town, South Africa mathematical physics
1998 Gowers, William Marlborough, Wiltshire, England functional analysis
1998 Kontsevich, Maxim Khimki, Russia, U.S.S.R. mathematical physics
1998 McMullen, Curtis Berkeley, California, U.S. chaos theory
2002 Lafforgue, Laurent Antony, France number theory
2002 Voevodsky, Vladimir Moscow, Russia, U.S.S.R. algebraic geometry
2006 Okounkov, Andrei Moscow, Russia, U.S.S.R. mathematical physics
2006 Perelman, Grigori U.S.S.R. geometry
2006 Tao, Terence Adelaide, Australia partial differential equations
2006 Werner, Wendelin Cologne, Germany geometry
2010 Lindenstrauss, Elon Jerusalem ergodic theory
2010 Ngo Bao Chau Hanoi, Vietnam algebraic geometry
2010 Smirnov, Stanislav Leningrad, Russia, U.S.S.R. mathematical physics
2010 Villani, Cédric Brive-la-Gaillarde, France mathematical physics
*Because Poland was under martial law in 1982, the scheduled meeting of the International Congress of Mathematicians in Warsaw was postponed until 1983.




Courtesy:  http://www.britannica.com/EBchecked/topic/206375/Fields-Medal and various other sources.







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