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.

(3) The inscription reads: TRANSIRE SUUM PECTUS MUNDOQUE POTIRI.

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:

CONGREGATI

EX TOTO ORBE

MATHEMATICI

OB SCRIPTA INSIGNIA

TRIBUERE

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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