The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.

The Fields Medal Committee is chosen by the Executive Committee of the International Mathematical Union and is normally chaired by the IMU President. It is asked to choose at least two, with a strong preference for four, Fields Medalists, and to have regard in its choice to representing a diversity of mathematical fields. A candidate's 40th birthday must not occur before January 1st of the year of the Congress at which the Fields Medals are awarded.

The medals and cash prizes are funded by a trust established by J.C.Fields

at the University of Toronto, which has been supplemented periodically, but is still significantly

underfunded. The discrepancy in 2018 was made up by the University of Toronto and

the Fields Institute.

The name of the Chair of the Committee is made public, but the names of other members of the Committee remain anonymous until the award of the prize at the Congress.

The details of the Award, the nomination, and the selection can be found in the Statutes for the Award.

- Material
- 14KT Gold

- Diameter
- 63.5 mm

- Finish
- Sandblasted, Engraved, Gold Plated & Lacquered

- Unit Price
- approx. 5,500 CAD

Obverse

The head represents Archimedes facing right.

- In the field is the word ΑΡXIMHΔΟΥΣ in Greek capitals and
- the artist's monogram and date RTM, MCNXXXIII.
- The inscription reads: TRANSIRE SUUM PECTUS MUNDOQUE POTIRI.

**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.

Eberhard Knobloch, August 5, 1998

- *Grigori Perelman declined to accept the Fields Medal.

- A silver plaque was offered to Andrew J. Wiles as a special tribute from IMU

- Shigefumi Mori (chair)

Hélène Esnault

Eduard Feireisl

Alice Guionnet

Nigel Hitchin

John Morgan

Hee Oh

Andrei Okounkov

M.S. Raghunathan

Kenneth A. Ribet

Terence Tao

- Ingrid Daubechies (chair)

Luigi Ambrosio

David Eisenbud

Kenji Fukaya

Étienne Ghys

Benedict Gross

Frances Kirwan

János Kollár

Maxim Kontsevich

Michael Struwe

Ofer Zeitouni

Günter M. Ziegler

- László Lovász (chair)

Corrado De Concini

Yakov Eliashberg

Peter Hall

Timothy Gowers

Ngaiming Mok

Stefan Müller

Peter Sarnak

Karen Uhlenbeck

- John M Ball (chair)

Enrico Arbarello

Jeff Cheeger

Donald Dawson

Gerhard Huisken

Curtis McMullen

Alexey Parshin

Tom Spencer

Michèle Vergne

- Yakov Sinai (chair)

James Arthur

Spencer Bloch

Jean Bourgain

Helmut Hofer

Yasutaka Ihara

H. Blaine Lawson

Sergei Novikov

George Papanicolaou

Efim Zelmanov

- Yuri I. Manin (chair)

John Ball

John Coates

J. J. Duistermaat

Michael Freedman

Jürg Fröhlich

Robert MacPherson

Kyoji Saito

Steve Smale

- Mumford (chair)

Caffarelli

Kashiwara

B. Mazur

Schrivjer

Sullivan

Tits

Varadhan

- Faddeev (chair)

Atiyah

Bismut

Bombieri

Fefferman

Iwasawa

Lax

Shafarevich

- Moser (chair)

Deligne

Glimm

Hörmander

Ito

Milnor

Novikov

Seshadri

- Carleson (chair)

Araki

Malliavin

Marchuk

Mumford

Nirenberg

Schintzel

C.T.C. Wall

- Montgomery (chair)

Carleson

Eichler

I.M. James

Moser

Prohorov

Szökefalvi-Nagy

Tits

- Chandrasekharan (chair)

Adams

Kodaira

Malgrange

Mostowski

Pontryagin

Tate

Zygmund

- H. Cartan (chair)

Doob

Hirzebruch

Hörmander

Iyanaga

Milnor

Shafarevich

Turán

- de Rham (chair)

Davenport

Deuring

Feller

Lavrentiev

Serre

Spencer

Thom

- Nevanlinna (chair)

P.S. Aleksandrov

Artin

Chern

Chevalley

Whitney

Yosida

- Hopf (chair)

Chandrasekharan

Friedrichs

P. Hall

Kolmogorov

L. Schwartz

Siegel

Zariski

- Weyl (chair)

Bompiani

Bureau

H. Cartan

Ostrowski

Pleijel

Szegö

Titchmarsh

- Bohr (chair)

Ahlfors

Borsuk

Fréchet

Hodge

Kolmogorov

Kosambi

Morse

- Severi (chair)

Carathéodory

G.D. Birkhoff

E. Cartan

Takagi

At the 1924 International Congress of Mathematicians in Toronto, a resolution was adopted that at each ICM, two gold medals should be awarded to recognize outstanding mathematical achievement. Professor J. C. Fields, a Canadian mathematician who was Secretary of the 1924 Congress, later donated funds establishing the medals, which were named in his honor. In 1966 it was agreed that, in light of the great expansion of mathematical research, up to four medals could be awarded at each Congress.

The Fields Institute, Toronto, Canada, organizes the Fields Medal Symposium. The goals of the program for the Fields Medal Symposium are to present the work of a Fields Medalist and its impact, to explore the potential for future directions and areas of its influence, to provide inspiration to the next generations of mathematicians and scientists, as well as to present the Medalist to a broader public.

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