What is the Fields Medal?

Source: By The Indian Express

Ukrainian mathematician Maryna Viazovska, chair of Number Theory at École polytechnique fédérale de Lausanne (EPFL) in Switzerland, was on 5 July 2022 named as one of four recipients of the 2022 Fields Medal, an honour that is often described the Nobel Prize in mathematics.

The Fields Medal is awarded by the International Mathematical Union (IMU), an international non-governmental and non-profit scientific organisation that aims to promote international cooperation in mathematics.

The IMU recognised Viazovska’s work on the sphere-packing problem in 8 and 24 dimensions, EPFL said in an announcement. Previously, the problem had been solved for only three dimensions or fewer.

The other winners were French mathematician Hugo Duminil-Copin of the University of Geneva; Korean-American June Huh of Princeton; and Briton James Maynard of the University of Oxford.

Viazovska, 37, is only the second female Fields Medalist, after the Iranian Maryam Mirzakhani in 2014.

Fields Medal

The Fields Medal is awarded every four years to one or more mathematicians under the age of 40 in recognition of “outstanding mathematical achievement for existing work and for the promise of future achievement”.

The winners are announced at the International Congress of Mathematicians (ICM), which was supposed to be held in Russia this year, but was moved to Helsinki.

The honour carries a physical medal of 14K gold, 63.5 mm in diameter and weighing 169 g, and with a unit price of approximately 5,500 Canadian dollars, according to the IMU website. There is also a cash award of CAD 15,000.

The obverse of the medal is embossed with the head of Archimedes facing right, and the Latin words “Transire suum pectus mundoque potiri”, translated as “To pass beyond your understanding and make yourself master of the universe”.

The reverse has the inscription “Congregati ex toto orbe mathematici ob scripta insignia tribuere”, or “The mathematicians having congregated from the whole world awarded (this medal) because of outstanding writings”.

History of the Medal

According to the IMU website, the 1924 ICM in Toronto adopted a resolution that at each conference, two gold medals would be awarded to recognise outstanding mathematical achievement.

The Canadian mathematician Prof J C Fields, who was secretary of the 1924 Congress, later donated funds to establish the medals, which were named in his honour. 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 IMU says.

The Fields Medal Symposium is organised by the Fields Institute, Toronto, Canada. “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,” the IMU says.

Indian-origin winners

Among the more than 60 mathematicians who have been awarded the Fields Medal since 1936, there are two of Indian origin — Akshay Venkatesh of the Institute for Advanced Study at Princeton, who won in 2018, the last time the honour was announced, and Manjul Bhargava of the Department of Mathematics at Princeton University, in 2014.

According to the IMU, Venkatesh was awarded the Medal “for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects”.

Bhargava was honoured for “developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves”.