Fields Medal: Meaning, History & Notable Winners

The Fields Medal Award is given every four years at the International Congress of Mathematicians (ICM). It honours exceptional mathematical achievement for current work as well as the hope of future achievement. Two to four medals are given to mathematicians who are under the age of forty on January 1 of the Congress year. The Fields Medal, named after Canadian mathematician J. C. Fields and created in 1936, is one of the most prestigious awards in mathematics and is sometimes referred to as the "Nobel Prize of Mathematics."

The Fields Medal had very different goals when it was first introduced in the 1930s. Its purpose was less about recognising outstanding academics and more about smoothing over international conflict. In reality, early committees purposefully avoided identifying the best young mathematicians in order to encourage relatively unknown individuals.

Since 2006, the prize has included a monetary reward of CA $15,000. . Fields was a driving force behind the award's creation, developing the medal himself and funding the monetary component.

The medal was first given to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas in 1936, and it has been given every four years since 1950. Its aim is to recognise and help younger mathematical researchers who have made significant contributions. Maryam Mirzakhani, an Iranian mathematician, became the first female Fields Medalist in 2014, one of sixty people to receive the prize.

History

The Fields Medal arose during a period of intense conflict in international mathematics, which influenced conceptions of its purpose. Its main promoter was John Charles Fields, a Canadian mathematician who spent his early career in a European mathematical community that was only starting to think of the field as an international endeavour.

The first International Congress of Mathematicians (ICM) was held in Zurich, Switzerland, in 1897, and was followed by ICMs in Paris in 1900, Heidelberg, Germany, in 1904, Rome in 1908, and Cambridge, United Kingdom, in 1912. The First World War ruined plans for a 1916 ICM in Stockholm, creating trouble for mathematicians.

When the dust had settled, angry researchers from France and Belgium took over, insisting that Germans and their wartime allies had no role in new foreign endeavours, congresses, or otherwise. They planned the first postwar meeting for 1920 in Strasbourg, a city that had recently been returned to France after being occupied by the Germans for half a century.

The US delegation won the right to host the next ICM in Strasbourg, but when its representatives returned home to begin fundraising, they noticed that the law of German exclusion discouraged many potential supporters. Instead, Fields took the opportunity to carry the ICM to Canada. The 1924 Toronto Congress was a disaster in terms of foreign attendance, but it ended with a small financial surplus. Years later, as the organisers were debating what to do with the remaining funds, the idea for an international medal arose.

Fields pushed the issue from his deathbed in 1932, endowing each ICM with two medals. The ICM in Zurich in 1932 appointed a committee to select the medallists for 1936 but left no guidance about how the committee should proceed. Instead, early committees were motivated by a memorandum titled ‘International Medals for Outstanding Discoveries in Mathematics' that Fields wrote shortly before his death.

The majority of the memorandum is procedural: how to manage funds, form a committee, communicate its decision, design the medal, and so on. In reality, Fields wrote that the committee should be “as free as possible” in determining winners. Fields stipulated that the medal should not be named after any individual or location, and he never intended for it to be named after himself. His most popular instruction, which was later used to justify an age restriction, was that the awards should be "in recognition of work already done" as well as "an encouragement for further achievement." In the context, however, this instruction served a different purpose: “to avoid invidious comparisons” amongst factious national groups over who deserved to win.

The first medals were given to Finnish mathematician Lars Ahlfors and United states Jesse Douglas in 1936. The next medals were not issued until 1950, due to the Second World War. Since then, they have been issued every four years.

Statutes

• The Fields Medal is presented every four years at the International Congress of Mathematicians to honour exceptional mathematical achievement for existing work and the hope of future achievement.

• The Fields Medal is given to an individual mathematician whose 40th birthday does not fall before January 1st of the year in which the Fields Medals are given.

• At any one ICM, no more than four Fields Medals are awarded. The award consists of a gold medal with Archimedes' profile and a CAD $15,000 cash prize.

• The Fields Medal Committee, which selects Fields Medal winners, is appointed by the International Mathematical Union's Executive Committee and is usually chaired by the IMU President. It is asked to choose at least two Fields Medalists, with a clear preference for four, and to consider representing a variety of mathematical fields in its selection. The Committee must follow the IMU Guidelines on conflicts of interest in its deliberations. The name of the Committee's Chair is made public, but the names of the Committee's other members remain confidential until the prize is awarded at the Congress.

• Nominations for this award must be sent to the Chair of the Prize Committee. Any nomination should include the candidate's name and affiliation, as well as the candidate's date of birth, as well as a summary of the work that qualifies the candidate for the award, written in terms that mathematicians of all backgrounds may understand, including references to the candidate's significant publications. Nominations are private and must not be revealed to the candidate. Nominations by oneself are strongly discouraged. The committee is free to consider non-nominated mathematicians.

• A person can not receive more than one IMU Award. A person can receive the Leelavati Prize in addition to one other IMU Award.

Advanced mathematics impacts our world in many more ways than ever before; the discipline is broader and more diverse than ever before, and its demographic problems and structural challenges are more pressing than ever. The Fields Medal has a significant impact on deciding what and who is important in mathematics.

The jury should leverage this position by presenting medals based on what mathematics should and should be, rather than what happens to grow fastest and shine brightest within entrenched standards and structures. By challenging themselves every four years to ask the unrecognised mathematics and mathematicians who deserve a spotlight, the prize givers could take a more active role in shaping the future of their discipline.

Fields Medal Winners from India

Akshay Venkatesh received the Fields Medal at the International Congress of Mathematics in Rio de Janeiro. He is the second Indian-origin individual to receive the award, following Manjul Bhargava, a Princeton University graduate, in 2014.

Akshay was honoured for his use of dynamics theory, which studies the equations of moving objects, to solve a number theory problem. It is the study of whole numbers, prime numbers, and integers. Akshay has received several awards for his contributions to mathematics. He has received the Salem Prize (2007), the Sastra Ramanujan Prize (2008), the Infosys Prize (2016), and the Ostrowski Prize (2017).

Maryam Mirzakhani, the First Female Fields Medalist 

Maryam Mirzakhani was a brilliant mathematician of her generation. She made significant contributions to the study of the dynamics and geometry of Riemann surfaces. Her willingness to drive a field in a new direction by always having a fresh point of view was just as remarkable as her theorems. Even among the most celebrated mathematicians, her raw talent was exceptional, and she was noted for having a passion for difficult problems.

She unintentionally became an icon. She was the first woman and the first Iranian to receive the Fields Medal. Mirzakhani was a role model for women, seeking a promising career in a male-dominated field. She embodied the country's intellectual heritage in Iran. And, for young scientists, she was a motivating force who rose above academic pressures. On July 14th 2017, she died of breast cancer at the age of 40.

Conclusion

The Fields Medal Award is given every four years at the International Congress of Mathematicians (ICM) Two to four medals are given to mathematicians who are under the age of forty on January 1 of the Congress year. The medal was first given to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas in 1936. Since 2006, the prize has included a monetary reward of CA $15,000. Maryam Mirzakhani, an Iranian mathematician, became the first female Fields Medalist in 2014, one of sixty people to receive the prize.