Every four years, the Fields Medal, the most prestigious award in the field of mathematics, is awarded to two, three, or four persons no older than forty who have made a significant contribution to mathematics. Though it is not quite as famous as the Nobel Prize and does not pay as much in prize money, the Fields Medal is one of its nearest equivalents in the field of mathematics (the more recently established Abel Prize is an even closer equivalent). There is no Nobel Prize for mathematicians.

The Fields Medal was first established with a bequest from Canadian mathematician John Charles Fields, who believed that mathematics deserved something similar to a Nobel Prize. The first one was awarded in 1936, to Lars Alfohrs of the University of Helsinki in Finland, and to American Jesse Douglas of MIT. After that, no Fields Medals were awarded until 1950. That year, Laurent Schwartz, from France’s University of Nancy, and Atle Sehlberg of Norway’s Insitutute for Advanced Study, won the prize.

In 2010, there are four winners. They were announced during the opening ceremony of the International Mathematical Congress, held this year in Hyderabad, India, on August nineteenth.

The four winners, and the reasons why they were chosen, are as follows:

Cedric Villani: Director of the Institut Poincare in Paris, France, Villani, 37, has made significant contributions to mathematical interpretations of concepts of physics. His work has resulted in several breakthroughs in mathematical and physical concepts that had never been fully understood.

Stanislav Smirnov: Born in St. Petersburg, Russia, in 1970, Smirnov has been a professor at the University of Geneva, Switzerland since 2003. He was the first to prove conformal invariance in certain two dimensional models used in physics. His work laid the foundation for Cardy’s Formula and provided a vital missing piece for the theory of Schramm-Lowener Evolution.

Elon Lindenstrasse: A professor at Hebrew University in Jerusalem, Lindenstrasse, 40, has made significant contributions to ergodic theory. His work is described by the International Congress of Mathematics as “exceptionally deep” and having an impact “far beyond ergodic theory.”

Ngo Bau Chau: Born in Hanoi, Vietnam, Chau, 38, is now a naturalized citizen of France. He holds a professorship at the Faculte des Sciences in Orsay, France, and is a Member of the Institute for Advanced Study in Princeton, USA. He has received an appointment at the University of Chicago, beginning in September 2010. He is being awarded the Fields Medal for, in the words of the International Congress of Mathematicians, “his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.”

All four of these winners have contributed new concepts to the field of mathematics. People unfamiliar with advanced mathematical concepts may best understand this by associating the award with the movie “Good Will Hunting,” in which the protagonist solves an equation believed to have no solution. The Fields Award is given to young mathematicians (a recipient cannot turn 40 any earlier than January first of the year when their prize is awarded) who have given mathematical concepts new meanings or new solutions.