Fields Medal: Feature Nobel Prize for Young Mathematicians

Short Short SUNITA CHAND & RAMESH CHANDRA PARIDA John Charles Fields

IELDS Medal is often described as the Besides the medal and a citation, it of mathematics initially developed to “Nobel Prize of Mathematics” for the also carries a monetary award of US $ understand celestial mechanics. It studies Fprestige it carries. However, there are 15,000. No doubt it is much less as dynamical systems, which are simply a number of differences between the two. compared to the 1.5 million US dollar Nobel mathematical rules that describe how a The Nobel Prize is referred to as “a life Prize, but that does not erode the system changes over time. Lindenstrauss boat thrown at a person who has already importance of the Fields Medal, because developed powerful theoretical tools and reached the shore”, because in most it is awarded by a highly prestigious body used them to solve a series of striking cases the recipient is already a very like the IMU. problems in areas of mathematics that are famous and well-established person in his seemingly far afield. These methods are field and the prize is merely a recognition, The Medal expected to give continuous insights which does not serve as an incentive for The Fields Medal was designed by a throughout mathematics for decades to him. Critics also sarcastically say that to Canadian sculptor R. Tait McKenzie. Its come. get it one of the most important criteria is obverse carries the image of Archimedes Chau received the medal “For his “long life”, as most of the awardees are and a quote attributed to him, which reads proof of the Fundamental Lemma in the usually very aged and are at the fag end “Transire suum pectus mundoque potiri” in theory of automorphic forms through the of their lives. Latin, whose English translation is “Rise In contrast, the Fields Medal is above oneself and grasp the world”. awarded to young mathematicians, Similarly, the Latin inscription on its reverse whose 40th birthday falls after the 1st of side reads “Congregati Ex Toto Orbe January of the year in which the award is Mathematici Ob Scripta Insignia Tribuere”. conferred. Therefore, not only does it carry In English it can be translated as “The recognition for original work, but also Mathematicians having congregated from provides incentive to serve as a stimulus the whole world awarded because of for renewed efforts to work along the line outstanding writing”. for the rest of their lives. The background of the medal has a Besides, unlike the Nobel Prizes, which representation of Archimedes’ tomb along are awarded every year, the Fields Medal with a carving illustrating his theorem on is given every four years. the spheres and cylinders, behind a branch of a tree. Its rim carries the name The Award of the awardee. The Fields Medal was conceived by the famous Canadian mathematician John Recent Awardees Charles Fields. Its first winners were Lars The four brilliant young mathematicians Ahlfors of Finland and Jesse Douglas of who recently received the Fields Medal the US, who won in 1936. Thereafter, from at the latest International Congress of the 1950 it has regularly been awarded every IMU, held at Hyderabad (India) in August four years during the International Congress are Elon Lindenstrauss of Israel, Ngo Bao of the International Mathematical Union Chau of Vietnam, Stanislav Smirnov of (IMU). So far, 52 young creative geniuses Russia and Cedric Villani of France. belonging to 15 countries, whose Lindenstrauss was nominated for the contributions have made wide impacts in award “For his results on measure rigidity in the field of mathematics, have received ergodic theory and their applications to it. number theory”. Ergodic theory is a field Obverse side of Medal (top), Reverse side of Medal SCIENCE REPORTER, OCTOBER 2011 38 Short Feature LIST OF FIELDS MEDALISTS introduction of new algebro-geometric Year Location of Name of Country Remarks methods”. It is considered as a corner International the Medalist stone of the subject. As a result, Chau Congress (IMU) removed one of the great impediments 1936 Oslo, Norway Lars Ahlfors Finland to a grand, decade-long programme to Jesse Douglas USA uncover hidden connections between 1950 Cambridge, US Laurent Schwartz France seemingly disparate areas of Atle Selberg Norway mathematics. Therefore, he provided a 1954 Amsterdam, Kunihiko Kodaire Japan Serre is the youngest solid foundation for a large body of theory Netherlands Jean-Pierre Serre France winner (27 years). and developed techniques that are likely 1958 Edinburg, UK Klaus Roth UK to unleash a flood of new results. Rene Thom France The honour was bestowed upon 1962 Stockholm, Lars Hormander Sweden Smirnov “For his igneous and astonishing Sweden John Milnor USA work on the existence and conformal 1966 Moscow, USSR Michael Atiyah UK Grothendieck boycotted invariance of scaling limits or continuum Paul Joseph Cohen USA the ceremony held in limits of lattice model in statistical physics”. Alexander France Moscow to protest Soviet The work confirms rigorously, what so far Grothendieck military action in East was accepted on merely heuristic Stephen Smale USA Europe. grounds. His success in analyzing lattice 1970 Nice, France Alan Baker UK Novikov was unable to model in statistical physics will be a stimulus Heisuke Hironaka Japan travel to the Congress for further work. Sergei Novikov Soviet due to restrictions The last but not the least, Villani Union placed on him by attracted the nomination “For his proofs of John G. Thompson USA Soviet Government. non-linear Landau damping and 1974 Vancouver, Enrico Bombieri Italy convergence of equilibrium for Boltzmann Canada David Mamford USA equation”. Formulated by Ludwig 1978 Helsinki, Pierre Deligne Belgium Margulis also could not Boltzmann (1872), the equation named Finland Charles Fefferman USA receive the medal due after him is not time-reversible. According Grigory Margulis Soviet to the same reason. to it, the molecules (gaseous) almost always Union Jacques Tits received it go from a state of greater order (e.g., Daniel Quillen USA on his behalf. enclosed in a beaker) to less order (e.g., 1982 Warsaw, Alain Connes France The Congress could not spread around the room). It means the William Thurston USA be held in 1982. entropy increases, but then the question Shing-Tung Yau USA Rescheduled in 1983. comes – how quickly? Villani and his co- 1986 Berkeley, US Simon Donaldson UK workers, through mathematical models, Gerd Faltings Germany found an answer that though entropy Michael Freedman USA always increases, sometimes it does so 1990 Kyoto, Japan Vladimir Drinfel’d Soviet Witten became the first faster and sometimes slower. Union and so far the only They also brought a deep Vaughan F.R.Jones New Zealand physicist to win the understanding of another controversial Shigefumi Mori Japan award. theory of the Soviet physicist Lev Edward Witten USA Davidovich Landau’s claim that under 1994 Zurich, Jean Bourgain Belgium certain circumstances a phenomenon Switzerland Pierre-Louis Lions France can approach equilibrium without Jean-Christophe Yoccoz France increasing entropy. Efim Zelmanov Russia Much of Villani’s works are his profound 1998 Berlin, Richard Borcherds UK Andrew Wiles recieved mathematical interpretation of the Germany Timothy Gowers UK silver plaque “Quantized physical concept of entropy, which he has Maxim Kontsevich Russia Fields Medal”as he was applied to solve a number of major Curtis T.McMullen USA more than 40 years old. problems inspired by physics. Furthermore, 2002 Beijing, China Laurent Lafforgue France his results have fed back into mathematics, Vladimir Voevodsky Russia enriching both the fields. 2006 Madrid, Spain Andrei Okounkov Russia Perelman refused the Grigoi Perelman Russia medal and did not Dr. Sunita Chand is Professor, Dept. of Mathematics, Terence Tao Australia attend the Congress. Institute of Technical Education & Research (ITER), Wendelin Werner France Siksha O Anusandhan (SOA) University, Jagamara, 2010 Hyderabad, Elon Lindenstrauss Israel Khandagiri, Bhubaneswar (Odisha); Email: India Ngo Bao Chau Vietnam [email protected] Stanislav Smirnov Russia Dr. Ramesh Chandra Parida is Retd. Professor, Cedric Villani France OUAT, 124/2445 Khandagiri Vihar, Bhubaneswar 2014 Seoul, South Korea (Odisha) 39 SCIENCE REPORTER, OCTOBER 2011