field_of_work victor kolyvagin
___MASK86___ ( from Greek  " máthma ",  knowledge , study , learning ) is the study of topics such as quantity ( numbers ), structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of ___MASK86___ . In ___MASK86___ , the Birch and Swinnerton - Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve . It is an open problem in the field of ___MASK4___ and is widely recognized as one of the most challenging mathematical problems . The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute , which has offered a $ 1 , 000 , 000 prize for the first correct proof . It is named after mathematicians Bryan Birch and Peter Swinnerton - Dyer who developed the conjecture during the first half of the 1960s with the help of machine computation . , only special cases of the conjecture have been proved . ___MASK4___ or , in older usage , arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . It is sometimes called " The Queen of Mathematics " because of its foundational place in the discipline . Number theorists study prime numbers as well as the properties of objects made out of integers ( e . g ., rational numbers ) or defined as generalizations of the integers ( e . g ., algebraic integers ). In ___MASK86___ , an elliptic curve is a plane algebraic curve defined by an equation of the form Victor Alexandrovich Kolyvagin ( Russian :          ) is a Russian ___MASK14___ who wrote a series of papers on Euler systems , leading to breakthroughs on the Birch and Swinnerton - Dyer conjecture , and Iwasawa ' s conjecture for cyclotomic fields . His work also influenced Andrew Wiles ' s work on Fermat ' s Last Theorem . Kolyvagin received his Ph . D . in ___MASK86___ in 1981 from Moscow State University , where his advisor was Yuri I . Manin . He then worked at Steklov Institute of ___MASK86___ in Moscow until 1994 . In 1990 he received the Chebyshev Prize of the USSR Academy of Sciences . Since 1994 he has been a professor of ___MASK86___ in the United States . He was a professor at Johns Hopkins University until 2002 when he became the first person to hold the Mina Rees Chair in ___MASK86___ at the Graduate Center Faculty at The City University of New York . Leonhard Euler ( 15 April 170718 September 1783 ) was a Swiss ___MASK14___ , physicist , astronomer , logician and engineer who made important and influential discoveries in many branches of ___MASK86___ like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic ___MASK4___ . He also introduced much of the modern mathematical terminology and notation , particularly for mathematical analysis , such as the notion of a mathematical function . He is also known for his work in mechanics , fluid dynamics , optics , astronomy , and music theory . The Clay ___MASK86___ Institute ( CMI ) is a private , non - profit foundation , based in Peterborough , New Hampshire , United States . CMI ' s scientific activities are managed from the President ' s office in Oxford , United Kingdom . The institute is " dedicated to increasing and disseminating mathematical knowledge ." It gives out various awards and sponsorships to promising mathematicians . The institute was founded in 1998 through the sponsorship of Boston businessman Landon T . Clay . Harvard mathematician Arthur Jaffe was the first president of CMI . In ___MASK4___ , Fermat ' s Last Theorem ( sometimes called Fermat ' s conjecture , especially in older texts ) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2 . The cases and have been known to have infinitely many solutions since antiquity . The University of Oxford ( informally Oxford University or simply Oxford ) is a collegiate ___MASK85___ university located in Oxford , England , United Kingdom . While having no known date of foundation , there is evidence of ___MASK15___ as far back as 1096 , making it the oldest university in the ___MASK17___ - speaking world and the world ' s second - oldest university in continuous operation . It grew rapidly from 1167 when Henry II banned ___MASK17___ students from attending the University of Paris . After disputes between students and Oxford townsfolk in 1209 , some academics fled northeast to Cambridge where they established what became the University of Cambridge . The two " ancient universities " are frequently jointly referred to as " Oxbridge ". Sir Henry Peter Francis Swinnerton - Dyer , 16th Baronet ( born 2 August 1927 ), commonly known as Peter Swinnerton - Dyer , is an ___MASK17___ mathematician specialising in ___MASK4___ at University of Cambridge . As a mathematician he is best known for his part in the Birch and Swinnerton - Dyer conjecture relating algebraic properties of elliptic curves to special values of L - functions , which was developed with Bryan Birch during the first half of the 1960s with the help of machine computation , and for his work on the Titan operating system . In ___MASK86___ , an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields . They were introduced by in his work on Heegner points on modular elliptic curves , which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product . Sir Andrew John Wiles ( born 11 April 1953 ) is a British ___MASK14___ and a Royal Society ___MASK85___ Professor at the University of Oxford , specialising in ___MASK4___ . He is most notable for proving Fermat ' s Last Theorem , for which he received the 2016 Abel Prize . Wiles has received numerous other honours . The President , Council and Fellows of the Royal Society of London for Improving Natural Knowledge , commonly known as the Royal Society , is a learned society for ___MASK45___ and is possibly the oldest such society still in existence . Founded in November 1660 , it was granted a royal charter by King Charles II as " The Royal Society ". The Society is the United Kingdom ' s and Commonwealth of Nations ' Academy of Sciences and fulfills a number of roles ; promoting ___MASK45___ and its benefits , recognising excellence in ___MASK45___ , supporting outstanding ___MASK45___ , providing scientific advice for policy , fostering international and global cooperation , education and public engagement . The society is governed by its Council , which is chaired by the Society ' s President , according to a set of statutes and standing orders . The members of Council and the President are elected from and by its Fellows , the basic members of the society , who are themselves elected by existing Fellows . As of 2016 , there are about 1 , 600 fellows , allowed to use the postnominal title FRS ( Fellow of the Royal Society ), with up to 52 new fellows appointed each year . There are also royal fellows , honorary fellows and foreign members , the last of which are allowed to use the postnominal title ForMemRS ( Foreign Member of the Royal Society ). The Royal Society President is Venkatraman Ramakrishnan , who took up the post on November 30 , 2015 .