John William Scott Cassels, FRS (born July 11, 1922 in Durham) is a leading English mathematician. Events 911 - Signing of the Treaty of Saint-Clair-sur-Epte between Charles the Simple and Rollo of Normandy. Year 1922 ( MCMXXII) was a Common year starting on Sunday of the Gregorian calendar. Durham (ˈdʌrəm in RP, locally ˈdʏrəm is a small city and main settlement of the City of Durham district of County Durham, England England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland A mathematician is a person whose primary area of study and research is the field of Mathematics.
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Biography
Educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh, Cassels graduated from the University of Edinburgh with an MA in 1943. Durham (ˈdʌrəm in RP, locally ˈdʏrəm is a small city and main settlement of the City of Durham district of County Durham, England George Heriot's School is an independent primary and secondary School on Lauriston Place in Edinburgh, Scotland, with Edinburgh ( ˈɛdɪnb(ərə Dùn Èideann) is the Capital of Scotland and is its second largest city after Glasgow. The University of Edinburgh (Oilthigh Dhùn Èideann founded in 1582 is a renowned centre for teaching and research in Edinburgh, Scotland, UK. A Master of Arts in Scotland is an academic degree in Humanities and Social sciences awarded by the Ancient universities of Scotland –
His academic career was interrupted in World War II when he was involved in cryptography at Bletchley Park. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes After the war he became a research student of Louis Mordell at Trinity College, Cambridge; he received his PhD in 1949 and was elected a fellow of Trinity in the same year. Louis Joel Mordell ( 28 January 1888 - 12 March 1972) was a British mathematician known for pioneering research in Number theory. Trinity College is a constituent college of the University of Cambridge in Cambridge, England. The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the "PhD" redirects here for other uses see PhD (disambiguation. A fellow in the broadest sense is someone who is an equal or a comrade
After finishing his major, Cassels spent a year lecturing in mathematics at the University of Manchester before returning to Cambridge as a lecturer in 1950. The University of Manchester is a " red brick " civic University located in Manchester, England. He was appointed Reader in Arithmetic in 1963, the same year he was elected as a fellow of the Royal Society of London. In the academic hierarchy in the United Kingdom and some universities in Australia and New Zealand, reader is the rank between Senior lecturer The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 In 1967 he was appointed as Sadleirian Professor of Pure Mathematics at Cambridge. The Sadleirian Chair is a Professorship in Pure mathematics at the University of Cambridge. In 1969 he became Head of the Department of Pure Mathematics and Mathematical Statistics. The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics and the Department of Applied Mathematics and He retired in 1984.
Mathematical work
He initially worked on elliptic curves. In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. In Number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between Convex sets and In Number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of Real numbers by Rational In Mathematics, particularly in Arithmetic geometry, the Weil-Châtelet group of an Abelian variety A defined over a field K In Mathematics, Galois cohomology is the study of the Group cohomology of Galois modules that is the application of Homological algebra to In Mathematics, a proof by infinite descent is a particular kind of proof by Mathematical induction. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. In Mathematics, particularly in Arithmetic geometry, the Weil-Châtelet group of an Abelian variety A defined over a field K
His mathematical style is mainly as a problem solver, prepared for example to tackle individual Diophantine equations by algebraic number theory and p-adic methods. In Mathematics, a Diophantine equation is an indeterminate Polynomial Equation that allows the variables to be Integers only In Mathematics, algebraic number theory is a major branch of Number theory which studies the Algebraic structures related to Algebraic integers In Mathematics, the p -adic number systems were first described by Kurt Hensel in 1897 His publications number around 200 papers.
Awards
External links
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