John William Scott "Ian" Cassels, FRS (11 July 1922 – 27 July 2015) was a British mathematician.

Biography

Cassels was educated at Neville's Cross Council School in

Durham Durham most commonly refers to: *Durham, England, a cathedral city and the county town of County Durham *County Durham, an English county * Durham County, North Carolina, a county in North Carolina, United States *Durham, North Carolina, a city in N ...

and

George Heriot's School George Heriot's School is a Scottish independent primary and secondary day school on Lauriston Place in the Old Town of Edinburgh, Scotland. In the early 21st century, it has more than 1600 pupils, 155 teaching staff, and 80 non-teaching staff. ...

in Edinburgh. He went on to study at the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

and graduated with an undergraduate

Master of Arts A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Th ...

(MA) degree in 1943. His academic career was interrupted in

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

when he was involved in

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years followin ...

. After the war he became a research student of

Louis Mordell Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...

; he received his PhD in 1949 and was elected a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

of Trinity in the same year. Cassels then spent a year lecturing in mathematics at the

University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univ ...

before returning to Cambridge as a lecturer in 1950. He was appointed

Reader A reader is a person who reads. It may also refer to: Computing and technology * Adobe Reader (now Adobe Acrobat), a PDF reader * Bible Reader for Palm, a discontinued PDA application * A card reader, for extracting data from various forms of ...

in Arithmetic in 1963, the same year he was elected as a fellow of the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

. In 1967 he was appointed as

Sadleirian Professor of Pure Mathematics The Sadleirian Professorship of Pure Mathematics, originally spelled in the statutes and for the first two professors as Sadlerian, is a professorship in pure mathematics within the DPMMS at the University of Cambridge. It was founded on a beque ...

at Cambridge. In 1969 he became Head of the

Department of Pure Mathematics and Mathematical Statistics Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ...

. He retired in 1984.

Mathematical work

He initially worked on

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s. After a period when he worked on

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental informatio ...

and

diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by r ...

, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the

Selmer group In arithmetic geometry, the Selmer group, named in honor of the work of by , is a group constructed from an isogeny of abelian varieties. The Selmer group of an isogeny The Selmer group of an abelian variety ''A'' with respect to an isogeny ' ...

with

Galois cohomology In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group ''G'' associated to a field extension ''L''/''K'' acts in a natur ...

and laying some of the foundations of the modern theory of

infinite descent In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold f ...

. His best-known single result may be the proof that the Tate-Shafarevich group of an elliptic curve, if it is finite, must have order that is a square; the proof being by construction of an

alternating form In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is a ...

. Cassels often studied individual Diophantine equations by algebraic number theory and p-adic methods. His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades.

Publications

*. Reviewed in *. Reviewed in * * * Reviewed in: Johnson, Charles (1983) Economics For Mathematicians (J. W. S. Cassels), SIAM Rev., 25(4), 596–597. AND Binmore, Ken (1982) CASSELS, J. W. S., Economics for mathematicians, The Bulletin of the London Mathematical Society, Volume XIV . G. Binmorep 269 * * *

References

External links

* {{DEFAULTSORT:Cassels, John William Scott 1922 births 2015 deaths English mathematicians Number theorists Fellows of the Royal Society Alumni of the University of Edinburgh Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Bletchley Park people People educated at George Heriot's School Sadleirian Professors of Pure Mathematics

Biography

Mathematical work

Publications

See also

References

External links