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Ian Grant Macdonald (born 11 October 1928 in London, England) is a British
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
known for his contributions to
symmetric function In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f ...
s,
special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined b ...
s,
Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...
theory and other aspects of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
,
algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in alg ...
, and
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
. He was educated at
Winchester College Winchester College is a public school (fee-charging independent day and boarding school) in Winchester, Hampshire, England. It was founded by William of Wykeham in 1382 and has existed in its present location ever since. It is the oldest of ...
and
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. ...
, graduating in 1952. He then spent five years as a
civil servant The civil service is a collective term for a sector of government composed mainly of career civil servants hired on professional merit rather than appointed or elected, whose institutional tenure typically survives transitions of political leaders ...
. He was offered a position at
Manchester University , 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 Univer ...
in 1957 by
Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...
, on the basis of work he had done while outside academia. In 1960 he moved to the
University of Exeter , mottoeng = "We Follow the Light" , established = 1838 - St Luke's College1855 - Exeter School of Art1863 - Exeter School of Science 1955 - University of Exeter (received royal charter) , type = Public , ...
, and in 1963 became a Fellow of
Magdalen College, Oxford Magdalen College (, ) is a constituent college of the University of Oxford. It was founded in 1458 by William of Waynflete. Today, it is the fourth wealthiest college, with a financial endowment of £332.1 million as of 2019 and one of the ...
. He became Fielden Professor at Manchester in 1972, and professor at
Queen Mary College, University of London Queen Mary University of London (QMUL, or informally QM, and previously Queen Mary and Westfield College) is a public university, public research university in Mile End, East London, England. It is a member institution of the federal University of ...
, in 1976. He worked on
symmetric products of algebraic curves In mathematics, the ''n''-fold symmetric product of an algebraic curve ''C'' is the quotient space of the ''n''-fold cartesian product :''C'' × ''C'' × ... × ''C'' or ''C'n'' by the group action of the symmetric group ''S'n'' on ''n'' ...
, Jordan algebras and the
representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
of groups over
local field In mathematics, a field ''K'' is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation ''v'' and if its residue field ''k'' is finite. Equivalently, a local field is a locally compact ...
s. In 1972 he proved the
Macdonald identities In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by . They include as special cases the Jacobi triple product identity, Watson's quintuple product identity, several iden ...
, after a pattern known to
Freeman Dyson Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum m ...
. His 1979 book ''Symmetric Functions and Hall Polynomials'' has become a classic. Symmetric functions are an old theory, part of the
theory of equations In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an ...
, to which both
K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometr ...
and
representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
lead. His was the first text to integrate much classical theory, such as
Hall polynomial In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian ''p''-groups. It was first discussed by but forgotten until it was rediscovered by , both of whom published no more th ...
s, Schur functions, the
Littlewood–Richardson rule In mathematics, the Littlewood–Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural number ...
, with the
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...
approach. It was both an expository work and, in part, a research monograph, and had a major impact in the field. The
Macdonald polynomial In mathematics, Macdonald polynomials ''P''λ(''x''; ''t'',''q'') are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald origi ...
s are now named after him. The Macdonald conjectures from 1982 also proved most influential. Macdonald was elected a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemati ...
in 1979. He was an invited speaker in 1970 at the
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...
(ICM) in Nice and a plenary speaker in 1998 at the ICM in Berlin. In 1991 he received the Pólya Prize of the
London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...
. He was awarded the 2009
Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have ...
for Mathematical Exposition. In 2012 he became a fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...
.


Selected publications

*Macdonald, I. G
''Affine Hecke Algebras and Orthogonal Polynomials.''
Cambridge Tracts in Mathematics, 157. Cambridge University Press, Cambridge, 2003. x+175 pp.  *Macdonald, I. G

Second edition. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. x+475 pp.  *Macdonald, I. G. ''Symmetric Functions and Orthogonal Polynomials.'' Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, New Brunswick, New Jersey. University Lecture Series, 12. American Mathematical Society, Providence, Rhode Island, 1998. xvi+53 pp.  * Atiyah, M. F.; Macdonald, I. G. ''Introduction to Commutative Algebra.'' Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. ix+128 pp. 
1994 pbk edition
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References


External links

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Biographical notice
{{DEFAULTSORT:Macdonald, Ian Grant 1928 births Living people People educated at Winchester College Alumni of Trinity College, Cambridge Mathematicians from London Symmetric functions Academics of Queen Mary University of London Academics of the University of Manchester Fellows of Magdalen College, Oxford Fellows of the American Mathematical Society Fellows of the Royal Society 21st-century British mathematicians 20th-century British mathematicians