The Mathematical Institute is the
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
department at the
University of Oxford
The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...
in England. It is one of the nine departments of the university's
Mathematical, Physical and Life Sciences Division. The institute includes both pure and applied mathematics (Statistics is a separate department) and is one of the largest mathematics departments in the
United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotlan ...
with about 200 academic staff.
It was ranked (in a joint submission with Statistics) as the top mathematics department in the UK in the 2021
Research Excellence Framework
The Research Excellence Framework (REF) is a research impact evaluation of British Higher Education Institutions (HEIs). It is the successor to the Research Assessment Exercise and it was first used in 2014 to assess the period 2008–2013. REF is ...
.
Research at the Mathematical Institute covers all branches of mathematical sciences ranging from, for example, algebra, number theory, and geometry to the application of mathematics to a wide range of fields including industry, finance, networks, and the brain. It has more than 850 undergraduates and 550
doctoral
A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...
or
masters students.
The institute inhabits a purpose-built building between
Somerville College
Somerville College is a constituent college of the University of Oxford in England. It was founded in 1879 as Somerville Hall, one of its first two women's colleges. It began admitting men in 1994. The college's liberal tone derives from its f ...
and
Green Templeton College on
Woodstock Road, next to the
Faculty of Philosophy.
History
The earliest forerunner of the Mathematical Institute was the School of Geometry and Arithmetic in the
Bodleian Library
The Bodleian Library () is the main research library of the University of Oxford. Founded in 1602 by Sir Thomas Bodley, it is one of the oldest libraries in Europe. With over 13 million printed items, it is the second-largest library in ...
's main quadrangle. This was completed in 1620.
Notable mathematicians associated with the university include
Christopher Wren
Sir Christopher Wren FRS (; – ) was an English architect, astronomer, mathematician and physicist who was one of the most highly acclaimed architects in the history of England. Known for his work in the English Baroque style, he was ac ...
who, before his notable career as an architect, made contributions in analytical mathematics, astronomy, and mathematical physics;
Edmond Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, Hal ...
who published a series of profound papers on astronomy while
Savilian Professor of Geometry
The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professor of Astronomy, Savilian Professorship of Astronomy) by Henry Savile (Bible translator), ...
in the early 18th century;
John Wallis
John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
, whose innovations include using the symbol
for
infinity
Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol.
From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophic ...
;
Charles Dodgson, who made significant contributions to geometry and logic while also achieving fame as a children's author under his pen name Lewis Carroll; and
Henry John Stephen Smith, another Savilian Professor of Geometry, whose work in
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
and
matrices
Matrix (: matrices or matrixes) or MATRIX may refer to:
Science and mathematics
* Matrix (mathematics), a rectangular array of numbers, symbols or expressions
* Matrix (logic), part of a formula in prenex normal form
* Matrix (biology), the ...
attracted international recognition to Oxford mathematics. Dodgson jokingly proposed that the university should grant its mathematicians a narrow strip of level ground, reaching "ever so far", so that they could test whether or not
parallel lines
In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. '' Parallel curves'' are curves that do not touch each oth ...
ever meet.
The building of an institute was originally proposed by
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
in 1930. Lectures were normally given in the individual
colleges of the university and Hardy proposed a central space where mathematics lectures could be held and where mathematicians could regularly meet. This proposal was too ambitious for the university, who allocated just six rooms for mathematicians in an extension to the
Radcliffe Science Library built in 1934. A dedicated Mathematical Institute was built in 1966 and was located at the northern end of
St Giles' near the junction with
Banbury Road in central north
Oxford
Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town.
The city is home to the University of Oxford, the List of oldest universities in continuou ...
. The needs of the institute soon outgrew its building, so it also occupied a neighbouring house on St Giles and two annexes: Dartington House on
Little Clarendon Street, and the Gibson Building on the site of the
Radcliffe Infirmary.
In 2008 the institute was given US$25 million — the largest grant ever for a mathematics department in the UK — to establish the Oxford Centre for Collaborative Applied Mathematics (OCCAM). Since 2013 the institute has been housed in the purpose-built
Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Ferma ...
Building in the
Radcliffe Observatory Quarter in
North Oxford, near the original Radcliffe Infirmary. Wiles, the university's Regius Professor of Mathematics, is known for proving
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...
. The design and construction of the building was informed by the academic staff to incorporate mathematical ideas;
Sir Roger Penrose designed a non-periodic pattern (a
Penrose tiling
A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of two-dimensional space, the plane by non-overlapping polygons or other shapes, and a tiling is ''aperiodic'' if it does not contain arbitrarily large Perio ...
) to decorate the ground at the entrance, and two structures where natural light enters the building have "crystals" illustrating concepts from
graph theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
and the vibration of a two-dimensional surface.
Research
The institute is home to a number of research groups and funded research centres. Groups in
mathematical logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
,
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
,
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
,
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
,
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
,
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
, and
mathematical physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...
date back to at least the 1960s. More recent groups include a
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
group, the Wolfson Centre for Mathematical Biology (WCMB), the Oxford Centre for Industrial Applied Mathematics (OCIAM) which includes a centre studying
financial derivatives
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements:
# an item (the "underlier") that can or must be bou ...
, and the Oxford Centre for
Nonlinear Partial Differential Equations (OxPDE). In the 21st century, the institute's research topics have come to include
quantum computing
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of wave-particle duality, both particles and waves, and quantum computing takes advantage of this behavior using s ...
,
tumour
A neoplasm () is a type of abnormal and excessive growth of tissue (biology), tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tiss ...
growth, and
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
, among other physical, biological, and economic problems. In 2012 the office of the President of the
Clay Mathematics Institute (CMI) moved to the Mathematical Institute as
Nick Woodhouse became CMI's president. The CMI offers the
Millennium Prizes of one million dollars for solving famous mathematical problems that were unsolved in 2000. The current CMI president,
Martin Bridson, is also based at the institute.
Like other university departments in the UK, the institute has been rated for the quality and impact of its research. In the 2008
Research Assessment Exercise
The Research Assessment Exercise (RAE) was an exercise undertaken approximately every five years on behalf of the four UK higher education funding councils ( HEFCE, SHEFC, HEFCW, DELNI) to evaluate the quality of research undertaken by British ...
, Oxford was joint first (with the
University of Cambridge
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
) for applied mathematics and third for pure mathematics. In the 2014
Research Excellence Framework
The Research Excellence Framework (REF) is a research impact evaluation of British Higher Education Institutions (HEIs). It is the successor to the Research Assessment Exercise and it was first used in 2014 to assess the period 2008–2013. REF is ...
, the institute submitted jointly with the Department of Statistics, getting the highest placement for mathematical sciences in the UK.
In the 2021 Research Excellence Framework, Oxford maintained its top place.
Teaching
The institute has more than 850 undergraduate students on four degree courses: Mathematics, Mathematics and Statistics, Mathematics and Philosophy, and Mathematics and Computer Science. Students decide during their degree whether to earn a
Bachelor of Arts (BA) after three years or to continue to a fourth year to earn a
Master of Mathematics (MMath).
In 2017, the time allowed for exams was increased from 90 to 105 minutes for each paper for all students, with one motivation being to improve women's scores and close the gender performance gap. The 550 postgraduate students take one of five courses to earn a
Master of Science (MSc) or conduct research to earn a DPhil (the Oxford name for a
Doctor of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original resear ...
).
''
The Guardian
''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...
''
's 2021 ranking of "Best UK universities for mathematics" placed Oxford at the top.
Outreach

The institute promotes understanding of mathematics outside the university by running public lectures, by hosting events for school students, and by supporting staff members who promote mathematics to the general public. Of those staff members, the best known are Sir
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...
,
David Acheson, and
Marcus du Sautoy
Marcus Peter Francis du Sautoy (; born 26 August 1965) is a British mathematician, Simonyi Professor for the Public Understanding of Science at the University of Oxford, Fellow of New College, Oxford and author of popular mathematics and popula ...
. Penrose, a former
Rouse Ball Professor of Mathematics
The Rouse Ball Professorship of Mathematics is one of the senior Chair (academic), chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathe ...
who has an
emeritus
''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus".
In some c ...
post at the institute, has written a series of popular books on mathematics and physics. Acheson has reached a wide audience through publishing, radio, and
YouTube
YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in ...
. Du Sautoy is the current
Simonyi Professor for the Public Understanding of Science and is known as a television and radio broadcaster as well as an author of popular books on mathematics.
Historical statutory professors

* Oxford's
Regius Professor of Mathematics was created in 2016 as part of
Queen Elizabeth's 90th birthday celebrations. Regius Professorships are awarded "to reflect an exceptionally high standard of teaching and research at an institution". The first and current holder of this chair is Sir
Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Ferma ...
.
* The
Savilian Professor of Geometry
The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professor of Astronomy, Savilian Professorship of Astronomy) by Henry Savile (Bible translator), ...
was created in 1619 by
Sir Henry Savile, at a time when the successes of astronomy and geometry prompted new interest in mathematical education.
* The
Wallis Professor of Mathematics was created in 1969 to celebrate
John Wallis
John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
, who was Savilian Professor of Geometry for 54 years.
* The
Waynflete Professor of Pure Mathematics was created as a result of a Royal Commission reviewing the university in 1877. It honours the 15th-century bishop
William of Waynflete, founder of
Magdalen College.
* The institute hosts the
Rouse Ball Professor of Mathematics
The Rouse Ball Professorship of Mathematics is one of the senior Chair (academic), chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathe ...
, a chair endowed in 1925 by
Walter William Rouse Ball. A Cambridge mathematician and historian of mathematics, Rouse Ball hoped that the new professor "would not neglect
hehistorical and philosophical aspects
f mathematics" The chair was initially advertised as a Chair in Mathematical Physics.
* The
Sedleian Professor of Natural Philosophy was established in 1621 by Sir William Sedley, 4th Baronet of
Aylesford. While some of the first holders of this chair had medical degrees, it has more recently become associated with applied mathematics.
* The
Simonyi Professor for the Public Understanding of Science was endowed in 1995 by the Hungarian software architect
Charles Simonyi
Charles Simonyi (; , ; born September 10, 1948) is a Hungarian Americans, Hungarian-American software architect.
He introduced the graphical user interface to Bill Gates for the first time who later described it as the first of two revolutiona ...
. Its first holder was the ethologist
Richard Dawkins
Richard Dawkins (born 26 March 1941) is a British evolutionary biology, evolutionary biologist, zoologist, science communicator and author. He is an Oxford fellow, emeritus fellow of New College, Oxford, and was Simonyi Professor for the Publ ...
. It has been associated with the institute since 2008, when the chair was taken up by
Marcus du Sautoy
Marcus Peter Francis du Sautoy (; born 26 August 1965) is a British mathematician, Simonyi Professor for the Public Understanding of Science at the University of Oxford, Fellow of New College, Oxford and author of popular mathematics and popula ...
.
Alumni
Sir
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...
was a member between 1961 and 1990.
Mary Cartwright, who earned her first degree and
doctorate
A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...
at Oxford, was the first female mathematician to be awarded Fellowship of the Royal Society and the first female president of the
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...
.
In popular culture
In 2015, the final episode, "What Lies Tangled", of the British television detective drama ''
Lewis'' was set and filmed in the Mathematical Institute. Sir Andrew Wiles played a professor who appears in the background of one shot.
References
Sources
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External links
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Oxford Mathematics on YouTube
{{DEFAULTSORT:Mathematical Institute, University of Oxford
1934 establishments in England
University and college buildings completed in 1966
University and college buildings completed in 2013
Departments of the University of Oxford
Mathematics departments in the United Kingdom
Mathematical institutes
Research institutes in Oxford