###### Mathematics

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## Introduction

The department is situated at the corner of Gower Place and Gordon Street on the main UCL site. It occupies floors five to eight above the Students’ Union and consists of lecture rooms, lecturers’ offices and the departmental office. There is also a student common room and a study room with a small library.

The Mathematics Department at UCL is an internationally renowned department within one of the world’s most prestigious universities. In the 2014 Research Excellence Framework exercise in which research outputs, research environment and impact of the research from university departments across the UK were judged, 82% of UCL's mathematical sciences research activity was judged to be either world-leading or internationally excellent. We were delighted to be among the strongest mathematical science departments in the UK: we are 6th (out of 53) in the UK in the amount produced of world-leading (4*) research publications.

The department’s reputation dates from 1826 when it was one of the founding departments of UCL and as such it is the third oldest university mathematics department in England. The first Professor of Mathematics was Augustus De Morgan who is famous for his laws of sets. It was he who posed the famous ‘Four Colour Problem’ when he was quoted as saying, “A student of mine asked me today to give him a reason for the fact which I did not know to be a fact – and do not yet. He says that if a figure be anyhow divided and the compartments differently coloured so that figures with any portion of common boundary line are differently coloured, four colours are wanted, but no more.” This problem eluded the efforts of mathematicians for over a hundred years and was eventually proved using 1,200 hours of computer time!

Another world-renowned professor was J J Sylvester. He was a pupil of De Morgan, and was one of the founders of modern algebra and, in particular, was responsible for introducing the term matrix.

The department’s Goldsmid chair in Applied Mathematics was founded specifically with the mathematician W K Clifford in mind. His work on geometry was a significant precursor of general relativity, and some of his analyses in non-Euclidean geometry are still considered as good models for various Einstein cosmologies. Another distinguished holder of this chair was Karl Pearson who was one of the founders of biometry and the use of statistics in many branches of science. He is remembered for the Pearson Significance Test in statistics. A more recent holder of the chair was Sir Harrie Massey, one of the foremost figures in space research and a leading world expert on atomic and molecular collisions.

Among recent members of the department was one of the twentieth century’s greatest theorists in fluid mechanics, Sir James Lighthill. He held the Lucasian chair at Cambridge which was once held by Newton and was recently held by Stephen Hawking.

Since its beginning, mathematics at UCL has been enhanced by its many outstanding members of staff. Indeed two of its students (and later staff) Professor Klaus Roth (1958) and Professor Alan Baker (1970) have gone on to win the Fields Medal, the mathematician’s equivalent of the Nobel Prize. Another former member of staff, Professor Tim Gowers, won the Fields Medal in 1998 for work he did while at UCL. In all there have only ever been six British winners of Fields Medals! Sir Roger Penrose, a UCL Mathematics graduate, is one of a very small elite who are members of the Order of Merit. Only one other mathematician is currently a member.

The department currently has around 50 members of academic staff of whom half are professors plus a number of Honorary Research Fellows. The department also has around 20 Postdoctoral Research Associates and welcomes a regular stream of distinguished visiting academics from the UK and abroad. The broad range of research interests is reflected in the large choice of courses available in the third and fourth years of the degree programmes, from functional analysis to fluid mechanics and from theory of traffic flow to financial mathematics. The world-rated research journal Mathematika is published by the department.

The department also includes CORU (the Clinical Operational Research Unit) which applies mathematics to a wide range of medically oriented research topics. The world-renowned London Mathematical Society is also closely associated with the department. The department also participates in CoMPLEX (Centre for Mathematics and Physics in the Life sciences and EXperimental biology).

The original prospectus for the Mathematics Department in 1826 stated:

“THE MATHEMATICAL SCIENCES are so justly valued as a discipline
of the reasoning faculties,
and as an unerring measure of human advancement, that the
commendation of them might seem
disrespectful to the judgement of the reader, if they did
not afford by far the most striking instance
of the dependence of the most common and useful arts upon
abstruse reasoning. The elementary propositions of Geometry were
once merely speculative; but those to whom
their subserviency to the speed and safety of
voyages, is now familiar, will be slow to
disparage any truth for the want of present
and palpable usefulness.”

Nearly all of this remains as true today as then!