Robert Alexander Rankin
FRSE
Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This soci ...
FRSAMD (27 October 1915 – 27 January 2001) was a
Scottish 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 ...
who worked in
analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...
.
Life
Rankin was born in
Garlieston
Garlieston ( gd, Baile Gheàrr Lios, IPA: paləʝeaːᵲʎis̪ is a small planned coastal village in the historical county of Wigtownshire in Dumfries and Galloway, south west Scotland. It was founded in the mid 18th century by Lord Garlies, la ...
in
Wigtownshire
Wigtownshire or the County of Wigtown (, ) is one of the historic counties of Scotland, covering an area in the south-west of the country. Until 1975, Wigtownshire was an administrative county used for local government. Since 1975 the area has f ...
the son of Rev Oliver Rankin (1885–1954), minister of
Sorbie
Sorbie ( gd, Soirbidh) is a small village in Wigtownshire, Machars, within the Administration area of Dumfries and Galloway Council, Scotland.
It is located midway between Wigtown and Whithorn on the A714 road.
Farming forms the principal loca ...
and his wife, Olivia Theresa Shaw. His father took the name Oliver Shaw Rankin on marriage and became Professor of
Old Testament
The Old Testament (often abbreviated OT) is the first division of the Christian biblical canon, which is based primarily upon the 24 books of the Hebrew Bible or Tanakh, a collection of ancient religious Hebrew writings by the Israelites. The ...
Language, Literature and Theology in 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 ...
.
Rankin was educated at
Fettes College
Fettes College () is a co-educational independent boarding and day school in Edinburgh, Scotland, with over two-thirds of its pupils in residence on campus. The school was originally a boarding school for boys only and became co-ed in 1983. In ...
then studied mathematics at
Clare College, Cambridge
Clare College is a constituent college of the University of Cambridge in Cambridge, England. The college was founded in 1326 as University Hall, making it the second-oldest surviving college of the University after Peterhouse. It was refounded ...
, graduating in 1937. At
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...
he was particularly influenced by
J.E. Littlewood
John Edensor Littlewood (9 June 1885 – 6 September 1977) was a British mathematician. He worked on topics relating to analysis, number theory, and differential equations, and had lengthy collaborations with G. H. Hardy, Srinivasa Raman ...
and
A.E. Ingham.
Rankin was elected a Fellow of Clare College in 1939, but his career was interrupted by the
Second World War
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 opposin ...
, during which he worked first for the Ministry of Supply then on
rocket
A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely fr ...
ry research at
Fort Halstead
Fort Halstead was a research site of Dstl, an executive agency of the UK Ministry of Defence. It is situated on the crest of the Kentish North Downs, overlooking the town of Sevenoaks, southeast of London. Originally constructed in 1892 as part ...
. In 1945 he returned to Cambridge as an assistant lecturer, and then moved to the
University of Birmingham
, mottoeng = Through efforts to heights
, established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...
in 1951 as Mason professor of mathematics. In 1954 he became
Professor of Mathematics, Glasgow
The Chair of Mathematics in the University of Glasgow in Scotland was established in 1691. Previously, under James VI's Nova Erectio, the teaching of Mathematics had been the responsibility of the Regents.
List of Mathematics Professors
* G ...
University
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...
, retiring in 1982.
In 1954 he was elected a Fellow of the
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
. His proposers were
William M. Smart,
Robert Garry
Robert Campbell Garry (1933) OBE FRSE (1900–1993) was a British physician and Professor of Medicine at the University of St Andrews and the University of Glasgow. During World War II, as an expert on human physiology, he advised on human ...
,
James Norman Davidson
James Norman Davidson CBE PRSE FRS (5 March 1911 – 11 September 1972) was a British biochemist, pioneer molecular biologist and textbook author. The Davidson Building at the University of Glasgow is named for him.
Life
He was the only child ...
and
Robert Pollock Gillespie
Robert Pollock Gillespie FRSE (1903–1977) was a Scottish mathematician. He was twice President of the Edinburgh Mathematical Society (1946–7 and 1968–9). He published several important books on mathematics.
Life
He was born on 21 Novembe ...
. He served as Vice President 1960 to 1963 and won the Society's Keith Prize for the period 1961–63.
Rankin had a continuing interest in
Srinivasa Ramanujan
Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis ...
, working initially with
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 ...
on Ramanujan's unpublished notes. His research interests lay in the distribution of
prime numbers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
and in
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...
s. In 1939 he developed what is now known as the
Rankin–Selberg method In mathematics, the Rankin–Selberg method, introduced by and , also known as the theory of integral representations of ''L''-functions, is a technique for directly constructing and analytically continuing several important examples of automor ...
. In 1977
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press
A university press is an academic publishing hou ...
published Rankin's ''Modular Forms and Functions''. In his review,
Marvin Knopp
Marvin Isadore Knopp (January 4, 1933 – December 24, 2011) was an American mathematician who worked primarily in number theory. He made
notable contributions to the theory of modular forms.
Life and education
Knopp was born on January 4, 1 ...
wrote:
:For, as much as any recent exposition of
modular function
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of ...
s, this book succeeds in getting near the research frontier, and in some instances even reaches it – no small feat in this theory. Only someone of Rankin's stature as a research mathematician and experience in the classroom could aspire to such an accomplishment in a self-contained work – beginning with first principles.
In 1987 Rankin received the
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...
from 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 S ...
.
Rankin died in
Glasgow
Glasgow ( ; sco, Glesca or ; gd, Glaschu ) is the most populous city in Scotland and the fourth-most populous city in the United Kingdom, as well as being the 27th largest city by population in Europe. In 2020, it had an estimated popul ...
on 27 January 2001.
Family
In 1942 he married Mary Ferrier Llewellyn.
See also
*
Rankin–Cohen bracket
Books
''An introduction to mathematical analysis'' Pergamon Press 1963; Dover 2007.
*''The modular group and its subgroups'', Madras, Ramanujan Institute, 1969.
*''Modular forms and functions'', Cambridge University Press 1977
References
External links
*
*
{{DEFAULTSORT:Rankin, Robert Alexander
1915 births
2001 deaths
People educated at Fettes College
Alumni of Clare College, Cambridge
Fellows of Clare College, Cambridge
20th-century Scottish mathematicians
Number theorists
Fellows of the Royal Society of Edinburgh
People from Dumfries and Galloway
Academics of the University of Glasgow
Academics of the University of Birmingham