Dr John Dougall

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 ...

(June 1867 – 24 February 1960) was "one of Scotland's leading mathematicians".. Two formulas are named Dougall's formula after him: one for the sum of a ₇''F''₆ hypergeometric series, and another for the sum of a

bilateral hypergeometric series In mathematics, a bilateral hypergeometric series is a series Σ''a'n'' summed over ''all'' integers ''n'', and such that the ratio :''a'n''/''a'n''+1 of two terms is a rational function of ''n''. The definition of the generalized hyper ...

Life

Dougall was born in June 1867 in

Kippen Kippen is a village in west Stirlingshire, Scotland. It lies between the Gargunnock Hills and the Fintry Hills and overlooks the River Forth, Carse of Forth to the north. The village is west of Stirling and north of Glasgow. It is south-east ...

, a small village near

Stirling Stirling (; sco, Stirlin; gd, Sruighlea ) is a city in central Scotland, northeast of Glasgow and north-west of Edinburgh. The market town, surrounded by rich farmland, grew up connecting the royal citadel, the medieval old town with its me ...

Scotland Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...

; his father, a watchmaker and postmaster, had nine children, among whom John was the eldest.. He was educated locally at Kippen School. He left school at age 13 to become a post office worker, but a year later entered

Glasgow University , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

, from which he earned an M.A. in 1886. (He was later given a doctorate by the same university.) After graduating, he taught mathematics at the

Glasgow and West of Scotland Technical College The University of Strathclyde ( gd, Oilthigh Shrath Chluaidh) is a public research university located in Glasgow, Scotland. Founded in 1796 as the Andersonian Institute, it is Glasgow's second-oldest university, having received its royal chart ...

before becoming an editor and translator of mathematical publications for

Blackie and Son Blackie & Son was a publishing house in Glasgow, Scotland, and London, England, from 1809 to 1991. History The firm was founded as a bookseller in 1809 by John Blackie (1782–1874) as a partnership with two others and was known as 'Black ...

, a Glasgow publisher. He died on 24 February 1960 in Glasgow. Dougall became a member of the

Edinburgh Mathematical Society The Edinburgh Mathematical Society is a mathematical society for academics in Scotland. History The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew Je ...

in 1885, and was president of the society for 1925–1926. He won the Makdougall-Brisbane Prize 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 ...

for 1902–1904, and was elected a Fellow of the Society in 1921. His proposers were

George Alexander Gibson George Alexander Gibson FRSE FRCPE (27 January 1854 – 18 January 1913) was a Scottish physician, medical author and amateur geologist. As an author he wrote on the diverse fields of both geology and heart disease. The Gibson Memorial Lecture ...

, Sir

Edmund Taylor Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathema ...

Cargill Gilston Knott Cargill Gilston Knott FRS, FRSE LLD (30 June 1856 – 26 October 1922) was a Scottish physicist and mathematician who was a pioneer in seismological research. He spent his early career in Japan. He later became a Fellow of the Royal Society, ...

, and James Gordon Gray. He frequently published mathematical works in the proceedings and transactions of these two societies. He was also an honorary president of the Glasgow Mathematical Association, and in 1936 he followed

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

as Gibson Lecturer at Glasgow University. At Blackie and Son, Dougall oversaw the publication of many advanced mathematics books, not only from English authors but also translations from writings in German and Italian by

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

Konrad Knopp Konrad Hermann Theodor Knopp (22 July 1882 – 20 April 1957) was a German mathematician who worked on generalized limits and complex functions. Family and education Knopp was born in 1882 in Berlin to Paul Knopp (1845–1904), a businessman in ...

Tullio Levi-Civita Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significa ...

Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis. Biography Born in Anc ...

, and others. Dougall's own contributions to mathematics include works on

Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...

Mathieu function In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation : \frac + (a - 2q\cos(2x))y = 0, where a and q are parameters. They were first introduced by Émile Léonard Mathieu, ...

s, hypergeometric series, and the

Schläfli double six In geometry, the Schläfli double six is a configuration of 30 points and 12 lines, introduced by . The lines of the configuration can be partitioned into two subsets of six lines: each line is disjoint from ( skew with) the lines in its own subse ...

. He also made contributions to the theory of

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

, for which he won the Makdougall-Brisbane Prize. He died at home, 47 Airthrey Avenue 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 25 February 1960.

Publications

Dougall translated

Max Born Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a n ...

's critical book ''Atomic Physics'', and

Émile Borel Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Math ...

's ''Space and Time'' into English

References

{{DEFAULTSORT:Dougall, John 1867 births 1960 deaths Alumni of the University of Glasgow Fellows of the Royal Society of Edinburgh 19th-century Scottish mathematicians 20th-century Scottish mathematicians