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 Literature, letters, judged to be "eminently distinguished in their subject". ...

(June 1867 – 24 February 1960) was "one of Scotland's leading

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, mathematical structure, structure, space, Mathematica ...

s".. 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 hype ...

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 Carse of Forth to the north. The village is west of Stirling and north of Glasgow. It is south-east of Loch Lo ...

, a small village near

Stirling Stirling (; ; ) is a City status in the United Kingdom, city in Central Belt, central Scotland, northeast of Glasgow and north-west of Edinburgh. The market town#Scotland, market town, surrounded by rich farmland, grew up connecting the roya ...

Scotland Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...

; 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 The University of Glasgow (abbreviated as ''Glas.'' in post-nominals; ) is a public research university in Glasgow, Scotland. Founded by papal bull in , it is the fourth-oldest university in the English-speaking world and one of Scotland's four ...

, 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 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.Iain Stevenson, ''Book Makers: British Publishing in the Twentieth Century''. London: The British Library, 2010, p. 77. History The firm was foun ...

, 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 ...

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 (RSE) 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 establis ...

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

George Alexander Gibson George Alexander Gibson (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 is named ...

, 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 mathemat ...

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 James Gordon Gray (1876 – 6 November 1934) was a Scottish mathematician and physicist. Life Grey was born in Glasgow in 1876, the third of eight children of Annie Gordon and Andrew Gray. He was educated at Friars Grammar School, in Bangor ...

. 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 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

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 i ...

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 signifi ...

Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the ...

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

Bessel function Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...

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 are real-valued parameters. Since we may add to to change the sign of , i ...

hypergeometric series In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

, and the Schläfli double six. He also made contributions to the theory of elasticity, for which he won the Makdougall-Brisbane Prize. He died at home, 47 Airthrey Avenue in

Glasgow Glasgow is the Cities of Scotland, most populous city in Scotland, located on the banks of the River Clyde in Strathclyde, west central Scotland. It is the List of cities in the United Kingdom, third-most-populous city in the United Kingdom ...

on 25 February 1960.

Publications

Dougall translated

Max Born Max Born (; 11 December 1882 – 5 January 1970) was a German-British theoretical physicist 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 ...

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

Émile Borel Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biograp ...

'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