# James Gourlay Clunie

### Born: 26 October 1926 in St Andrews, Fife, Scotland

Died: 5 March 2013 in York, England

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**James Clunie**was known as Jim to his friends and colleagues. As a child he suffered from an attack of polio which affected his health for the rest of his life. He attended Madras College in St Andrews but these were difficult years since, when he was 13 years old, World War II began. St Andrews was not badly affected by bombing raids, despite being close to the air base at Leuchars. However, studies at school were made considerably more difficult due to the war. After the war ended, the headmaster wrote in 1947:-

One of the reasons that the headmaster was able to say that they had maintained their high standards was the fact that several of the former pupils, including Clunie, were by this time being highly successful at university.During the war years we had to work in trying conditions - black-out restrictions, shorter school days, potato holidays, overcrowding etc. but we have, I think, fully maintained the high standards of the school.

Clunie graduated from Madras College in 1945 having been awarded the Sir William Robertson Medal as Dux in Science and the Tullis Medal as Dux in Mathematics. In the autumn of 1945 he matriculated at the University of St Andrews where he studied mathematics, applied mathematics and physics. Herbert Turnbull was the Regius professor of mathematics and head of the mathematics department. Applied mathematics had been built up by Dan Rutherford who was also teaching in the department during Clunie's four years as an undergraduate. Clunie graduated with a First Class Honours B.Sc. in Mathematics in 1949 and for his outstanding performance he was awarded the Carstairs Prize. In his final two honours years he had studied the five compulsory topics, Geometry, Algebra, Analysis, Statics, and Dynamics. There were also five optional courses on offer from which he had to choose two. Clunie chose the optional courses Statistics and Special Functions. Although Clunie's performance had been outstanding in all the courses he took, he was not the best student in his year; this distinction went to Iain Adamson.

After graduating, Clunie went to Aberdeen to undertake research at the University of Aberdeen where his thesis advisor was Archibald James Macintyre. He was awarded his Ph.D. by the University of Aberdeen in 1952 for his thesis

*On Certain Topics Concerning the External Behaviour of Functions*[1]:-

The two papers referred to in this quote areIn his PhD thesis Jim developed what quickly became the 'modern' approach to the subject of Wiman-Valiron theory, published in two papers in the Journal of the London Mathematical Society.

*The determination of an integral function of finite order by its Taylor series*(1953) and

*On the determination of an integral function from its Taylor series*(1955). In the first of these, Clunie begins his Introduction as follows:-

He also expresses his thanks to his thesis advisor Archibald Macintyre:-This paper contains a revised account, for integral functions of finite order, of Wiman's analysis of the determination of an integral function by its power series. The method used differs in several particulars from previous accounts. ...

These two papers were certainly not the only ones he published over these years. Other papers are:I wish to express my gratitude to Dr A J Macintyre for suggesting the problems treated in this paper, and for his advice and criticism throughout the work.

*An extension of quasi-monotone series*(1953);

*On Bose-Einstein functions*(1954);

*Univalent regions of integral functions*(1954);

*The asymptotic paths of integral functions of infinite order*(1955);

*On a theorem of Collingwood and Valiron*(1955);

*The asymptotic behaviour of integral functions*(1955);

*Note on integral functions of infinite order*(1955);

*Note on a theorem of Parthasarathy*(1955);

*The maximum modulus of an integral function of an integral function*(1955); and

*Series of positive terms*(1955).

After the award of his doctorate from the University of Aberdeen, Clunie was appointed as a lecturer in mathematics at the University College of North Staffordshire, which was in Keele, Newcastle-under-Lyme, Staffordshire, and became Keele University in 1961. He married Nancy Tuff (born 22 October 1922) at Newcastle-under-Lyme at the beginning of 1955. Their daughter Fiona was born on 25 October 1955. Clunie did not remain at the University College of North Staffordshire until it became Keele University for, in 1956, he moved to London. Walter Hayman was appointed as the first Professor of Pure Mathematics at Imperial College, London, in 1956 and immediately began to build a major research centre for complex analysis. Clunie was one of Hayman's first appointments to Imperial College. He lived at 45 St Andrews Avenue, Wembley, a very appropriate address for someone who was born in St Andrews! At Imperial College he had an exceptionally productive research career [1]:-

Let us give a little more detail to the highlights of Clunie's research which are indicated in this quote. The paper in which he introduced the 'Clunie constant' wasAt Imperial College, Jim's complex analysis research flourished and he wrote many hugely influential papers, and supervised seven research students. His papers included one on the coefficients of univalent functions, published in Annals of Mathematics, that led to the introduction of the so-called 'Clunie constant'; another in the Journal of the London Mathematical Society that contains a result now known as 'Clunie's lemma'; and a joint paper in Crelle's Journal with Professor J Milne Anderson and Professor Christian Pommerenke that established the theory of so-called Bloch functions.

*On schlicht functions*(1959) but he continued the investigation in numerous later papers including

*On meromorphic schlicht functions*(1959) and

*On the coefficients of univalent functions*(1974). This 1974 paper was written jointly with Christian Pommerenke (born 17 December 1933 in Copenhagen). Pommerenke had studied at the University of Göttingen where he habilitated but he had spent the years 1965-67 at Imperial College, London, where he worked closely with Clunie. Returning to the quote above, let us note that 'Clunie's lemma' appeared in his paper

*On integral and meromorphic functions*(1962). The theory of Bloch functions was developed in the three-author paper

*On Bloch functions and normal functions*(1974). Clunie's co-authors on this paper were Christian Pommerenke and J Milne Anderson. James Milne Anderson (born 1938) was a Ph.D. student of Clunie's at Imperial College and was awarded his doctorate for his thesis

*The Behaviour of Integral and Subharmonic Functions*in 1963. He taught at University College, London.

Clunie spent the academic year 1959-60 in the United States. With his wife and daughter, he left Southampton on 26 August 1959 bound for New York on the liner Bremen and they returned on the liner Queen Elizabeth. They left New York and arrived in Southampton on 13 July 1960. At the age of 39, Clunie was promoted to a professorship at Imperial College in 1964. Terry Sheil-Small gives some insight into his influence as a teacher [2]:-

Terry Sheil-Small tells a nice story about Clunie's love for beer [2]:-Jim Clunie was Professor of Pure Mathematics at Imperial College when I arrived in September1965as an undergraduate. He taught me complex analysis and functional analysis. I was extremely lucky to be assigned one of his tutees. He was responsible for converting me from being[interested in]fluid dynamics to being a real mathematician. We were never colleagues in the same department. Jim was struck down by polio as a child, so giving a lecture had always been a bit of a struggle.

In 1981 he reached the age of 55 which made retirement possible. Because his health problems made lecturing so difficult, he took the opportunity to retire from his chair at Imperial College but he had no intention of giving up mathematical research. He took up a research fellowship at the Open University in Milton Keynes where he worked until 1986 when he accepted a research fellowship at York University.Jim's love of beer is legendary. At a mathematics meeting at the University of Durham in the1980s, the bursar remarked that the consumption of alcohol was extremely high. He could only recall one occasion when the consumption was even higher, and that was a conference organized by Professor Clunie in1979.

We have already noted Clunie's love of beer, but we should say a little more about his personality [1]:-

We also quote a nice story recounted by Terry Sheil-Small which again recalls Clunie's love of beer [2]:-Jim was regarded extremely warmly by many friends, and widely respected as a wise and knowledgeable colleague with a fine sense of humour. Indeed, his general knowledge was extraordinary, and his ability to complete 'The Times' crossword before breakfast at conferences legendary.

Clunie died peacefully in Lamel Beeches Nursing Home on 5 March 2013, aged 86 years. He was survived by his daughter Fiona, her husband Simon, and his granddaughter Alex. The funeral took place at York Crematorium on Friday, 5 April. His daughter paid this tribute to her father:-Once, Jim was external examiner for a PhD thesis. For the oral examination, he arrived at the university very early, and so headed straight for the bar. There he enjoyed some beer and a lengthy conversation with a mathematics student. He was able to announce later that he had examined the student in the bar!

Dear Dad, though I am grieving I know your struggle is over and you had the peaceful ending you always wanted. If only you could have known it would be like that. There will be bagpipes at your funeral!(Not real ones!)I'll miss our Sunday lunches and reading the papers while you snoozed.

**Article by:** *J J O'Connor* and *E F Robertson*

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