**Paddy Kennedy**'s parents were Pat Kennedy (born 1883) and Kit O'Sullivan (born 1897). Pat and Kit Kennedy were married in 1920 and had five children: Tadhg Kennedy, Mary Anne (Nancy) Kennedy, Patrick Brendan Kennedy, Kitty Kennedy and Joan Kennedy. Pat Kennedy, Paddy's father, had been an apprentice carpenter in his father's firm but, despite being the eldest son, had gone against the tradition of following the family trade and he had joined the police force in 1923. He joined at a significant time, just after the end of the Irish Civil War (1922-23) which followed the establishment of the Irish Free State. Paddy's mother Kit was the daughter of the blacksmith Patrick O'Sullivan from near Castlemaine. Paddy's [1]:-

The family moved to Ballylongford in 1936 when Pat Kennedy was stationed there. However, he wanted to be transferred to Cork so that his children might be able to receive a good secondary education. In 1937 when Paddy was eight years old, after a year in Ballylongford, he did manage to achieve the transfer to Cork and, in 1941, Paddy entered the North Monastery secondary school in Cork. This school, on the north side of the city, had an excellent reputation and dated back to 1811. Known as 'the Mon', the school had a particularly strong reputation for science. In 1946, while at the North Monastery School, Kennedy won the Honan Scholarship to University College Cork. This scholarship had been set up in 1909 by Isabella Honan who was the last of a Cork merchant family that had made its fortune from the butter trade.... mother's family were quiet-spoken and rather introverted people and pledged teetotallers.

Kennedy entered University College Cork in 1946 aiming at a science degree. This had not been his original intention which was to study medicine, but he had been persuaded that he should read for a science degree. He graduated in 1949 with a B.Sc. degree with First Class Honours in Mathematics and Mathematical Physics. In the year he graduated, Kennedy took part in the Irish Chess Championship which was held in Galway. The Championship was organised as a 7-round, 16-player Swiss-system tournament. The Swiss system means that players are drawn to play against an opponent who, as far as possible, has the same score. Kennedy won each of the 7 rounds achieving the maximum score of 7/7. This runaway win put him 2^{1}/_{2} points clear of the next best player. The reference [3] gives each of Kennedy's seven games. David Kennedy, the son of Paddy Kennedy, writes [3]:-

After graduating with a B.Sc. from Cork, Kennedy continued to study there for his Master's Degree. He was given a £300 per annum position as a Demonstrator in the Mathematics and Mathematical Physics Departments at Cork for 1949-50. This money allowed him to help support his elder brother Tadhg's studies at College. Paddy Barry writes [1]:-His result will probably never be equalled. Not only did he win at the first attempt, but he also won with a100% record. The quality of his play was remarkable for a player who had never played outside of Cork prior to that event. According to Noel Mulcahy, a number of characteristic features can be seen in his games(see[3]for details of his games)at the championships. Firstly, a logical approach: he nearly always played what the position demanded, whether this involved a wild attack or precise manoeuvres. Secondly, a lack of nerves: in a crucial game(against J A Flood, see[3])he played an incredibly risky-looking line where his King was badly exposed. It must have taken a great deal of self-confidence and reliance on his own judgement and calculations. Finally, patience and a willingness to work hard at a position to build up small advantage.

The 'Crawford Tech' referred to in this quote is the Crawford Municipal Technical Institute which was founded in 1912. It trained students in Science and Engineering and is now part of the Cork Institute of Technology. Mathematics and chess were not the only two passions in Kennedy's life, however for he [2]:-Very unusually he was not renewed as Demonstrator for1950-51and had to support himself by teaching in the Crawford Tech. This sowed the seeds of animosity in him towards those who made the decision.

Tilly Fleischmann (1882-1967) was a famous Irish pianist, born in Cork of German descent, who, in addition to performing, taught the piano for over sixty years to advanced pupils.... was also a very promising pianist. He had lessons in1950from Mrs Tilly Fleischmann and learnt very quickly to play Chopin. She said of him at the time that he was the only pupil she had had, who never played a wrong note. He was also very interested in listening to music, chiefly Beethoven, and his general conversation suggested the arts man rather than the scientist.

In 1951 Kennedy completed his M.Sc. studies and was examined by Vicenzo Consolato Antonino Ferraro (1902-1974) who, at that time, was professor of applied mathematics at the University College of the South West at Exeter (now the University of Exeter). Ferraro was particularly impressed by Kennedy's work in analysis and recommended that he study for a Ph.D. with Walter Hayman at Exeter. Kennedy was awarded an M.Sc. with First Class Honours from the National University of Ireland, and was awarded the Travelling Studentship in Mathematical Sciences of the National University of Ireland. He took Ferraro's advice and went to Exeter to undertake research advised by Hayman. Hayman had been appointed as a Lecturer in Mathematics at Exeter in 1947 and Kennedy became his first research student. Hayman writes [2]:-

Kennedy's first paper wasThe following two years were very happy for us both. We were young and enthusiastic and had long conversations about functions walking in Rougemont gardens and other places around Exeter. I had recently returned from America full of the ideas of Maurice Heins(1915-2015)and put Paddy onto a question raised by Heins. This he solved in a thoroughly elegant manner. But the teaching was both ways. Heini Halberstam(1926-2014)and I and some of our other colleagues benefited from a course on probability and measure theory given by Paddy. Paddy was a wonderful conversationalist and tremendous good company. I have known few greater joys in life than sitting opposite him each smoking a cigarette and chatting, oblivious of time.

*On a conjecture of Heins*which he submitted to the

*Proceedings*of the London Mathematical Society on 12 September 1953. The paper is related to a conjecture of Heins on subharmonic functions and gives positive results. Kennedy promises a further paper giving an example of a class of integral functions which shows these positive results are best possible and provides a counter-example to Heins' conjecture. Kennedy gives the following acknowledgement:-

Kennedy was appointed as an assistant lecturer in mathematics at Aberystwyth in autumn 1953. He married Pamela Fishwick in March 1954 in Aberystwyth; they had three children, David Patrick Kennedy, Anne Deirdre Kennedy, and Jane C Deborah Kennedy. He was awarded a Ph.D. by the National University of Ireland in 1954 for his thesisI wish to express my gratitude to Mr W K Hayman, whose guidance and advice were invaluable at all stages of the preparation of this paper. The author is a Travelling Student of the National University of Ireland.

*Asymptotic Values on Integral Functions*. At this time National Service was compulsory and, as someone living in Wales, he would have had to have served in the British Army for a year. This was not a pleasant prospect for a patriotic Irishman so he only taught in Aberystwyth for a year before returning to Cork as a lecturer in mathematics taking up the appointment in the autumn of 1954. The vacancy had occurred since Henry St John Atkins, the Professor of Mathematics at University College Cork, had become became president of the college. Barry writes [1]:-

He continued with a remarkable research output, with papers:Kennedy's objectives from the start in1954were to raise standards, to do rigorous mathematics, to modernise the courses, and to encourage and help all the other staff to be active in research.

*Integrability theorems for power series*(1955),

*Conformal mapping of bounded domains*(1956), and

*A class of integral functions bounded on certain curves*(1956). In this last mentioned paper, submitted in March 1955, Kennedy writes:-

His remarkable publication record continued with:I wish to express my warm thanks to Mr W K Hayman for much valuable advice during the preparation of this paper. ... The material of this paper forms part of a Thesis submitted for the Ph.D. degree of the National University of Ireland.

*A note on uniformly distributed sequences*(1956),

*Fourier series with gaps*(1956),

*General integrability theorems for power series*(1957),

*Fourier series with gaps. II*(1957),

*Remark on a theorem of Zygmund*(1958),

*On the coefficients in certain Fourier series*(1958). This last mentioned paper acknowledges support as follows:-

Some of Kennedy's papers listed below also acknowledge the same source of support. Further papers were: (with WK Hayman)Research supported in part by the Air Research and Development Command, United States Air Force, through its European Office ...

*On the growth of multivalent functions*(1958),

*A remark on continuity conditions*(1959),

*A property of bounded regular functions*(1959), and

*On a theorem of Hayman concerning quasi-bounded functions*(1959).

Paddy Barry was a research student at Cork advised by Kennedy. He writes [1]:-

[Kennedy was appointed Professor of Mathematics at Cork in 1956. He was awarded the D.Sc. by the National University of Ireland in 1960 and was elected a Fellow of the Royal Irish Academy in 1962. He took study leave in 1961-62 and on his return to Cork he applied for the chair of mathematics at the University of York. This was a new university which opened in 1963 with just 230 students. Kennedy was the first professor of mathematics, appointed before the university opened. He worked at building the mathematics library and appointing staff to the mathematics department before the opening in 1963.Kennedy]was very enthusiastic about, and interested in, mathematics. He was an excellent teacher, committed to proof, explained clearly, was unhurried, gave model notes , exhorted, encouraged and inspired. He prepared a booklet on real analysis for students. He was informal with senior students; I had most of my post-graduate lectures from him on a2ft x2ft table in the College restaurant. He won the admiration and loyalty of repeated classes of students. I regard him as having been a watershed in the department. Before him there were oldish courses and little research for a long time. Soon after he arrived there was fairly normal activity.

In 1965 Kennedy was appointed as External Examiner in Mathematics for the National University of Ireland. The first students who had entered the University of York in 1963 were due to take their final examinations in the summer of 1966. Hayman writes:-Throughout his career as a university teacher Paddy threw himself with great gusto into academic politics. He saw things in black and white colours and had no hesitation in telling everybody that it would be iniquitous to do anything but A even when it was fairly clear that course B would in fact be adopted. Coming from a very young Professor such an attitude sometimes caused resentment. It also caused him a great deal of disappointment when some of the things he hoped for did not come off. He could not be above the battle. If he was in something, whether it was a committee or a problem in mathematics he was in it up to the neck. In this way he got a good deal done both mathematically and in building up the departments at both Cork and York, but at high cost to his nerves.

On the night of 8 June 1966, Kennedy took his own life in a hotel in Nottingham.He was extremely conscientious and his final tragic breakdown can only be attributed to excessive and quite unnecessary worry about his students and his work.

We should say a little more about Kennedy's chess career. He was the youngest winner of the Irish Chess Championship at age 20 in 1949 with a 7/7 score which has never been equalled. One might have expected him to have gone on to a stunning chess career but, rather strangely, he never again displayed the brilliance he had shown at the 1949 Championship. His son, David, explains that there was [3]:-

At the time of his death Kennedy was writing a book on the applications of subharmonic functions to function theory. Hayman completed the book and... a falling off in the quality of his play in autumn1949and he resigned from the Cork Championship after playing(and winning)only two games. Mulcahy suggests this may have been down to a sense of anti-climax after the Irish coupled with unexpected difficulty in beating weaker players. About the same time, nerves began to affect him and his remaining formal competition results were poor.

*Subharmonic functions. Vol. I*was published in 1976 with Kennedy and Hayman as joint authors. D H Armitage writes in a review of the book:-

Hayman writes an Acknowledgement section in the book:-This book gives a clear and attractive account of the theory of subharmonic functions in domains of Euclidean spacesR^{m}(m≥ 2)and illuminates the connections and analogies with classical complex variable theory particularly well.

This project was started by my friend and former student Professor P B Kennedy. His tragic death in1966made it impossible for him to finish the work. I hope it may serve as a memorial to a deeply conscientious and extremely charming person whom I still miss greatly.

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

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