# Frederick Valentine Atkinson

### Quick Info

Pinner, Middlesex, England

Toronto, Canada

**Frederick Atkinson**was an English mathematician who worked in functional analysis and spent most of his career in Nigeria, Australia and Canada.

### Biography

**Frederick Atkinson**was known as Derick from the time he was young. His father was George Arthur Atkinson, a journalist and film critic on the Daily Telegraph, and his mother was Dorothy Boxer. Dorothy was George Atkinson's second wife and they had two children with Derick having a sister Anne four years his junior. Derick entered Reddiford School in Pinner in 1922, then later he attended Alleyn's School. His parents moved to Dulwick and, in 1929 Derick was attending Dulwich College Preparatory School. At this time his ability in mathematics became evident and he topped his class in geometry, algebra, and arithmetic. His parents, however, did not see their son as a future mathematician, rather his father wanted him to enter the diplomatic service while his mother hoped that her son would enter the Church.

In the summer of 1929 Atkinson was accepted into St Paul's School in West Kensington. It was a famous school with an outstanding reputation and Atkinson flourished as a mathematician there. He received the highest praise for his mathematical achievements and the only note of criticism was the fear that he would concentrate too much on mathematics. He was elected to a Senior Foundation Scholarship in 1932 and, after sitting the Mathematical Scholarship Examinations at Queen's College, Oxford, in 1933 he was awarded an open scholarship and matriculated at the College in 1934. During his undergraduate years he shared a room for part of the time with J L B Cooper. The two became life-long friends. Atkinson graduated B.A. with First Class Honours in Mathematics in 1937. He continued to study at Oxford working on his doctoral thesis advised by Titchmarsh. He submitted his thesis

*Mean Value Theorems for the Riemann Zeta Function*in 1939 and, after being examined by Hardy, Littlewood and Titchmarsh, he was awarded his doctorate. He was then appointed to a Junior Research Fellow position at Magdelen College.

World War II broke out around the time that Atkinson took up his fellowship. He resigned the fellowship in October 1940 so that he might undertake war work with the Intelligence Corps. Atkinson was interested in languages and spoke Urdu, German, Hungarian and Russian. He also was proficient in Latin and Ancient Greek, and had some knowledge of French, Italian, and Spanish. He began visiting Ladislav and Agnes Haas, whose first language was Hungarian and had recently arrived from Czechoslovakia, in order to practise speaking Hungarian and Russian with them. Ladislav and Agnes had two daughters and, after a couple of years, Atkinson proposed to Dusja Haas. They were married in 1943 and had three children, Stephen, Vivienne and Leslie. Rooney writes in [3]:-

One of Dusja's favourite stories is that Derick proposed to her in Hungarian, their only common language, and her reaction was: He doesn't know what he is saying!Atkinson was in the Intelligence Corps from 1940 to 1946. Part of this time he spent at Bletchley Park involved in code breaking, but for around three years he was in India breaking Japanese codes. After his war service came to an end he returned to Oxford where he taught for two years as a lecturer in Christ Church. In 1948, shortly after he was reappointed for a further two years at Oxford, he was offered the chair of mathematics at University College, Ibadan, Nigeria. Atkinson resigned his Oxford post and accepted the professorship in Ibadan. His letter of appointment states [1]:-

Your duties will initially be to develop your department as a centre of teaching and research.Atkinson held the chair at Ibadan for seven years before moving to Australia in 1956 to Canberra College. Four years later he moved to Canada to take up a professorship at the University of Toronto. He held this position from 1960 until he retired in 1981. For the final six years of this period he was Chairman of the Department of Mathematics.

We noted above that Atkinson's doctoral dissertation was on the Riemann zeta function. In fact much of his early research followed on from this beginning with papers such as

*A summation formula for p(n), the partition function*(1939),

*The mean value of the zeta-function on the critical line*(1941),

*A divisor problem*(1941),

*The Abel summation of certain Dirichlet series*(1948),

*A mean value property of the Riemann zeta-function*(1948),

*The mean-values of arithmetical functions*(1949), and

*The mean-value of the Riemann zeta function*(1949). The most important of these early results was probably the last of these papers in which he found the second term in the asymptotic expansion of the mean square average of the zeta function on the critical line. A new phase of his work began when he began to study eigenfunction expansions both for difference equations and differential equations. He published the important book

*Discrete and continuous boundary problems*in 1964. He wrote in the Preface:-

The essential unity of our subject has not always been apparent; the wealth of its applications and interpretations are perhaps responsible for this. ... We shall pursue our task from three directions. We shall present the theory of certain recurrence relations in the spirit of the theory of boundary problems for differential equations. Second, we shall present the theory of boundary problems for certain ordinary differential equations, emphasizing cases in which the coefficients may be discontinuous, or may have singularities of delta function type. Finally, we give some account of theories which unify the topics of differential and difference equations, relying mainly on the method of replacement by integral equations.In 1972 he published another important book

*Multiparameter eigenvalue problems*. Patrick J Browne gives high praise to the work which, he writes, is:-

... an invaluable and indispensable introduction to the subject. The author's tidy but none-the-less flowing style is complemented by sound and clear exposition throughout.Rooney [3] describes Atkinson's personality:-

In personality, Derick seemed a very quiet man, but a little probing revealed immense depth, perspicacity and ability.He also describes his hobbies:-

Derick's main hobby was music, for he was a fine pianist and a near professional quality player of the piano accordion. Indeed, while in Nigeria, Derick organized and played in a dance orchestra at faculty dances. Another enjoyment for him was giving parties, ably complemented by Dusja, who is a masterly cook. ... Other interests included gardening and carpentry; when Derick began to run out of space for books in his house, he lined the basement with bookshelves constructed by himself.Atkinson received many honours for his contributions including election to fellowship in the Royal Society of Canada (1967), election to fellowship in the Royal Society of Edinburgh (1975), and the McDougall- Brisbane Prize of the Royal Society of Edinburgh for 1974-76 for his paper

*Limit-n criteria of integral type*(1974). He served as nineteenth president of the Canadian Mathematical Society during 1989-91. He also received the Humboldt Prize of the German Government in 1992.

In August 1992, after returning from Europe where he was presented with the Humboldt Prize, Atkinson suffered a massive stroke. He survived for a further ten years during which time he could not speak and he was partly paralysed. His wife Dusja cared for him throughout this long and difficult final illness.

### References (show)

- A B Mingarelli, A glimpse into the life and times of F V Atkinson,
*Math. Nachr.***278**(12-13) (2005), 1364-1387. - P G Rooney, Obituary : Frederick Valentine Atkinson,
*Austral. Math. Soc. Gaz.***30**(2) (2003), 100. - P G Rooney, Frederick Valentine Atkinson,
*Proc. Roy. Soc. Canada***1**(2) (2002), 65-67.

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update November 2006

Last Update November 2006