# Ralph Duncan James

### Quick Info

Liverpool, England

Salt Spring Island, British Columbia, Canada

**Ralph Duncan James**was an English-born Canadian mathematician who worked on number theory and mathematical analysis.

### Biography

**Ralph James**' father was John Herbert James (born in Micheldever, Hants about 1872) who was an elementary school teacher. His mother was Rose Annie Joabel James (born in Liverpool about 1872). He had a sister Nora Kathleen Rose (born in 1910).

Ralph James spent the early years of his life in England, then went to Vancouver in Canada when his parents emigrated. His school education was in Vancouver and after graduating from high school he remained in Vancouver studying mathematics at the University of British Columbia. After the award of his undergraduate degree, James had intended to train to become an actuary, but he was persuaded to continue his studies at the University of British Columbia, completing a Master's Degree in mathematics with Frederick S Nowlan. It was through Nowlan's advice, and also his help, that James then went to the University of Chicago where he studied for his doctorate under L E Dickson. James was awarded a doctorate from Chicago in 1932 for his thesis

*Analytical Investigations in Waring's Theorem*on number theory.

James was awarded a National Research Council Fellowship to enable him to undertake postdoctoral study working with E T Bell at the California Institute of Technology during 1932-33 and also for a second year at the University of Cambridge in England working with G H Hardy. After the year 1933-34 spent in England, James returned to the United States where he was appointed to the University of California at Berkeley. He remained there from 1934 to 1939. He moved back to Canada in 1939 when he accepted the position of Professor and Head of the Department of Mathematics at the University of Saskatchewan. While there he published a number of papers such as

*Integers which are not represented by certain ternary quadratic forms*(1939),

*Elementary note on prime number problems of Vinogradoff's type*(1942), and

*On the sieve method of Viggo Brun*(1943). In the second of these James applied Vinogradov's method of dealing with the problem of the number of representations of a large number as a sum of three primes to a some quite general problems. In the paper

*On the sieve method of Viggo Brun*James takes the sieve method which had been used by Buchstab in 1940 to establish results on prime numbers, and applies it to obtain results about infinite subsets of primes, such as primes in arithmetic progression.

In 1943 James was invited to become a Professor of Mathematics at the University of British Columbia. His first paper published after his move to the University of British Columbia was

*A generalized integral*(1946) written with Walter H Gage. Zygmund writes:-

In certain problems (for example, in the theory of uniqueness of trigonometric series) it is desirable to define a second integral of a given function without defining the first integral. In this paper the authors develop the theory of such a second integral which they call a second Perron integral.In 1948 James became Head of the Department of Mathematics at the University of British Columbia. He continued his interest in number theory and the Perron integral. He addressed the American Mathematical Society on

*Recent progress in the Goldbach problem*and his lectures was published in the Bulletin of the American Mathematical Society in 1949. In the talk he described methods which he had used in his 1942 and 1943 paper we mentioned above. In 1950 he wrote, this time a single author paper,

*A generalized integral. II*. Zygmund , who was much influenced by these ideas on the second Perron integral, wrote:-

The main result of the present paper is that the sum of an everywhere convergent trigonometric series is integrable in the proposed sense, and the series itself is the Fourier series of the sum.Some later papers continuing this theme were

*Generalized nth primitives*(1954),

*Integrals and summable trigonometric series*(1955), and

*Summable trigonometric series*(1956). Papers continuing the number theory theme include (with I Niven)

*Unique factorization in multiplicative systems*(1954), and

*The factors of a square-free integer*(1968).

James contributed in a major way towards the development of mathematics in North America. He was Editor-in-Chief of the

*American Mathematical Monthly*from 1957 to 1962. For many years he was on the Editorial Boards of the Canadian Journal of Mathematics and of the Pacific Journal of Mathematics. He also served as President of the Canadian Mathematical Society (then called the Canadian Mathematical Congress) from 1961 to 1963. In fact all the previous presidents had served terms of four years, but James felt that this was too long a period to hold the position so it was reduced to a two year term. He served two terms on the Council of the American Mathematical Society.

When James died, the Senate of the University of British Columbia made a tribute:-

In 1973, Ralph James retired as Head of the Mathematics Department at UBC after holding that position for 25 years, one year before his official retirement as Professor of Mathematics, to coordinate activities for the 1974 International Mathematics Congress held in Vancouver. He continued to teach at the University of British Columbia for two further years. ... Ralph James served his university very well in many capacities. He was on many important committees, and he was a member of Senate for 13 consecutive years. He represented the Faculty of Graduate Studies from 1950 to 1957, and the Faculty of Arts and Sciences from 1957 to 1963. He was well known in Faculty meetings where he was an articulate and forceful debater, a telling critic, and an aggressive proponent of his well thought-out views and principles. Underneath the facade, however, he was a humane and human being of gentleness, compassion, sensitivity, intelligence and integrity. Senate extends to his wife, Rose, and to the other members of his family its deepest sympathy.

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Written by J J O'Connor and E F Robertson

Last Update November 2006

Last Update November 2006