Ralph Duncan James (8 February 1909,

Liverpool Liverpool is a city and metropolitan borough in Merseyside, England. With a population of in 2019, it is the 10th largest English district by population and its metropolitan area is the fifth largest in the United Kingdom, with a popul ...

, England – 19 May 1979,

Salt Spring Island Salt Spring Island or Saltspring Island is one of the Gulf Islands in the Strait of Georgia between mainland British Columbia, Canada, and Vancouver Island. The island was initially inhabited by various Salishan peoples before being settled b ...

British Columbia British Columbia (commonly abbreviated as BC) is the westernmost province of Canada, situated between the Pacific Ocean and the Rocky Mountains. It has a diverse geography, with rugged landscapes that include rocky coastlines, sandy beaches, ...

, Canada) was a Canadian

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, structure, space, models, and change. History On ...

working on

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

. Born in Liverpool, Ralph moved with his parents to

Vancouver Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the ...

when he was 10 years old. After graduating from

high school A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' lower secondary education'' (ages 11 to 14) and ''upper seconda ...

, Ralph attended

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

. After graduating, he continued in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, writing a master’s thesis on ''Tangential Coordinates''. Proceeding to

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, he studied

and

Waring's problem In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural num ...

under

L. E. Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...

. In 1932 he was a awarded a Ph.D. on the strength of his dissertation ''Analytical Investigations of Waring's Theorem''. He continued post-graduate study, first with E. T. Bell at

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, then in 1934 with

G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. He published in the

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

and extended some work of

Viggo Brun Viggo Brun (13 October 1885 – 15 August 1978) was a Norwegian professor, mathematician and number theorist. Contributions In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the ' ...

in 1938. Ralph James was a

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

of mathematics at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

from 1934 to 1939. He was then called to

University of Saskatchewan A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

where he became Head of the mathematics department.Prominent people
from

In 1943 he began his long tenure at

, becoming Head of the department in 1948. James made contributions to the theory of the Perron integral and to solution of

Goldbach's conjecture Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold ...

. Since 1978, the

Canadian Mathematical Society The Canadian Mathematical Society (CMS) (french: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the ...

have awarded the

Coxeter–James Prize The Coxeter-James Prize is a mathematics award given by the Canadian Mathematical Society (CMS) to recognize outstanding contributions to mathematics by young mathematicians in Canada. First presented in 1978, the prize is named after two renown ...

in his honor.

Papers

Ralph Duncan James published the following papers in the course of his career: * 1934:

Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...

"On the representation of integers as sums of pyramidal numbers" * 1934:

36(2):395–444 "The value of the number g(k) in Waring's problem" * 1938: ''Transactions of the American Mathematical Society'' 43(2):296–302 "A problem in additive number theory" * 1939:

Duke Mathematical Journal ''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas Joseph Miller Thomas (16 ...

5:948–62 "Integers which are not represented by certain ternary quadratic forms" * 1942: (with

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

)

American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United ...

64:539–52 "Elementary note on prime number problems of Vinogradoff’s type" * 1943:

Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. I ...

49:422–32 "On the sieve method of Viggo Brun" * 1946: (with

Walter Gage Walter Henry Gage, (March 5, 1905 – October 3, 1978) was a Canadian professor and educational icon, widely acknowledged to have had a large impact on students during his 50 year career at the University of British Columbia, where he rose f ...

) ''Transactions of the Royal Society of Canada'' Section III(3) 40:25–35 "A generalized integral" * 1949: Bulletin of the AMS 55:246–60 "Recent progress on the Goldbach problem" * 1950:

Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The cur ...

2:297–306 "A generalized integral II" * 1954: (with

Ivan Niven Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian-American mathematician, specializing in number theory and known for his work on Waring's problem. He worked for many years as a professor at the University of Oregon, and was presiden ...

)

Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ' ...

5:834–8 "Unique factorization in multiplicative systems" * 1955: Bulletin of the AMS 61:1–15 "Integrals and summable trigonometric series" * 1956:

Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisati ...

6:99–110 "Summable trigonometric series" * 1968:

Canadian Mathematical Bulletin The ''Canadian Mathematical Bulletin'' (french: Bulletin Canadien de Mathématiques) is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Antoni ...

11:733–5 "The factors of a square-free integer" * 1970:

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...

77(1):94 "Review: ''Studies in Number Theory''"

References

Ralph James dies suddenly at Salt Spring Island home
from ''Gulf Islands Driftwood'', May 23, 1979, page 3. * * {{DEFAULTSORT:James, Ralph Duncan 1909 births 1979 deaths Number theorists 20th-century Canadian mathematicians British emigrants to Canada Presidents of the Canadian Mathematical Society The American Mathematical Monthly editors