# Roland George Dwight Richardson

### Born: 14 May 1878 in Dartmouth, Halifax, Nova Scotia, Canada

Died: 17 July 1949 in South River Lake, Antigonish, Nova Scotia, Canada

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**Roland Richardson**was the son of George Josiah Richardson (1828-1898), a teacher in Dartmouth and Lawrencetown, Annapolis, Nova Scotia, and Rebecca Archibald Newcomb (1837-1923) [1]:-

Roland had a younger brother Ralph Percy Richardson, born on 2 November 1879 in Dartmouth.His mother was a direct descendant of the seventeenth century Simon Newcomb, from whom also sprang Simon Newcomb, the Nova Scotia-born astronomer, fourth president of the American Mathematical Society.

The family moved to a number of different town in Nova Scotia, being in Eastern Passage, Halifax, Nova Scotia in 1881, and Parkers Cove, Annapolis, Nova Scotia in 1891. After completing his secondary education, Richardson was appointed as a teacher at the fishing village of Margaretsville in Annapolis County, Nova Scotia. He began his tertiary education in Acadia University, Wolfville, Nova Scotia, in 1896. This university, first called Queen's College, was founded by Baptists in 1838. Renamed Acadia College in 1841, it had become Acadia University in 1891, five years before Richardson began his studies there. He graduated with an A.B. in 1898 and then returned to his teaching job in Margaretsville.

In 1899 Richardson was appointed as principal of the High School in Westport, Nova Scotia. One of the pupils at Westport was Louise Janet MacHattie who had been born on 6 December 1879 in South River Lake, Nova Scotia, Canada. Their friendship grew over the following years and, as we explain below, they married in 1908. Richardson continued as principal of the High School in Westport for three years before, in 1902, he entered Yale University. He graduated with an A.B. in 1903 and was awarded a Master's degree in the following year. In 1904, having earned an A.M., he was appointed as an Instructor in Mathematics at Yale and at the same time began to undertake research advised by James Pierpont. In the autumn of 1896 Pierpont had become an Assistant Professor at Yale, then in 1898 he had been appointed as a full professor. After attending the Deutsche Mathematiker-Vereinigung in Munich in September 1899 he had become interested in the theory of functions of a real variable and integration, and published the papers (P1)

*On multiple integrals*(1905) and (P2)

*On improper multiple integrals*(1906). He had also published the book (B)

*Lectures on the Theory of Functions of Real Variables*(1905). Given these research interests it was natural that he should steer Richardson in this direction. In 1906 he published his first paper

*Improper multiple integrals*which builds on Pierpont's work in the book and two papers just mentioned. Richardson writes in his paper:-

Richardson was awarded his Ph.D. in 1906 for his thesisThis paper is a continuation of a recent article[P2]by Professor Pierpont in this journal. In that article attention is called to the fact that two methods for defining improper multiple integrals are available; one being that ordinarily followed; the other, that due to de la Vallée-Poussin. In the present paper the theory will be developed from the latter point of view. ... In this paper we shall regard the field of integration as limited. In a later paper various conditions for continuity, inversion of the order of integration, and reduction of multiple integrals to multiply iterated integrals will be discussed for both finite and infinite fields. In general it will be assumed that, in any partial aggregate in which the integrand is limited, the integral exists. In nearly all cases, however, the reasoning will hold for an upper or a lower integral. In any instance where the notation is not explained, the reader is referred to the paper cited above, or to a recent treatise[B]on the theory of functions by the same author.

*Improper Multiple Integrals*. His next paper was 34 pages long and was presented to the American Mathematical Society in three parts; on 28 April 1906, on 3 September 1906, and on 27 April 1907. The three parts formed the paper

*The integration of a sequence of functions and its application to iterated integrals*which was submitted to the Society in January 1908 and published in its

*Transactions*later that year. The paper begins as follows:-

The papersThe fundamental principle involved in this memoir is the integration of a sequence of functions. As this depends essentially upon an inversion in the order of passing to a limit, applications are readily made to several important topics. In particular, the equality of a multiple integral and the corresponding iterated integrals is here treated, also the integration of a series term by term, and the differentiation of both series and definite integrals. Hitherto in the integration of sequences the condition of uniform convergence in some form has played an important role. In this paper the methods are entirely independent of any such condition of convergence.

*Improper multiple integrals*(1906) and

*The integration of a sequence of functions and its application to iterated integrals*(1908) contain material from his doctoral thesis.

In 1907 Richardson accepted the offer of an appointment as assistant professor of mathematics at Brown University. This offer was made with the condition that he spend the academic year 1908-09 at the University of Göttingen in Germany undertaking study and research. He married Louise Janet MacHattie, the daughter of Alexander John and Janet McHattie, on 4 June 1908 in Montreal Canada. On the following day, they sailed for Europe. While in Germany he attended the eightieth convention of German naturalists and physicians held at Cologne on 20-26 September 1908. Richardson writes in [2]:-

In 1909 Richardson returned to his position as Assistant Professor of Mathematics at Brown University. He continued in this role until 1912 when he was promoted to associate professor. Three years later, in 1915, he became a full professor and head of the Department of Mathematics. In 1926, in addition to his other roles, he was appointed as dean of the Graduate School. Roland and Louise had one son, George Webdell Richardson, born 7 July 1920 in Providence, Rhode Island.Mathematics and astronomy together formed one of the thirty-one sections. The total attendance was about two thousand, of which the Deutsche Mathematiker-Vereinigung as a sub-division claimed nearly one hundred. ... Under the influence of President Klein, the mathematical society devoted the meetings largely to the problems of applied mathematics ...

On 30 December 1929 he completed his naturalisation documents which contains the following details. His address was 44 University Avenue, Providence, Rhode Island, his occupation was college dean and his age is 51 years. It gives the personal description: Colour - white; Complexion - light; Colour of eyes - blue; Colour of hair - brown; Height - 5 feet 11 inches; Weight - 180 lbs. In fact it was only in May 1932 that the process was completed and he become a naturalized citizen of the United States.

We quote from [1] concerning Richardson's achievements at Brown:-

You can read Richardson's own description of his efforts at Brown University to develop applied mathematics at THIS LINK.Richardson arrived at Brown shortly after a "Graduate Department," with its own Dean, had been organized, and when only one member of the mathematics department was offering advanced courses. The number of such courses had been appreciably increased when he became chairman of the department. Soon he was a member of more than one important administrative committee including the Graduate Council. In1926he was appointed the successor to the Dean of the Graduate Department which became the Graduate School in the following year. He held this position until1948, when he became listed among "Officers Emeriti." Both within and without the University the School became recognized as a really vitalizing intellectual force. This development, for which the Dean was almost wholly responsible, led to Brown's election in1933as an institutional member of the Association of American Universities. Even though by1928Richardson's duties as dean and secretary, in addition to demands upon him as chairman of a department, had forced him to give up his own scientific research, he had through the years been laying sure foundations for the establishment of a strong department, for attracting not only candidates for the doctorate in mathematical analysis, but also those seeking post-doctoral inspiration. From1929until his retirement as chairman in1942,28Ph.D. degrees in mathematics had been awarded at Brown. In1938(after more than a decade of earlier consideration)when the American Mathematical Society was active in the establishment of Mathematical Reviews, Richardson was mainly instrumental in arranging not only that Brown should provide housing for the project, but also that its chief editor should be brought from Europe as a professor, adding strength to his department.1930

As early asthe Council of the American Mathematical Society had given earnest consideration to the important problem of providing a means of publication for research memoirs in the field of applied mathematics. The seed thus sown in the secretary's thought, fertilized and greatly expanded by needs connected with World War II, led to a splendidly conceived pioneer undertaking. The following descriptive extract is taken from the Brown University Faculty Meeting records for October,1949: "In the summer of1941, through his[Richardson's]efforts and with financial aid from foundations and government, there was established at Brown a Program of Advanced Instruction and Research in Applied Mechanics. Able men, including many who had come to this country from abroad, were brought here to teach, and substantial numbers of students(at one time exceeding a hundred)were recruited. Under war conditions the original educational aim of the Program, to train a succession of able young doctors in applied mathematics, especially in the various fields of mechanics, was of necessity modified. The demand by government and industry for the services of young men trained even for the short space of a year provided sufficient evidence of the usefulness of this Program for war purposes. At the same time substantial amounts of investigation connected with the war were carried on by the staff. To supplement the Program, Brown University in1943founded the Quarterly of Applied Mathematics, a journal which renders international service in its field. In1946the original educational aim of this Program was restored and the Program reorganized under the name Graduate Division of Applied Mathematics." During1943-46the dean was also a member of the applied mathematics panel of the National Defense Research Committee.

In December 1920 Richardson became the Secretary of the American Mathematical Society. He took over from Frank Cole who was the Society's second Secretary serving from 1896 to 1920. Raymond C Archibald, the author of [1], was in an excellent position to witness Richardson's contributions as Secretary:-

A number of articles written by Richardson were important in taking an overview of different aspects of mathematics instruction in America. As an example, we give a short extract from his paperBy my attendance at Council meetings throughout the whole of Richardson's term of office as secretary, and through constant personal contacts, I became convinced that his contributions and influences towards this status were indeed great. He had a thorough grasp of every topic which he presented, in excellent form, for the Council's consideration; he was endowed with infinite capacity for taking pains, and was always forward-looking, receptive to new ideas, while constantly mindful of the Society's finances. In personal relations he was remarkably kindly and cooperative, and inspired confidence and affection. No American mathematician was more widely known among his colleagues and the careers of scores of them were notably promoted by his time-consuming activities in their behalf. And such help was being freely rendered up to the time of his death. Richardson was deeply appreciative of the Council's action not only in presenting to him a beautifully hand-illuminated copy of the resolution of appreciation adopted by the Council upon his retirement as secretary, together with a silver coffee set, and for Mrs Richardson a handbag, but also in dedicating to him the1941volume of this Bulletin.

*The Ph.D. Degree and Mathematical Research*(1936) (see [7]) in which he looks at the number of college teachers of mathematics in America at THIS LINK.

Richardson attended the International Congress of Mathematicians at Zurich, Switzerland, on 4-12 September. In the article [3] he gives an excellent account of that Congress. Let us give one small quote:-

MathSciNet list 79 publications by Richardson but the article [1] lists only 35. The discrepancy arises since the many reports which he published in theIt is of interest to note that the first International Mathematical Congress was held in Zurich in1897and that the president of that gathering, Dr Geiser, was present at this meeting. The1932Congress was organized by the University and the Technical Institute of Zurich, and Professor Fueter of Zurich presided in admirable fashion. The first scientific session was presided over by Hilbert and he was given a great ovation.

*Bulletin*of the American Mathematical Society as Secretary of the Society are listed individually in MathSciNet, but only as a single item in [1]. Only 15 of his publications are research papers, however, since his duties prevented him from having the time to undertake research for much of his career.

Richardson received many honours for his contributions in addition to those bestowed by the American Mathematical Society mentioned in a quote above. He received a D.C.L. from Acadia University (1931), an LL.D. from Lehigh University (1941) and an LL.D. from Brown University. He was elected a fellow of the American Academy of Arts and Sciences, serving on the Council 1932-34, and again as vice-president in 1945-49. He was also elected a fellow of the American Association for the Advancement of Science, a member of the Deutsche Mathematiker-Vereinigung, and a member of the Circolo Matematico di Palermo.

His death in 1949 was due to a thrombosis. He was buried in Camp Hill Cemetery, Halifax, Nova Scotia, Canada.

Let us end this biography by quoting from Raymond C Archibald about Richardson's personal qualities:-

He had insight and remarkable organizing abilities, associated with exceptional mental powers. His complete honesty of character, natural wisdom, and selfless devotion to high educational ideals, commanded the admiration of his associates. He was endowed with a spirit of unaffected friendliness, the desire to play a part in helping and encouraging others to achieve the best of which they were capable, and as a result he was blest with a host of friends. There was never-ending hospitality at his home. Indirectly Mrs Richardson contributed in no small measure to the happy solution of many of her distinguished husband's problems.

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

**List of References** (9 books/articles)

**Mathematicians born in the same country**

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