# Gilbert de Beauregard Robinson

### Born: 3 June 1906 in Toronto, Ontario, Canada

Died: 8 April 1992 in Toronto, Ontario, Canada

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**G de B Robinson**'s parents were Percy James Robinson (1873-1953) and Esther Toutant Beauregard (1870-?). Percy Robinson was born in Whitby, Ontario and studied at the University of Toronto, graduating in 1896. Esther Beauregard was a French girl who also studied at the University of Toronto, graduating in 1894. She was one of the first women to graduate from the University and was a grandnephew of the Confederate general Pierre Gustave Toutant Beauregard (1818-1893). Percy and Esther married on 3 July 1905 in York, Ontario.

St Andrew's College was founded in Toronto in 1899. It was a boys independent school and Percy Robinson was appointed as the first classics master at the school from its foundation. But Percy Robinson was, as his son and the subject of this biography explains in [3], much more than a classics teacher. He was also an artist who painted in oil, in his own words:-

Percy Robinson is best known today as a historian, writing the classic book... experimenting within the range of certain methods which seem specially adapted to interpret the most typical Canadian scenery to Canadians in an original and forceful manner.

*Toronto during the French Regime, 1615-1793*(1933).

G de B Robinson was brought up in Toronto and attended St Andrew's College where his father was the classics teacher. The school was modelled on the typical British independent school and, during the years that Robinson studied there, the headmaster was Dr D Bruce Macdonald. St Andrew's College had moved to Rosedale in 1905 and it was at that site when Robinson was a pupil. At the age of ten, he entered the school in 1916 but, while he was a pupil there, Canada was involved in World War I and between 1918 and 1920 the school building was used as a military hospital. During these years pupils attended classes in the buildings of Knox College. Robinson, who had the nickname "Cicero" at school, fully participated in school life [4]:-

Excellent teaching by Mr Fleming at St Andrew's College must be one of the reasons for Robinson developing a passion for mathematics. He wrote a delightful article"Cicero" Robinson - The fun maker of the form. He may frequently be found playing catch in the classroom with some of his cricket enthusiasts. He is also a tennis player ... "Cicero" is quite a sprinter, and was one of our three representatives on Sports Day. Robinson expects to study mathematics and physics at Toronto with a view to a professorship, and we have no doubt we will find him some day at the head of his department.

*Newton vs. Einstein*for the midsummer 1923

*St Andrew's College Review*(see [13]). He graduated from St Andrew's College in 1923 having been awarded top prizes for both sport and academic achievement. At the Prize Giving on 30 November 1923, Robinson was ranked 1st in the Upper VI, won the Governor General's Medal, the Headmaster's Medal, the Wyld Prize in Latin, and the Christie Cup for proficiency in shooting. The Editorial in the Christmas 1923

*St Andrew's College Review*begins [7]:-

He began his university studies of mathematics and physics at the University of Toronto in 1923 and was ranked first in each of his years at University College. Robinson graduated from the University of Toronto in 1927 and undertook research at Cambridge University in England. He had been awarded one of the two scholarships granted to Toronto University for proficiency in Mathematics, under the John H Moss foundation. He reported to the St Andrew's College what life was like for him during his first year at Cambridge [12]:-The first thing which calls for editorial notice is the excellent record made by Gilbert Robinson in the senior matriculation examinations last June. Robinson obtained first class honours in seven papers and second class in three. He did not apply for a scholarship but has received the Headmaster's medal which is given only in exceptional circumstances. We congratulate him heartily.

He explained in [14] about his studies in Cambridge (we have made minor additions to the quote below):-Gilbert Robinson, who, as we announced in the Mid-Summer number, was awarded one of the coveted Moss Scholarships for proficiency in Mathematics, is now studying for his Ph.D. at St John's College. Since he headed his class each year, he was accorded the unusual honour of being allowed to forego the usual Tripos examination at Cambridge. He writes that between rowing in one of the eights, lectures and study, his time is fully occupied.

After two years at Cambridge, he returned to Toronto where he taught for an academic year before returning to Cambridge to complete his research. He was awarded a Ph.D. in 1931 for his thesisOn my arrival at St John's College in September1927, I was assigned to M H A Newman as supervisor, with F Puryer White as my tutor. White was a geometer and Newman a topologist and I attended lectures by both of them as well as Henry Baker's Tea Party and a course on the theory of functions by J E Littlewood. Much as I enjoyed working in topology it was the group theory which was involved that fascinated me. No lectures on Algebra were given in Toronto or Cambridge in those days so I had to read it up for myself. I still have the copies of Felix Klein's 'Icosahedron' and William Burnside's 'Theory of Groups' which I bought in1928. I must have told Jacques Chapelon(1884-1973)of my interests and of the Riemann surfaces that I had encountered, for he tells me in a letter written May9,1928that he had been lecturing on the same subject in his graduate course in Toronto. He goes on: "I think that you are in the right path in trying to improve your general knowledge of mathematics before entering research work. Do not hasten to begin this work and avoid working in a well known domain: there is little to discover in such domains. You must know of course the general theory of algebraic functions and Riemann surfaces, but I wonder if it would be wise to try to find something new in these well explored fields. Do not forget to study the theory of groups, one of the most fundamental fields of Modern Mathematics." Newman had reached the same conclusion and had been in touch with Alfred Young who agreed to take me on. I well remember the appointment to meet him at the Blue Boar Hotel where he and his wife used to stay when he came to Cambridge. It was just before my return to Toronto for the summer. He gave me a copy of 'On Quantitative Substitutional Analysis III' which had just come out and told me to read Miller, Blichfeldt and Dixon. In that first year I had gotten to know all the geometers at Henry Baker's weekly Tea Party - Semple, Edge, Duval, Todd and Coxeter. Dirac sat at the head of the graduate students table in Hall at St John's.

*On Certain Finite Linear Groups and their Configurations of Associated Points*. In September 1931 he submitted his paper

*On the Geometry of the Linear Representations of the Symmetric Group*to the

*Proceedings*of the London Mathematical Society. It was published in 1931 and contains the acknowledgement:-

Robinson was appointed as a lecturer at the University of Toronto and, two years later he was promoted to Assistant Professor in Mathematics. On 1 September 1936, Robinson was married to Joan Turner Howard of Toronto; they had two children, a son John and a daughter Nancy. We note that, like his father, John Robinson attended St Andrew's College, Toronto, graduating in 1964.My best thanks are due to Dr Alfred Young for his continued interest and advice during the course of this work.

Robinson spent the whole of his career on the Faculty of the University of Toronto until he retired in 1971. However, from 1941 to 1945 he undertook war work in Ottawa with the National Research Council of Canada. The work he undertook on codes and cyphers is described in [1]. He was appointed director of the 'Signals Intelligence Examination Unit' which was Canada's first civilian unit that worked solely on the encryption and decryption of communication signals. It was an important part of Canada's contribution during World War II. He was one of the founders of the decoding section which gave Canada some influence in this area after the war ended. For his war work, Robinson was made a Member of the British Empire (M.B.E.) in 1946.

Most of Robinson's research papers investigate representations of the symmetric group. His early papers include:

*Note on an equation of quantitative substitutional analysis*(1935) and

*On the fundamental region of an orthogonal representation of a finite group*(1937). He wrote three papers entitled

*On the Representations of the Symmetric Group*which were published in the

*American Journal of Mathematics*in 1938, 1947, and 1948. The Introduction to the first of these begins:-

Robinson wrote six papers entitledIn the study of the irreducible representations of the symmetric group two methods are available. The first is an application of the Frobenius-Schur theory of the characters which is valid for any group, the second is the 'substitutional analysis' of Alfred Young. Neither of these methods tells the whole story, and they should be used in conjunction.

*On the modular representations of the symmetric group*which appeared in 1951, 1952, 1952, 1954, 1955, and 1955. The first three and the sixth were published in the

*Proceedings*of the National Academy of Sciences of the U.S.A. The other two were published in the

*Canadian Journal of Mathematics*.

We must mention at this point some important books authored by Robinson:

*The Foundations of Geometry*(1940);

*Representation theory of the symmetric group*(1961); and

*Vector Geometry*(1962).

John Todd, reviewing

*The Foundations of Geometry*, writes [16]:-

Harry Levy, reviewing the same book, writes [11]:-This little book is an account of the axiomatic foundations of projective and Euclidean geometry, written in a most attractive manner; it should appeal to those who are disposed to consider this subject difficult or obscure. ... the author succeeds in combining rigour of treatment with simplicity and elegance in exposition. ... This work deserves to be widely read; it should dispel some at least of the mysticism which still seems to be associated with the subject by some mathematicians.

Henry George Forder, reviewing the second edition, writes [8]:-... this is a most excellent book, and it will inspire many students of mathematics.

Dudley Ernest Littlewood begins a review ofThe first edition of this book was reviewed in the 'Gazette', and the appearance of the second edition, so soon after, is a testimony to the author's skill and one of the few signs of a return to civilisation.

*Representation theory of the symmetric group*as follows:-

Certainly Howard Levi of Hunter College does not find Robinson'sThis book gives an account of the ordinary matrix representations, and of the modular matrix representations of the symmetric groups. There are other books on ordinary representations, though the author has a distinctive approach based largely on the work and methods of Alfred Young. The greater part of the book, however, and by far the more significant, is the account of the modular representations of the symmetric groups. Much work has been done on this in recent years, the author being a significant contributor. This book, which describes clearly the main features of this development, is very welcome.

*Vector Geometry*particularly impressive [10]:-

May I [EFR] add a personal note. In the autumn of 1976 I spent a month at the University of Toronto as the invitation of Donald Coxeter. Robinson, who was retired but came into the Department most days, was extremely kind to me during this visit and went out of his way to help make my visit a good one. He had spent the earlier part of the year in Europe, taking part in a workshop in Strasbourg on the symmetric group, then going to Aachen to work with Gordon James and Adalbert Kerber on new edition of his bookThe geometric objects discussed in this book are, for the most part, the lines, planes, conics, and quadric surfaces of Euclidean two and three space. Some of the treatment is in terms of vectors; most is not. Projective, affine, elliptic and hyperbolic geometries are mentioned briefly - so briefly, in some instances, as to render the text almost meaningless to a reader who does not already know the subject. The topics from Euclidean geometry receive a more detailed exposition, but the result is not very different from chapters on analytic geometry in dozens of American calculus textbooks which make a nod in the direction of vectors. The book also contains a chapter on groups and linear transformations, which does not seem to tie in with the rest of the book.

*Representation theory of the symmetric group*. Before returning to Canada he had visited his daughter Nancy Hill who was, at this time, living in London, England.

Robinson, together with Donald Coxeter, founded the

*Canadian Journal of Mathematics*which began publishing in 1949. He was managing editor of the

*Journal*for thirty years. After his death:-

He was honoured by being elected a fellow of the Royal Society of Canada in 1944. He was a founding member of the Canadian Mathematical Congress in 1945, giving an address to the Congress on the Foundations of Geometry. He gave many years of service to the Canadian Mathematical Society and served as the third president of the Society (1953-1957) [6]:-... the G de B Robinson Award was inaugurated to recognize the publication of excellent papers in the 'Canadian Journal of Mathematics' and the 'Canadian Mathematical Bulletin' and to encourage the submission of the highest quality papers to these journals.

George Francis Denton Duff (1926-2001), a colleague of Robinson's at the University of Toronto from 1952, writes in [6] of Robinson'sHe undertook many professional and administrative responsibilities at various times, including the presidencies of Section III of the Royal Society of Canada, of the University of Toronto Settlement and the Faculty Club, of the Society for History and Philosophy of Mathematics, as Chairman of the NRC Associate Committee on Mathematics, and as Vice President(Research)of the University in1965-71. He received several medals and other awards from the federal and provincial governments for these and similar community services.

... personal qualities of clear insight, quiet resolution, perseverance and industry, self-discipline, and commitment, broadened by a charitable understanding of his profession and community.

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

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