The Educational Times and its Canadian Contributors
CSHPM Notes brings scholarly work on the history and philosophy of mathematics to the broader mathematics community. Authors are members of the Canadian Society for History and Philosophy of Mathematics (CSHPM). Comments and suggestions are welcome; they may be directed to the column’s editors:
Amy Ackerberg-Hastings, independent scholar (aackerbe@verizon.net)
Nicolas Fillion, Simon Fraser University (nfillion@sfu.ca)
In the nineteenth century, few publications offered a space in which amateur and professional mathematicians could engage with challenging problems and intellectual discourse. One such platform may be found within the mathematical problems section of The Educational Times and Journal of the College of Preceptors. The English algebraist William Clifford claimed that The Educational Times did more to encourage original mathematical research than any other European periodical [6]. Although the majority of submissions came from European contributors, we find submissions from all over the world, including modest participation from Canada that is described later in this column.
Figure 1. The cover of the May 1861 issue of Educational Times. University College London.
The Educational Times: A Stamped Monthly Journal of Education, Science, and Literature began publication in October 1847. In April 1861, the journal was officially adopted by a pedagogical organization as their official publication and renamed The Educational Times and Journal of the College of Preceptors (ET). The journal functioned under that title until 1923, when it became Education Today. The College of Preceptors, established in London in 1846 and given a Royal Charter in 1849, endeavored to promote sound learning, advance interest in education among the middle class, and provide means for raising the status and qualifications of teachers. The journal contained pedagogical articles, notices of available scholarships, lists of successful candidates on examinations given by the College, and notices of vacancies for teachers and governesses, as well as news of scientific societies, incisive book reviews, and textbook advertisements. As in many contemporaneous journals, perhaps the most compelling feature for many of its readers was its section devoted to mathematical problems and their solutions.
Mathematical problems were first introduced to ET readers in May 1848. By March 1849, a regular mathematical column had been established, with sequentially numbered problems first appearing the following August. Approximately 18,575 problems had appeared in print by 1918 [2], with contributed solutions for nearly 73 percent of them.
In an era when most mathematical textbooks lacked diverse problem collections, ET proved to be an invaluable resource for mathematics students, professionals, and enthusiasts searching for mathematical practice and challenges. In England, many readers and contributors were drawn to ET’s mathematical section, including those who, for social, religious, or institutional reasons, were excluded from the dominant academic structures at Oxford or Cambridge.
As the journal evolved, so did the complexity of many submissions. Although early problems focused on Euclidean geometry, conic sections, trigonometry, analytic geometry, and solving algebraic equations, the mathematical section soon began to include more advanced problem areas such as probability, calculus, and basic mechanics. Roughly 18.6 percent of solutions, sometimes the only submitted solution, were attributed to the original proposer. Of the roughly 1,880 contributors, about 13% used pseudonyms. The majority of contributors came from England (62.24%), India (7.74%), Ireland (7.16%), France (5.56%), and the United States (5.29%).
Sound leadership of the problem section undoubtedly facilitated its success. The first editors of ET’s mathematical department were Richard Wilson and James Wharton of St. John’s College, Cambridge. They were succeeded by Stephen Watson of Haydon Bridge, Northumberland, in the late 1850s. In 1862, William John Clarke Miller became editor. At the time, he was a mathematical master at Huddersfield College in Yorkshire. In 1876, Miller relocated to London to become registrar, secretary, and statistician of the General Medical Council. He remained editor of the mathematical department of ET until 1897. Miller was succeeded by Daniel Biddle, a physician and Fellow of the Royal Statistical Society. Constance Marks, a University of London graduate, served as the last editor of the ET mathematical department [3].
Figure 2. Sample problems from ET’s three Canadian contributors. Woolly Mathematics.
Since the mathematics section of ET was so popular but the space for it was so restricted, Miller took action to alleviate the situation. From 1862 to 1918, problems and solutions that had appeared in ET were republished semiannually together with additional solutions and mathematical articles in Mathematical Questions with Their Solutions from the Educational Times (MQ). In addition, MQ contained solutions to many problems that, due to lack of space, had not appeared in ET. When Marks became editor in 1901, she added subject and author indices to several MQ volumes, as well as short articles and poetry. In addition, contributions by women increased dramatically during Marks’s editorship, with one-third of the articles authored by women [3].
Many distinguished scholars contributed to ET. The first publications of G. H. Hardy and Bertrand Russell appeared as solutions to problems in ET. Other eminent contributors from the United Kingdom and Ireland included John Couch Adams, Harry Bateman, William Burnside, Arthur Cayley, Augustus De Morgan, Charles Dodgson, Henry Dudeney, Francis Galton, Thomas Kirkman, Joseph Larmor, James Clerk Maxwell, L. J. Mordell, L. J. Rogers, J. J. Sylvester, Peter Tait, and William Thomson (Lord Kelvin).
Participation from Continental Europe included contributions from Austria, Belgium, France, Germany, Russia, Spain, Switzerland, and the Netherlands. More notable contributors included Eugène Catalan, Gaston Darboux, Jacques Hadamard, Édouard Lucas, and Jacob Steiner. Contributions were also received from Australia, Ceylon, Hong Kong, India, Malaysia, Mauritius, and New Zealand. Srinivasa Ramanujan was one of the 131 contributors from India.
From North America, most contributions came from the United States, where contributors included Benjamin Finkel, Asaph Hall, Artemas Martin, Benjamin Peirce, and Christine Ladd. We also find at least a handful of contributors with connections to Canada. Three contributors who participated while living in Canada were Raymond Clare Archibald, John Cadenhead Glashan, and Angus MacMurchy. Of these three, only Archibald held an academic position.
Figure 3. Raymond Clare Archibald. MacTutor.
Raymond Clare Archibald (1875–1955) was born in South Branch, Colchester County, Nova Scotia. He was educated at home until age 10. His family moved to Sackville, New Brunswick, where he attended Mount Allison Academy for Boys before matriculating at Mount Allison College at age 13. He graduated with honors, taught for a year at Mount Allison, and then entered the graduate program at Harvard, where he earned his master’s degree. He spent a year at the Humboldt University of Berlin before enrolling at the University of Strasbourg, where he received his doctorate in 1900 [5]. He started contributing to ET while in Europe.
When Archibald returned to Canada in 1900, he taught mathematics at Mount Allison Ladies College until 1907. He then spent a year teaching at Acadia University before accepting a position at Brown University in Providence, Rhode Island. His next 35 years were spent at Brown, where he authored a number of books and articles on the history of mathematics and bibliographic studies. He served a term as president of the Mathematical Association of America and 16 years as librarian for the American Mathematical Society. After retiring from Brown in 1943, he returned to Mount Allison to curate a library he had founded in 1905 in honor of his mother. Archibald’s contributions to ET totaled 23 posed problems and 10 solutions.
Figure 4. The title page of Glashan’s Arithmetic for High Schools. Internet Archive.
John Cadenhead Glashan (1844–1932) of Strathroy, Ontario, was the Chief Inspector of Ottawa Public Schools from 1876 to 1910. He was the author of the popular Arithmetic for High Schools and Collegiate Institutions (Toronto, 1890) as well as Public School Arithmetic and Mensuration (Toronto, 1894). Glashan’s contributions to ET appeared from 1875 to 1879. He solved two problems and proposed two that went unsolved. Between 1878 and 1901, he published eight articles in the American Journal of Mathematics. In 1902, he was elected a member of the Royal Society of Canada, the first professional organization of scientists in Canada. He had four papers appear in the Proceedings of the Royal Society of Canada [7, p. 363]. In 1924 he offered to donate his mathematical library to the American Mathematical Society if they would cover the cost of transportation, but the offer was not accepted.
Figure 5. MacMurchy’s obituary. Find a Grave.
Angus MacMurchy (1860–1931) was born in Toronto and attended Toronto Grammar School and the University of Toronto, where he graduated with a first class in mathematics in 1882. He was called to the bar in 1885. He worked as a solicitor for the Ontario District of the Canadian Pacific Railway and was appointed to the King’s Council in 1908. He was elected a bencher of the Law Society of Upper Canada. He authored books on railway law, as well as a biographical work on two prominent 19th-century brothers in Toronto [4]. He served on the board of governors of the University of Toronto and was elected president of the University Alumni Federation. Each year, the Faculty of Law at the university awards the Angus MacMurchy Gold Medal to the student in the graduating class with the highest cumulative average. MacMurchy was an active contributor to ET from 1878 to 1893, posing ten problems and solving sixteen.
The absence of widespread Canadian participation may be somewhat explained by Archibald and Charbonneau’s observation that mathematics was in a nascent state at most Canadian institutions in the second half of the nineteenth century, and very little mathematical research was done in Canada before the International Congress met in Toronto in 1924 [1, pp. 171, 174]. Yet, it may be fair to claim that Canadian contributions to ET offered a small step toward the professionalism of mathematics in Canada that would later blossom.
References
[1] Archibald, Thomas, and Louis Charbonneau. (1995) Mathematics in Canada before 1945: A preliminary survey. In Mathematics in Canada, edited by Peter Fillmore, vol. 1, 1–90. Ottawa: Canadian Mathematical Society. Reprinted (2005) in Mathematics and the Historian’s Craft: The Kenneth O. May Lectures, edited by Glen Van Brummelen and Michael Kinyon, 141–182. CMS Books in Mathematics. New York: Springer.
[2] Delve, Janet. (1994) The development of the mathematical department of the Educational Times from 1847 to 1862. PhD Thesis, Middlesex University.
[3] Despeaux, Sloan E. (2017) Constance Marks and the Educational Times. In Women in Mathematics, edited by Janet L. Beery, et al., 219–229. Cham, Switzerland: Springer.
[4] MacMurchy, Angus. (1918) Sketch of the life and times of Joseph Curran Morrison and Angus Morrison, Presidents of St. Andrew’s Society, 1850–54. Toronto.
[5] Tattersall, J. J. and S. L. McMurran. (2004) Raymond Clare Archibald: A Euterpean Historian of Mathematics. New England Mathematics Journal 36(2), 31–41.
[6] A Testimonial to Mr. W. J. C. Miller. (1897) Educational Times 50, 331.
[7] Zitarelli, David E. (2019) A History of Mathematics in the United States and Canada. Vol. 1. Providence, RI: American Mathematical Society.
Jim Tattersall, professor emeritus of mathematics at Providence College, Rhode Island, and Shawn McMurran, mathematics professor at California State University, San Bernardino, have collaborated for over three decades on projects exploring the history of mathematics. Their interest in The Educational Times emerged during research into the women of Girton College, Cambridge, and while delving into the R. C. Archibald archives at Brown University. They have since contributed to the Educational Times online database.
