Thomas Muir: ‘Lad O' Pairts’: The Life and Work of Sir Thomas Muir (1844–1934), Mathematician and Cape Colonial Educationist

It is a commonplace that history is written by the winners. It is just as true that biographies are usually written about the winners. Biographies of mathematicians are usually written about those who had significant impact on mathematics and its institutions. Your average everyday mathematician is (usually justly) forgotten.

Peter Elliott’s biography of Thomas Muir is only a partial counterexample. To be sure, Muir the mathematician was competent but not exceptional. Today his name is little known except perhaps by specialists in determinantal identities and historians who are interested in the early days of linear algebra.

Peter Elliott is a lawyer who has written several books about the history of his family; this one follows that pattern: Thomas Muir was his great-grandfather. Elliott has little mathematical training, so Muir’s mathematics, while present, is not discussed in detail. Instead, the main focus of his story is Muir’s other role: as Superintendent-General of Education of Cape Colony, in what is now South Africa.

It need not have been that way. As a middle-aged mathematician in Scotland, Muir was looking for a permanent position in some warmer place. (He had been advised that a warmer climate would be beneficial for his wife.) He had an offer to become the chair of the mathematics department in the new Leland Stanford University in California. One wonders what would have happened if that offer had been accepted. Instead, Muir met Cecil Rhodes, then the Prime Minister of the Cape Colony, who was looking for a superintendent-general of education. Rhodes’s forceful personality won the day: Muir and his family moved to Cape Town in 1892.

Muir grew up as a mathematician just as the glory days of determinants were about to end. He stuck to the old methods, however, and seems not to have been too interested in the new ideas about matrices. The only sign we have of his noticing the sea change is a letter from 1931, in which Muir says that he “welcomed the light matrix proofs in contrast to the heavy-footed method of 35 years ago.” By then, of course, even matrices were losing their central role to the new subject of linear algebra.

Those who have heard of Muir today are probably those interested in the history of mathematics, especially the convoluted history that led to linear algebra. Muir’s four-volume The Theory of Determinants in the Historical Order of Development catalogs pretty much every single paper on the subject written until 1900. It is not so much a history as an annotated bibliography: each new paper is noted and its contents are described, sometimes in great detail. In addition to “determinants in general” one finds chapters on “antisymmetric determinants,” “alternants,” Wronskians, Jacobians, and many other exotic flavors. The book is certainly a massive achievement, the result of Muir’s dogged hard work reading and analyzing many papers in many languages.

Much of this work seems to have been done while Muir was engaged in organizing, reforming, and centralizing the educational system of the Cape Colony. To him, mathematical work was a kind of recreation, taking him away from the everyday work of an educator which is the major focus of this book.

Elliott has little mathematical training, so Muir’s mathematics, while present, is not discussed in detail. Muir’s surviving mathematical writings (kept at the National Library of Scotland) are not investigated. There is a fuller account of Muir’s mathematics in Pieter Maritz’s article “Sir Thomas Muir, 1994–1934” (Linear Algebra and its Applications, 411 (2005), 3–67). One tantalizing fact is noted. Muir maintained correspondence with many mathematicians, and a list of those letters survives, with a note at the end: “all burned 17/7/1932.”

While the historical research is well done, Elliott’s biography gives little sense of Muir’s personality. Perhaps to compensate for this, the second half of the book contains a diary that Muir wrote during his rail tours of the country and its schools. This certainly gives us a little bit of Muir the man; for example, it confirms that “working a little mathematics” was a standard way for him to while away some time. Muir remains nebulous, however, most of the entries consisting of “arrived at [some city], met with [someone], discussed [school] business.” Perhaps he was indeed so focused on his work and his intellectual interests that there is little else to say.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.