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From Servant to Queen: A Journey Through Victorian Mathematics

John Heard
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Ackerberg-Hastings
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We generally think of “What is this good for?” as one of the archetypal student questions, perhaps just as exasperating as, “Will this be on the test?” and “Did I miss anything important today?” Yet, as John Heard (an independent scholar) argues, rather than automatically dismissing questions of utility, most 19th-century British professors and practitioners — as well as the wider public — valued practical application as their default mode. Thus, in that place and time, academic mathematicians had to create the subject of pure mathematics and advocate for it. By the 20th century, Heard concludes, they had indeed successfully convinced their audiences that it did not matter if their researches ever resulted in applications.
To arrive at that destination, Heard guides readers through a thematic discussion that is also roughly chronological. He mostly balances his attention between individuals, institutions and organizations, and cultural contexts. Thus, readers encounter the lingering influence of Newtonian fluxions, the dominance of the Cambridge Mathematical Tripos, the early years of the London Mathematical Society (LMS), a survey of 19th-century developments in physics and technology, the separation of pure mathematicians from the standard narrative of professionalization, and efforts by pure mathematicians to justify their subject by appealing to its beauty. Mathematicians treated in detail include: Augustus De Morgan, T. A. Hirst, Arthur Cayley, Henry J. S. Smith, J. J. Sylvester, Percy MacMahon, Isaac Todhunter, George Salmon, Lord Rayleigh, and Bertrand Russell. The life and career of J. W. L. Glaisher is singled out for a chapter-length case study that subtly likens him to the leading character in an ancient Greek drama. Endnotes appear with every chapter, with a “select bibliography” and index at the back of the book.
The topics will be familiar to anyone who has read the history of 19th-century English mathematics (my change of geographical adjective is intentional); Heard’s originality lies in his methodology. He analyzes the evidence found in these mathematicians’ books, articles, speeches, and correspondence through a lens of publicity and marketing. In other words, how did the men employ rhetoric, activities, and relationships to explain and justify their ideas? For instance, they fostered a culture in the LMS Proceedings celebrating the certainty offered by pure mathematics, and they delivered addresses distinguishing the subject from Britain’s tradition of mixed mathematics. Eventually, they asserted that aesthetics were as inherently valuable in mathematics as in the visual and literary arts. Thus, they transformed the discipline from the assistant to the sciences to the ruler of them all.
This book’s subtitle struck me as equally important for understanding Heard’s argument; this is “[one] journey through Victorian mathematics,” not “the” journey. Because of my own interests, I noticed the near-omission of Scotland and of an acknowledgment that the physical sciences also had significant development in theoretical directions during the 19th century. (John Playfair and Lord Kelvin are among those who make cameo appearances, with greater attention given to James Clerk Maxwell.) Readers looking for the technical details of symbolical algebra, invariant theory, logic, and other well-known pursuits of English mathematicians will have to consult other sources. 
While his approach falls within intellectual and cultural history, Heard’s volume also continues the tradition established by 1981’s Social History of Nineteenth Century Mathematics, edited by Herbert Mehrtens, Henk Bos, and Ivo Schneider (Birkhäuser). In a bit of academic synergy, I simultaneously reviewed this book for CHOICE, where I recommended its reading level as accessible for all audiences. I stand by that assessment here. Works in MAA Reviews that would make good next choices for readers of From Servant to Queen include Karen Hunger Parshall’s 2006 biography of Sylvester, Tony Crilly’s biography of Cayley that appeared the same year, and the collections Mathematics Unbound (AMS/LMS, 2002) and Mathematics in Victorian Britain (Oxford, 2014). The final chapter of the latter volume, by Jeremy Gray and reassessing the historical significance of the English pure mathematicians, provides an especially thought-provoking additional perspective on the subject matter.


Amy Ackerberg-Hastings is an independent scholar who researches the histories of American and Scottish mathematics education in the 18th and 19th centuries, among other things. Recent contributions to the Birkhäuser book series Research in History and Philosophy of Mathematics include “John Playfair’s Approach to ‘the Practical Parts of the Mathematics’“ and “The Misnamings of Playfair’s Axiom.”