**Kevin Lambert.**
*Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries.*
Science and Culture in the Nineteenth Century Series. Pittsburgh: University of Pittsburgh Press, 2021. 330 pp.
$55.00 (cloth), ISBN 978-0-8229-4683-0.

**Reviewed by** Zeynep Kuleli-Karasahan (Johns Hopkins University)

**Published on** H-Sci-Med-Tech (June, 2022)

**Commissioned by** Penelope K. Hardy (University of Wisconsin-La Crosse)

Wisdom tells us never to judge a book by its cover, but the front of *Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries—*which depicts Victorian mathematician William Thomson (1824-1907) holding a green notebook while getting his portrait painted—does a good job of reflecting author Kevin Lambert’s main argument: that understanding materials like the notebook is key to understanding Victorian mathematics. Informed by scholarship in history and philosophy of science, this book focuses on objects and the material environment in the development of eighteenth- and nineteenth-century British mathematics. More specifically, Lambert argues that "symbols"—abstract ideas and concepts in mathematics—are in a dynamic relationship with "things," or the material media available to mathematicians.

This well-researched book explores the relationship between mathematics and the material environment in late Georgian and early Victorian England from a new perspective. In exploring the material culture of Victorian mathematics, Lambert calls the material environment a taskscape, a central concept borrowed from anthropologist Tim Ingold (*The Perception of the Environment: Essays in Livelihood, Dwelling, and Skill* [2000]). Taskscape refers to the interrelationship between the landscape and the tasks performed in it; building, painting, or writing letters contribute to one’s physical landscape, and in turn, the changing landscape affects the tasks performed there. In his nuanced use of taskscape, Lambert gives agency not only to humans but also to objects, such as pens, paper, stamps, batteries, and museum collections, to inform the abstract thinking processes of mathematicians. Investigating the novel developments in the paper industry, postal system, museological sciences, and libraries that were part of the rapidly changing taskscape of the Victorian era, Lambert shows how nineteenth-century mathematicians thought *through and with* their environments.

*Symbols and Things* consists of three parts divided into seven chapters. The first two parts sketch the background for nineteenth-century mathematics. Part 1, "Distributing," focuses on the emergence and distribution of modern mathematics textbooks and journals in the eighteenth century. By drawing attention to the material form, the proliferation of cheap paper, and numerous non-mathematicians like printers, booksellers, publishers, and the audience for these texts, Lambert shows how the emergence, distribution, and disappearance (as in the case of the *Ladies' Diary* [1704-1840], a mathematical periodical intended for the female audience) of these texts depended on the social and material environment. Complementary to the previous section, part 2, "Assembling," explores how the establishment of museums and libraries shaped the theoretical thinking of nineteenth-century mathematicians. In chapter 3, Lambert shows how George Peacock's philosophy of mathematics, which he claims shaped the development of British mathematics, was informed by his immediate material environment at the Cambridge Philosophical Society, which housed many collections of specimens, objects, maps, ethnographic reports, and travelogs.

The final part, "Practicing," investigates how experimental objects, correspondence, and reading and writing practices shaped nineteenth-century mathematicians’ theories. In chapter 6, Lambert explores reading and writing practices by taking a very close look at Thomson’s use of notebooks as well as published and manuscript material to develop his theoretical work. Thomson’s note-taking and note-making practices show that he had a dynamic relationship with notebooks, essays, journals, and articles, which would “become part of his extended mind” when he used them (p. 172). In chapter 7, Lambert elaborates on the ways mathematicians thought together enabled by the Royal Mail system. Exploring the letter book of William Rowan Hamilton and Peter Guthrie Tait, he shows how the two mathematicians thought together about quaternions, which was “a new kind of mathematics” Hamilton invented (p. 173). Their correspondence had transformative consequences as Tait came “to see ... the value of quaternions for physical applications, especially electromagnetism” through their intensified exchange from a distance (p. 196). In chapter 5, Lambert shows how Victorian mathematicians employed a variety of theoretical and physical tools, such as experiments, diagrams, and imaginary fluids, to study the phenomena of polarity, which brought “electromagnetic phenomena and complex numbers ... into correspondence with one another” (p. 121). In this chapter, there is some significant analysis of the nature of theoretical work. Regarding the appropriateness of mathematics for deciphering the language of nature, Lambert argues and skillfully demonstrates that this appropriateness does not come naturally but rather from the fact that both natural/physical phenomena (electromagnetic field) and mathematical concepts (Hamilton’s quaternions and the modern vector calculus) were studied *through *and* with* the same objects, like wires, magnets, and batteries.

This book weaves a number of historiographies together, but the main argument builds on studies of the materiality of mathematics, as well as on histories of the book and reading and writing practices. By studying the Victorian mathematics at Cambridge, Lambert complements Andrew Warwick’s work, *Masters of Theory: Cambridge and the Rise of Mathematical Physics* (2003), which explores the role of training in relation to theoretical developments at Cambridge. Lambert does not fully explain his preference for the terms “mathematical and theoretical work” and “mathematicians/theorists and theoretical physicists” over Warwick’s and others’ use of “mathematical physics” and “mathematical physicists” when referring to his timeframe and major historical actors.

Focusing on the material culture of mathematics at any given period in history is, in essence, a reflection on the boundary between material and immaterial. By carefully tracing the interactions between the theoretical mind and rapidly changing material media in the Victorian era, Lambert succeeds in pointing out the blurry line between theoretical and physical, humans and things, mind and matter. He pursues this overarching philosophical inquiry throughout the book with a central analogy he establishes in the introduction between Victorian mathematicians and Victorian road workers, drawn from Ford Madox Brown’s painting, *Work* (1852-65). Lambert likens theoretical work to physical work through such features as using tools, working together, paying attention to one another’s work, and leaving physical traces behind. The analogy of road work to theoretical work throughout the book makes a coherent and convincing argument.

Lambert’s focus on material form does not mean he takes a reductionist or a socio-material determinist viewpoint. Quite the contrary; he thinks that individuals are not imprisoned by their material media. Rather, they choose what topic to study and when to use a text or notebook. As Lambert shows with the case of Peacock in chapter 3, the history of mathematics has been seen as an indisputable demonstration of the progress of the human mind in the nineteenth century. However, a significant implication of the book is that the human mind does not progress in a teleological manner; instead, it changes in an interactive dialogue with the world around it.

Lambert does a fascinating job in *Symbols and Things* illustrating the matter-form-ladenness of abstract thought and theory in Victorian mathematics. He demonstrates the significance of the material form in studying the materiality of mathematics by showing how mathematicians’ mindware is extended into their environments by tools, technologies, and practices in a rapidly industrializing society. This book would be of interest to historians and philosophers of science as well as to philosophers of mind, particularly those who are interested in the historical analysis of the workings of the theoretical mind.

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**Citation: **
Zeynep Kuleli-Karasahan. Review of Lambert, Kevin, *Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries*.
H-Sci-Med-Tech, H-Net Reviews.
June, 2022.

**URL:** http://www.h-net.org/reviews/showrev.php?id=57548

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