The stereotype of the solitary mathematician is widespread, but practicing users and producers of mathematics know well that our work depends heavily on our historical and contemporary fellow travelers. Yet we may not appreciate how our work also extends beyond us into our physical and societal environments.

Kevin Lambert takes what might be a first crack at this perspective in his book Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries (University of Pittsburgh Press, 2021). An historian of science, Dr. Lambert has shifted in his view of mathematics as a language of science to one as a material practice. Expanding on ideas from historians, archeologists, philosophers, and other scholars of human activity, and through several interweaving vignettes of mathematical work during a technologically dynamic period in British history, he argues that mathematical practice, communication, and even thought occur to a large degree outside the bodies of the persons performing them.

In this interview, we explore Kevin's journal to and through this book project. We discuss how such ideas as Andy Clark's extended mind informed his approach, and we review several of the lively stories—the co-creation of the long-distance mathematical community with the research journal, Peacock's museological argument for the adoption of symbolic algebra, and the foundational entanglement of electromagnetism, quaternions, and the philosophy of space, among others—he drew out of historical and archival sources. (Here i cannot resist mentioning Tait's collection of his intensive correspondence with Hamilton that transformed how quaternions were applied in physics and even conceptualized as mathematical objects.) We close with some thoughts on our own materially extended cognitive work and where Kevin's interests are currently driving him.

Suggested companion works:

• ChatGPT, as a cutting-edge extension of human thought

• work by Courtney Ann Roby, including the forthcoming The Mechanical Tradition of Hero of Alexandria: Strategies of Reading from Antiquity to the Early Modern Period

• Algorithmic Modernity: Mechanizing Thought and Action, 1500-2000, edited by Morgan G. Ames and Massimo Mazzotti

• work by Emily Miller Bonney, for example "A Reconsideration of Depositional Practices in Early Bronze Age Crete"

Kevin Lambert is a historian of science and mathematics in the early modern and modern periods and professor in the liberal studies department at California State University, Fullerton. His recent book Symbols and Things explores mathematics as a way of thinking outside the body and through the material environment. He also recently published a chapter in the volume Algorithmic Modernity that traces the genealogy of algorithmic practices. He is now working on the problem of writing longue durée histories of science. He is close to completing a paper called “Malthus in the Landscape” that investigates the temporalities of global histories. He is also exploring the problem of writing a global history of the early modern sciences without the prism of the so called “Scientific Revolution.” His work can be found on ResearchGate.

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