[HIST635: Early Modern England] By the Numbers Review
Matt Zilic
4/30/2026
In By the Numbers: Numeracy, Religion, and the Quantitative Transformation in Early Modern England (2024), Jessica Marie Otis examines how numbers became central to the ways sixteenth- and seventeenth-century English men and women understood faith, society, and governance. This transformation, which she describes as something that “completely reconfigured the way English men and women understood the world around them” (2), can be broadly understood as the transition from Roman numerals and other older systems of calculation to the widespread adoption of Arabic numerals. While Otis ultimately traces how Arabic numerals became dominant, she emphasizes that it is necessary to examine numbers “through the lens of early modern English culture—and, crucially, [to] defamiliarize the Arabic numeral numeracy we so often take for granted” (13).
Jessica Otis is a dual-trained scholar with degrees in both mathematics and history. She earned her PhD from the University of Virginia in 2013 and now focuses on the cultural history of early modern England. As a digital historian, she has also worked to make historical scholarship more accessible to wider audiences. Her “Death by Numbers” project reflects this commitment to digital history and public scholarship.
By the Numbers effectively combines both her mathematical and historical training, though the book leans more heavily toward cultural and social history. It is divided into two parts: part one “establishes the variety of early modern English number symbols,” while part two “consists of three case studies that place numbers in conversation with broader developments in English history” (11).
The first two chapters provide an overview of the broader cultural shift in numeracy as older systems such as Roman numerals and tally sticks gradually became less central. Chapter 1 examines the symbolic numerical systems used by early modern English men and women, dividing them into three categories: performative, object-based, and written (14). Otis makes an important distinction regarding the adoption of Arabic numerals: it was not a sudden or wholesale transformation, but rather a gradual process as trust in the system developed over time. A mixture of Roman and Arabic numerals was common, as shown in Thomas Hassall’s account book, which used both systems until 1636 (38). Although the use of Arabic numerals increased significantly after the Restoration, Otis notes that they did not become standard until the eighteenth century (41). She also reminds readers that numbers carried political and cultural meanings. One telling example is Oliver Cromwell’s insistence that tally sticks be written in English rather than Latin in order “to make them more widely legible” (24).
Trust in numbers plays a central role in Chapter 2. Otis argues that “symbolic systems were differentiated from each other by their material characteristics, which helped form the basis for people’s trust judgments” (43). Arabic numerals were especially vulnerable to mistrust because they could be easily altered or misread due to poor handwriting. Even early adopters often continued to use Roman numerals for sensitive financial information. While Otis does not present a single definitive reason for the triumph of Arabic numerals, she concludes that “the advantages of the system’s versatility outweighed the potential security risk” (62).
Chapter 3 focuses on the teaching of mathematics outside England’s elite, Latin-based schools, particularly among “those merchants, craftsmen, and other account-keepers” (63). It was this group of “middling men” who drove the expansion of numeracy and created a strong market for mathematical textbooks as literacy rates increased. This point is especially important because it highlights the close relationship between literacy and numeracy.
Chapter 4 examines how early modern English people perceived and quantified time. Otis identifies an increasingly personal relationship with time during the seventeenth century, as calendars entered the household through almanacs and “encouraged people to place themselves at the center of their own personal calendars” (90). She contrasts this with older religious calendars, where feast days such as the Feast of Saint Thomas functioned as both sacred observances and chronological markers, “a date in itself, but also the twenty-first day of December” (89). This chapter also engages strongly with historiography, particularly the work of historians such as Keith Wrightson and Mark Hailwood.
In Chapter 5, Otis explores how early modern England quantified risk. She traces the development of the concept of “odds” and shows how people increasingly understood uncertainty in terms of chances and probability. This “probabilistic mode of thought” (115) was closely tied to gambling, and the chapter features significant discussion of religious responses to games of chance. One especially engaging example is the dispute between the Puritan preachers James Balmford and Thomas Gataker over the morality of gambling. God’s providence, a theme that runs throughout the book but becomes especially prominent in the later chapters, often stood in tension with gambling practices.
This chapter also explores the rise of insurance schemes, particularly for maritime cargo. Otis shows how insurance expanded rapidly in both England and continental Europe, but rather than viewing insurance strictly as protection against loss, she frames it as a form of structured betting. The most fascinating examples come from the eighteenth century, when “it was possible to purchase insurance on the likelihood of births, marriages, cuckoldry, highway robbery, the fall of a besieged city, and even death by drinking gin” (103–131). These policies may remind modern readers of prediction markets such as Polymarket or Kalshi.
The final chapter connects mathematics to both religious and secular life through parish registers, which “became the foundation for…more general seventeenth-century attempts to use demographic data for social analysis” (141). Here, Otis examines the quantification of the English people themselves. She argues that by the end of the seventeenth century, bureaucrats had increasingly divorced demographic data “from any particular political agenda,” transforming censuses from tools of government administration into broader methods for understanding populations and society (141).
Otis draws from an extensive range of primary sources throughout the book, including mathematics textbooks, account books, insurance records, almanacs, parish registers, and mortality bills. These are supported by an impressive body of secondary scholarship, reflected in nearly forty pages of bibliography.
One of the most compelling ways Otis engages with her sources is through marginalia, which she calls “the surest indicator of the symbolic system used for calculation” (59). In the context of mistrust toward Arabic numerals, marginal notes reveal how readers actually performed calculations. Beyond mathematics, marginalia also helps track the ownership and use of specific books across generations. Otis uses these annotations to show how textbooks passed “through the hands of at least half a dozen annotators” (69). She argues that such books remained in use for decades, particularly among female students, who “had less access to institution-based education and were more likely to be taught arithmetic at home” (69). This evidence is further supported by graphs in the appendices, particularly a table contrasting the total number of arithmetic textbooks with the number containing annotations.
Another source the book uses particularlywell is the London Bills of Mortality, which quantified disease and death. Of all numerical records, these were among the most publicly accessible: “they could be purchased for a penny apiece, or families could purchase an annual subscription for 4s.” Interest in local mortality was driven by more than curiosity—it was also a practical tool for risk assessment. During plague outbreaks in the sixteenth and seventeenth centuries, Otis shows that people used the bills to decide whether they should leave the city. The diary of Samuel Pepys is especially useful in illustrating this behavior.
By the Number is an engaging and illuminating study of a subject that has received comparatively little attention. One area where the book could have gone further is in comparing England to mainland Europe. A lingering question is the extent to which this numerical transformation was uniquely English or part of a broader continental development occurring at roughly the same time. Nevertheless, Otis’s extensive research and clear writing make the book both compelling and accessible. It is a work that will appeal to both academic and general readers interested in the histories of religion, knowledge, and early modern society.