In 1603, after six years of construction, Count Wolfgang II von Hohenlohe put the finishing touches on a new two-story laboratory in his residence Schloss Weikersheim. Many of the basic elements of his laboratory can be seen in the frontispiece from a work of theosophical alchemy, Amphitheatrum sapientiae aeternae (Amphitheater of Eternal Wisdom, 1609), by the physician and alchemist Heinrich Khunrath (1560–1605); see Figure 13.1. Although this frontispiece foregrounds the spiritual dimension of alchemy (for example, in the kneeling figure of the alchemist), it also illustrates the practical tools of the alchemical laboratory that Khunrath would have known from his work with Central European princes and alchemists.

As in the frontispiece, Wolfgang II’s roomy laboratory had large, bright windows with extra-deep sills where vessels could be placed, as well as smaller window vents to allow smoke and steam to escape. One corner was occupied by a raised flat stone hearth or forge (like those used by blacksmiths), and, looming over it, a smoke hood, like the one shown in the engraving, to draw away vapors. (This did not, however, protect the laboratory workers from the many poisonous fumes that often billowed up from operations to fill the room.) A large set of fixed bellows mounted at the side of the hearth fanned the coals in the forge and heated the smaller furnaces that were probably contained within it. Connected to the main chimney of the hearth in the Weikersheim laboratory were four brick furnaces, including one called a Faule Heinz, or Lazy Harry, on which many distillations could be carried out simultaneously; an assaying furnace in which refined gold and silver were assayed to determine their purity and ores were tested for metal content; and, probably, a sublimation furnace in which substances were heated until they vaporized and then condensed back to solidity by rapid cooling.

Three kinds of narratives have shaped the historiography concerning the relationships between science and the Christian religion. Stories about the “conflict between religion and science,” in the words of J. W. Draper, or the “warfare of science and theology,” in the words of A. D. White, captured the imagination of Western secular intellectual elites in the nineteenth century. As Draper put it in 1875, “The history of Science is not a mere record of isolated discoveries; it is a narrative of the conflict of two contending powers, the expansive force of the human intellect on one side, and the compression arising from traditional faith and human interests on the other.” In stories of this sort, the victory of science over religion lies at the heart of the admirable march of reason that began in Greek antiquity and culminated in the scientism of the nineteenth century. This historiographical tradition rests on a selective, and highly moralized, presentation of a few episodes of real clash between scientific ideas and religious authority, such as the Counter-Reformation Church’s condemnation of Galileo Galilei (1564–1642) or nineteenth- and twentieth-century Christian rejections of evolutionary theory, framed by an essentialized understanding of science and theology conceived in terms of the self and its enemies.

Although this story remains surprisingly influential, especially in the popular historiography of science, more recent scholars have developed two alternative and contrasting narratives. A number of theologians, scientists, and some historians have argued that the more typical – and more commendable – relationship between religion and science has involved a separate and peaceful coexistence.

In our times, the domain of the physical sciences is reasonably well defined. Although, at its edges, the less empirically grounded parts of the physical sciences may merge into philosophical speculation, it is no compliment to a scientist to characterize his or her work as “philosophical.” In this respect, we have moved a considerable distance from the early modern period. For many European thinkers in the sixteenth and seventeenth centuries, an account of the world around them was radically incomplete without a larger background picture in which to embed it, a picture that often included elements such as the basic categories of existence and the relation of the natural world to God. Many shared the sense of the interconnectedness of knowledge and felt the need for what might be called a foundation for the science that treats the natural world.

The project did not have precise boundaries, nor is it easy to characterize what it is that we are talking about when we are talking about the foundations of our understanding of the physical world. In many ways, the enterprise of providing foundations for a view of the physical sciences was shaped by two traditions, the Aristotelian tradition in philosophy and the Christian tradition in theology. As I shall argue in more detail, the Aristotelian tradition was a common element in the intellectual background of every serious thinker of the period and provided a model for what a properly grounded science should look like. Even for many of those who would reject the Aristotelian tradition in favor of other ancient traditions (such as atomism or Hermeticism) or other views of the world not obviously connected with ancient philosophical traditions, the Aristotelian tradition was hard to escape.

It is difficult to refer to the early modern man of science in other than negative terms. He was not a “scientist”: The English word did not exist until the nineteenth century, and the equivalent French term – un scientifique – was not in common use until the twentieth century. Nor did the defined social and cultural position now picked out by “the scientist’s role” exist in the early modern period. The man of science did not occupy a single distinct and coherent role in early modern culture. There was no one social basis for the support of his work. Even the minimal organizing principle for any treatment of the man of science – that he was someone engaged in the investigation of nature – is, on reflection, highly problematic. What conceptions of nature, and of natural knowledge, were implicated in varying cultural practices? The social circumstances in which, for example, natural philosophy, natural history, mathematics, chemistry, astronomy, and geography were pursued differed significantly.

The man of science was, however, almost always male, and to use anything but this gendered language to designate the pertinent early modern role or roles would be historically jarring. The system of exclusions that kept out the vast numbers of the unlettered also kept out all but a very few women. And although it is important to recover information about those few female participants, it would distort such a brief survey to devote major attention to the issue of gender (see the following chapters in this volume: Schiebinger, Chapter 7; Cooper, Chapter 9; Outram, Chapter 32).

Between the High Middle Ages and the end of the seventeenth century, the discipline of alchemy underwent a succession of remarkable changes, both in its internal configuration and in its outward dispersion. In a word, alchemy moved from a rather marginal position as a discipline concerned mainly with mineralogy, metallurgy, and the products of chemical technology to the center of the European stage, where it became the basis for a comprehensive theory of matter and the justification of a heterodox new medicine, occupying the best minds of the age. All the same, alchemy retained a striking continuity between its medieval and early modern incarnations. Up to the beginning of the Enlightenment, the writers of the popular new genre of “chymical textbooks” were paying tribute to Hermes Trismegistus, an ancient and numinous figure who supposedly founded the art of alchemy (see Copenhaver, Chapter 22, this volume). Until the last quarter of the seventeenth century, these textbook authors made no strict demarcation between “alchemy” and “chemistry,” and despite a misconception popular among historians, they did not normally disavow the transmutation of metals.

The modern distinction between alchemy and chemistry, wherein the former refers exclusively to the transmutation of base metals into gold, is a caricature popularized above all by the philosophes of the French Enlightenment. In the Middle Ages, alchemy was commonly viewed as a subordinate and artisanal branch of physics, a sort of “applied science” based on general principles supplied by natural philosophy. It was classed within the field of “meteorology,” that is, the study of matter below the sphere of the moon.

During the early modern period, “mathematics” was generally understood to mean the study of number and magnitude, or of quantity in general. There were two varieties: “pure” mathematics and, using a term that became common around 1600, “mixed mathematics.” The former studied number and magnitude in abstraction, whereas the latter studied them in composite occurrence; that is, linked to (mostly material) objects. By 1700, mixed mathematics was extensive indeed: In the German philosopher Christian Wolff’s (1679–1754) paradigmatic Elementa matheseos universae (Elements of All Mathematics, 3rd ed., 1733–42), it comprised mechanics, statics, hydro-statics, pressure in air and fluids, optics, perspective, spherical geometry, astronomy, geography, hydrography, chronology, sundials, explosives, and architecture, both military and civil. By 1500, most of these fields were small if they existed at all; the rapid expansion of “mixed mathematics” is a characteristic feature of the early modern period. Compared with the mixed variety, pure mathematics had fewer domains. Wolff summarized it under the headings arithmetic, geometry, plane trigonometry, analysis of finite quantities (i.e., letter algebra and analytic geometry), and analysis of infinite quantities (i.e., differential and integral calculus); the last two were created in the seventeenth century.

In this chapter, we follow this early modern demarcation of pure mathematics; when using the term “mathematics,” unless explicitly indicated otherwise, we refer to pure mathematics so defined. The demarcation was in terms of the subject matter; it did not correspond to professional dividing lines. Few if any scholars identified themselves exclusively as pure mathematicians. Yet the principal stimuli for development in early modern pure mathematics were internal to its own traditions, stemming from classical and medieval pure mathematics.

As is well known, astrology finally disappeared from the domain of legitimate natural knowledge during the seventeenth and eighteenth centuries, although the precise contours of this story remain obscure. It is less well known, albeit clearly documented, that astrology was taught from the beginning of the fourteenth century as an important part of the arts and science curriculum at the great medieval and Renaissance universities, including Padua, Bologna, and Paris. There, astrology was studied within three distinct scientific disciplines – mathematics, natural philosophy, and medicine – and served to integrate several highly developed mathematical sciences of antiquity – astronomy, geography, and geometrical optics – with Aristotelian natural philosophy. This astrologizing Aristotelianism provided fundamental patterns of interpretation and analysis in pre-Newtonian natural knowledge. Thus, the history of astrology – and, in particular, the story of its protracted criticism and ultimate rejection as a source of what the learned considered legitimate natural knowledge – is central for understanding the transition from medieval and Renaissance natural philosophy to Enlightenment science. The role of astrology in this transition was neither obvious nor unproblematic. Indeed, astrology’s integration of astronomy and natural philosophy under the aegis of mathematics had much in common with the aims of the “new science” of the seventeenth century. Thus it becomes necessary to explain why this promising astrological synthesis was rejected in favor of a rather different mathematical natural philosophy.

Historians have often linked two quite separate phenomena: the gendering of early modern natural inquiry as a masculine form of activity in theory and, to a large extent, in practice, and the gendering of nature as female in many early modern texts and images. There is no necessary logical connection between these two phenomena, despite persistent and profound historiographical investments in their linkage, most notably as part of broader critiques of the scientific enterprise by writers with feminist commitments. But there are important and interesting historical connections, which this chapter seeks to explore.

The critical focus on the masculine nature of scientific activity has had the longer history. Antivivisection campaigns in nineteenth-century Britain and America, for example, often (though not always) overlapped with feminist concerns. Antivivisectionists saw biological science in particular as indelibly marked by cruelty toward the animals it used as experimental subjects and by an attitude toward nature that placed more emphasis on advancing scientific knowledge than on respect for the natural world. Others claimed more generally that certain qualities of the scientific enterprise reflected its “masculine” character, that is, were rooted in force and power, as were gender relations in society as a whole. One such writer was Clémence Royer (1830–1902), the first French translator of the works of Charles Darwin (1809–1882), a member of Paul Broca’s (1824–1880) Anthropological Society, and a lifelong activist for feminist and other movements of social reform. In her Le bien et la loi morale (The Good and the Moral Law) of 1881, she described science as masculine in its practitioners and thereby “masculine” in its practices.

In the early sixteenth century, “geography” was not yet a well-established science. Thus, it was quite remarkable that Erasmus of Rotterdam (ca. 1469–1536), one of the era’s leading theologians and humanists, introduced the first Greek edition of the Geography of Ptolemy (ca. 100–170), published in Basel in 1533, by claiming that “hardly any other of the mathematical disciplines is more attractive or more necessary.” Erasmus called attention to the changing status of this newly emerging area of study and emphasized its importance. Only recently, he argued, had traditional limits of knowledge been overcome and scholastic speculations transformed into a clear new view of the earth: