“A Magazine of all perfection”: Mathematics in the Early Modern Satire Histrio-Mastix – Early Modern Mathematics

What would someone like Marston, who was educated at Oxford between 1592 and 1594, have known about mathematics? The heritage of ancient Greek mathematics continued to suffuse the literate culture of Europe during his lifetime. Although some institutions were beginning to restructure their curricula, many universities and schools continued to organise their courses of study according to the so-called ‘seven liberal arts’: the ‘quadrivium’ of arithmetic, music, geometry, and astronomy; and the ‘trivium’ of grammar, logic, and rhetoric. Increasingly, though, the essence of studying mathematics was coming to be the clear deductive structure found in the Elements of Euclid (ca 295 BCE), especially Books I–II. While students could put these theorems and constructions to practical use, the main benefit of the Elements was its ability to model proper reasoning and disciplined mental habits that could be employed in a wide range of activities [Karp and Schubring 2014; Grant 1999]. Yet, popular understandings of mathematics often hearkened back to the earlier models.

Figure 4. Geometrical construction by John Dee (1527–ca 1608), in the style of Euclid’s
famous axiomatic deductive structure that set the standard for rigorous proof to Early Modern readers.
Folio 53, Parallaticae commentationis praxeosque nucleus quidam (London, 1573). Internet Archive.

University professors and mathematical practitioners had long pursued other studies that were understood as mathematical sciences because they were accomplished with geometry or arithmetic: optics (the science of vision), horology (the science of keeping time), the architecture of fortifications, navigation, geography, and bookkeeping [Katz 2014]. These subjects often appeared as personifications in depictions of the mathematical sciences, for instance in frontispieces [Remmert 2011]. People knowledgeable in these areas were often able to put their skills to work in commercial endeavours or in the military, and, although the distinction between “pure” and “applied” mathematics that we understand today did not emerge until the late 19th century, the term “mixed mathematics” was coming into use to designate those mathematical activities that seemed to reside fully in the physical world [Brown 1991; Oki 2013]. 

Figure 5. In his translation of Euclid’s Elements, Dee produced a hierarchical map (“Groundplat”) of the mathematical sciences. Note that geometry and arithmetic are the two “principal” sciences, whereas the derived mathematical sciences include disciplines such as astronomy, statics, and navigation. Fold-out plate at page 64, The Elements of Geometrie of the Most Auncient Philosopher Evclide of Megara (London, 1570). Internet Archive.

At the same time, some intellectuals were pushing forward European knowledge of more abstract mathematics. One major development was the introduction around 1600 of logarithms by John Napier (1550–1617) and others, which had both theoretical and practical implications [Clark and Montelle 2011]. Another strand that praised Euclid and other Hellenistic mathematicians as representing the epitome of exact knowledge would culminate with the work of René Descartes (1596–1650) that started in the 1630s. Researchers, of which there were very few scattered across Europe, were concentrated within Jesuit orders and connected by ‘networks of letters,’ with the network that would be centred around the French mathematician Marin Mersenne (1588–1648) becoming particularly significant. And, the so-called pre-calculus that preceded the formulation of the infinitesimal calculus by Isaac Newton (1647–1727) and Gottfried Wilhelm Leibniz (1646–1716) in the second half of the 17th century began to unfold during this period [Bos 1996; Smolarski 2002].

Mathematics thus encompassed a wide variety of ideas and activities at the turn of the 17th century. Some of these variations on the meaning of mathematics and mathematicians found their way into the plays of the period, as did the debates over how mathematics related to scholastic philosophy and provided insight into the universe around us. As we shall see in the next few sections, Histrio-Mastix was situated right in the middle of the break from a traditional understanding of mathematics towards a new, more modern one that has come to epitomise the Scientific Revolution.

For the cultural historian, Early Modern portrayals of mathematicians present a conundrum since the public image and the actual historical professional were out of sync: On the one hand, the mathematical sciences were rapidly developing, extending their foundations in philosophy and the classical fields of arithmetic and geometry into broad areas of physical science. And on the other hand, as we shall argue, the representation of the mathematician as a professional and cultural character underwent substantial literary development. Thus, changes in the characterisation of the mathematician can serve as a proxy for understanding fundamental developments in the views of mathematics as a discipline and its cultural expressions. Studies of other contemporary plays show that mathematicians were often portrayed as absent-minded, sexually inept, aloof, and confined to an ‘inner world’—while simultaneously being depicted as possessing a privileged access to hidden knowledge, cunning, and manipulation. All of these character traits, we must assume, resonated with the Early Modern audience, providing us with an indication of how the field of mathematics and its practitioners were viewed during a period of large-scale transformation in scientific knowledge and practice.