Cultures and practices of mathematics
in the Early Modern period
Jackie Stedall and Benjamin Wardhaugh
In recent years the historiography of mathematics has extended beyond the study of particular texts, topics, or mathematicians to a broader understanding of what mathematics has been and what it has meant to practise it. Mathematics is no longer perceived to be certain and immutable, but an ever-changing set of activities, evolving in response to social and historical demands as well as to its own internal problems and difficulties.
This course will examine mathematical ideas and practices, predominantly but not exclusively in England, during the Early Modern period. This period saw European mathematics evolve from a few rudimentary rules and skills, known only to a few, into a diverse and rapidly expanding range of knowledge including both the highly practical and the highly abstract, ars and scientia. Many of those who practiced mathematics were well respected, others were treated with suspicion, even derision. What did Early Modern mathematics consist of? What, if any, common practices or purposes can we find in the lives of navigator, almanac maker, Gresham professor, or aspiring algebrist?
The starting points and perspectives of the eight lectures in this course are diverse, in an attempt to convey the range of cultures and practices that were regarded as mathematical. We will draw extensively both on contemporary source material and on recent and current research. No specialist mathematical knowledge is required, only a willingness to engage with the material at a number of levels.
1. Patterns of publication and the reputation of mathematics
This session will introduce the resources and techniques we can use to survey and quantify the very large number of early modern print publications which refer to or discuss mathematics. Who were their authors and readers? What was the typical career pattern of a mathematical writer? How and why did the reputation and status of mathematics, dogged by its associations with astrology and with magic, change during this period?
2. Classical influences
Mathematics, like every other area of intellectual endeavour in the Early Modern period was reinvigorated by the rediscovery, translation, and publication of Classical texts. This lecture will examine some of the key texts (of Euclid, Archimedes, Apollonius, Diophantus) that influenced the development of mathematics, and will examine the ways in which their contents were received, absorbed, and eventually superseded.
3. Numeracy: astrology, gunnery and commerce
What did mathematics mean to those who used it for their work or recreation? The early modern period saw the publication of a large number of mathematical handbooks aimed at different groups, who were expected to find them useful. Mathematics could be used to point cannon more accurately, to keep track of the earnings of a small business, or to determine which were the lucky and unlucky days in the coming month. How far were these uses perceived as part of a single discipline, ‘mathematics’, and what is the role, the extent, and even the meaning of ‘numeracy’ in the early modern period?
4. ‘How algebra was entertained in Europe’
Today it is difficult to say exactly what algebra is, and that was the case even in the seventeenth century, when it had already acquired a number of names: ‘the great art’, ‘the cossic art’, ‘the analytic art’, ‘specious logistic’, ‘universal arithmetic’ as well as the ‘barbaric’ term ‘algebra’. This lecture will examine the texts and practices behind these labels, and trace the increasing scope and power of algebra in seventeenth-century mathematical discourse. We will also discuss the rise of notation and mathematical symbolism, an integral but not defining feature of algebra.
5. ‘Mixed sciences’: astronomy and harmonics
This session will explore the rich print and manuscript sources for the use of mathematics to model two very different elements of the physical world. Both astronomy and harmonics were part of the quadrivium, but their status in seventeenth-century mathematics was very different. Astronomy remained a prestigious activity, with a wealth of publications and substantial patronage for both individuals and, increasingly, institutions. Mathematical music was the activity of a small minority, who searched in vain for public recognition or financial reward.
6. Dissemination and communication
Mathematics is often an intensely social activity, whose skills, like those of other traditional ‘arts’, are passed on through personal teaching and example as well as through written texts. The evidence of such personal interactions is, however, transient and easily lost. This lecture will examine in depth a case study, of Harriot’s method of tabular interpolation, showing the preservation and dissemination of unpublished mathematical material over a period of some sixty years through personal contact, conversations, letters, and the circulation of manuscripts.
7. Mathematical careers in the universities and the Royal Society
During this period the professional identity of ‘mathematicians’ began to emerge. What was the role of those in the Royal Society and the English universities whose work mainly or partly consisted of mathematics? John Wallis was able to base a career around mathematical work, but Christopher Wren is now remembered solely as an architect, Isaac Barrow as a theologian and Isaac Newton mainly as a natural philosopher, while lesser-known figures like John Pell and Nicolaus Mercator lived more peripatetic lives on the fringes of university or Royal Society culture.
8. Isaac Newton (1642–1727)
Newton was honoured in his lifetime and afterwards chiefly for his Principia mathematica philosophiae naturalis (1687) but as a young man during the 1660s he made mathematical discoveries of other kinds, which were alone sufficient to secure his reputation. We will look at his work in his annus mirabilis of 1664–65, and follow the subsequent fate of his ideas up to the priority dispute with Leibniz. In doing so we will touch upon a number of themes that are significant in other contexts also: publication strategies, mathematical nationalism, and the increasing role of learned societies and journals.