# Book chapters

'Two books on the elements of algebra', to be published in Mathematical Book Histories. Printing, Provenance, and Practices of Reading (Philip Beeley and Ciarán Mac an Bhaird, eds), Trends in the History of Science, Cham: Birkhäuser

We examine two early nineteenth-century algebra textbooks held in the Russell Library: Bewick Bridge's Treatise on the Elements of Algebra and James Wood's Elements of Algebra. We consider their contents, their readership, and their place within nineteenth-century mathematical publishing.

'Language use in Russian mathematics journals', to be published in Circulation des mathématiques dans et par les journaux: Histoire, territoires, publics (Hélène Gispert, Philippe Nabonnand and Jeanne Peiffer, eds).

The (linguistic) problems experienced by Western mathematicians in their attempts to access the mathematical work of the Soviet Union during the years of the Cold War are well documented. Nevertheless, there have been times over the past three centuries when Russian mathematicians have deliberately chosen to publish in Western European languages in order to increase their international readership. I will begin this chapter by surveying some of the mathematical journals that were available in/from Russia prior to the twentieth century, before considering the language policies of journals under the Soviet regime, with a particular focus on one journal: Matematicheskii sbornik. I adopt a data-led approach, whose pros and cons I assess at the end of the chapter.

During the late-eighteenth and early-nineteenth centuries, so-called Literary and Philosophical Societies (‘Lit & Phils’) emerged in many towns and cities across the British Isles. Their goal was to promote the understanding of a range of subjects at the local level, with science, broadly defined, usually being the major focus. The organizers of these societies often professed an interest in all strands of knowledge – including mathematics. In practice, however, the lecture programme of a typical Lit & Phil rarely featured topics that might permit any mathematical content, and where mathematics did appear, it was usually with a strongly practical or educational bias. Nevertheless, there are notable exceptions: the Manchester Literary and Philosophical Society, for instance, regularly featured lectures on mathematical topics. In this chapter, I offer a preliminary account of the handling of mathematics by a number of Lit & Phils, compare this briefly with the central position occupied by mathematics at meetings of the British Association for the Advancement of Science, and reflect on the disciplinary biases of these societies.

The tremendous growth of the mathematical sciences in the Europe of the early modern period was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants’ accounts, instrument making, teaching, navigation, and gauging. Mathematics in many ways shaped the knowledge culture of the age, extending through the Industrial Revolution to the nineteenth century. In this first chapter, we set the scene for the varied examples of practical mathematics that follow in the remaining essays. We begin with a preliminary discussion of the example of seventeenth-century England before moving out into the wider contexts covered by this book. We summarise the contents of the following chapters and draw out common themes.

At the beginning of the nineteenth century, the Sedleian Chair had passed smoothly into the hands of mathematicians. Its first occupant during the century, George Leigh Cooke, may not have been the most active of professors, but the teaching that he did do, and his academic interests, such as they were, served to secure the chair as one in applied mathematics. When Cooke died in 1853, the university was in the throes of reforms imposed upon it by the government, with the improvement of the professoriate and the provision of scientific teaching in the university being central to those reforms. Cooke’s successor as Sedleian Professor, Bartholomew Price (1818–1898), was of the pro-reform party, and had previously pushed for the changes in policy from which he now benefitted. Like Cooke before him, Price would go on to hold the chair for over four decades. During this time, he built a career as a prominent academic administrator, politician, and accountant, revived the fortunes of the University Press, and eventually rose to the Mastership of his alma mater Pembroke College. Alongside these various other roles, he would carry out his Sedleian teaching with the greatest of diligence, and produce a series of highly-regarded textbooks. Over several decades, Price worked gradually to raise the standard of mathematical study in the university. A few short papers aside, he was not a mathematical researcher, but as an administrator, teacher, and publisher he had an enormous impact on mathematics in Oxford, and in Britain more generally.

Following the death of Thomas Hornsby in 1810, the remainder of the nineteenth century saw just two Sedleian Professors, who each held the post for over forty years. The first of these, George Leigh Cooke (1779–1853), was a university figure from a very traditional mould: a churchman first and foremost, who would eventually abandon his Oxford duties for those of his parish. Nevertheless, Cooke carried out his Sedleian teaching much more dutifully than most of his eighteenth-century predecessors, at least at the beginning of his tenure. At the same time, he was a defender of Oxford’s traditional emphasis on classics, and placed a limit on the mathematics that an undergraduate ought to learn. We might therefore view him as a transitional figure in the development of the Sedleian Chair and of mathematical study in Oxford.

The Sedleian Professorship of Natural Philosophy is one of Oxford’s oldest chairs, founded in the early part of the seventeenth century, alongside a number of other such posts, most notably the Savilian Professorships of Geometry and Astronomy, with which it has always been closely associated. Originally a university position whose sole duty was to lecture on natural philosophy, the Sedleian Chair has developed over four centuries into a role that encompasses both teaching and research. Along the way its focus has been narrowed from natural philosophy to applied mathematics. Indeed, the Sedleian Chair arguably has had the most interesting and varied development of any such professorship, with several twists and turns along the way. In this first chapter, we describe the foundation and general trends in the development of the chair by way of providing background for the stories of the individual professors that follow in the remaining chapters.

The century between the Savilian Chairs of Halley and Rigaud was one of great activity in astronomy, and especially in Oxford, at a time when all the Geometry professors were primarily astronomers, and the Astronomy and Geometry Chairs were largely interchangeable. This chapter looks at the achievements, both mathematical and astronomical, of the occupants of the Geometry Chair, as well as those of some of their contemporaries, and puts paid to the myth that Oxford science was backward during the 18th century.