The Evolution of Mathematics in Ancient China: From the newly discovered 數 Shu and 算數書 Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics

The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that make it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Also discussed here are developments of new techniques and justifications given for the problems that were a significant part of the growing mathematical corpus, and which eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics. What follows is a revised text of an invited plenary lecture given during the 10th National Seminar on the History of Mathematics at UNICAMP in Campinas, SP, Brazil, on March 27, 2013.

Terrain, politics, history

This article is based on the 2019 Dialogues in Human Geography plenary lecture at the Royal Geographical Society. It has four parts. The first discusses my work on territory in relation to recent work by geographers and others on the vertical, the volumetric, the voluminous, and the milieu as ways of thinking space in three-dimensions, of a fluid and dynamic earth. Second, it proposes using the concept of terrain to analyse the political materiality of territory. Third, it adds some cautions to this, through thinking about the history of the concept of terrain in geographical thought, which has tended to associate it with either physical or military geography. Finally, it suggests that this work is a way geographers might begin to respond to the challenge recently made by Bruno Latour, where he suggests that ‘belonging to a territory is the phenomenon most in need of rethinking and careful redescription; learning new ways to inhabit the Earth is our biggest challenge’. Responding to Latour continues this thinking about the relations between territory, Earth, land, and ground, and their limits.

England's Immigrants, 1330–1550: Aliens in Later Medieval and Early Tudor England

This article, a revised and annotated version of a plenary lecture given at the North American Conference on British Studies meeting in October 2018, considers the place and significance of aliens in England's history between the expulsion of the Jews in 1290 and the arrival of the French and Dutch Protestants from the 1540s onward. It draws extensively on a new database of immigrants to England between 1330 and 1550, which itself relies principally on the remarkable records generated by a tax on aliens resident in England, collected at various points between 1440 and 1487. Aliens emerge as a significant element in English society—sometimes chastised, sometimes subject to violence and other abuse, but also recognized clearly for their contribution to the economy. If immigrants were sometimes seen as a potentially disruptive presence, they were also understood to be a natural and permanent part of the social order.