In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly of higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation.

In this essay, we study the history of Dirichlet’s theorem with an eye towards understanding the methodological pressures that influenced some of the ontological shifts that occurred in nineteenth century mathematics. In particular, we use the history to understand some of the reasons that functions are treated as ordinary objects in contemporary mathematics, as well as some of the reasons one might want to resist such treatment.

This Tale from the Field focuses on the interpretation by workers of the precarious nature of blue-collar formal employment in Russia. In an ethnographic sketch based on over two years in the field, I follow an individual, Sergei, as he relies more and more on informal and other sources of income instead of waged labour in the increasing number of multi-national enterprises which have come to Russia to set up factories. Why does Sergei, and many like him, still young or without memory of Soviet labour practices, ‘choose’ exit from the formal economy at the very moment when wages and conditions are finally increasing? Why is the informal economy as a ‘choice’ so important to blue-collar workers despite the hunger for labour in traditional production industry?

The historiography of religion in modern Britain has been dominated in recent years by controversy over the sociological theory of secularization. This review of the literature on secularization in modern Britain traces its apparent persuasiveness in part to assumptions about religious decline and renewal which are central to Christian soteriology. Recognition of the nature of secularization theory discloses a monolithic notion of religion itself. Closer attention to the complexity of religious experience may yield an account of religion more attuned to the contours of social change in modern Britain.

White-necked Picathartes Picathartes gymnocephalus is a globally ‘Vulnerable’ bird endemic to the highly threatened Upper Guinea forests in West Africa. In an environment under a high level of threat, the high breeding site fidelity (or breeding site persistence) of this species enables long term monitoring of colony site occupancy, colony size and other breeding parameters, which provide multiple indicators of population status. We surveyed known colony sites and searched for new sites in three recent breeding seasons in order to assess the current population status in the most important part of their range in Sierra Leone, the Gola Forest. We found 157 active nests at 40 colonies, equating to at least 314 adult birds. Less than half of the known colonies were protected by the Gola Forest Reserve. Colonies outside the reserve tended to be confined to larger rocks and subject to disturbance from human activities in close proximity, but did not have fewer active nests in them. Colonies outside the reserve were also more likely to be inactive in a given year whereas all colonies inside the reserve were active in every survey year. A predictive distribution model indicated that the survey region could have as many as 234 nests equating to at least 468 breeding birds. There was no evidence that mean colony size had declined since surveys undertaken in the 1980s and 1990s but it was not possible to compare colony abandonment rates inside and outside the reserve over that time period. Clutch and brood sizes were similar in each year, though brood size appeared slightly lower in the third survey year possibly because of a slightly later survey date. Mean clutch and brood sizes reported during the study period were similar to those found in the 1980s and 1990s. We conclude that the population of White-necked Picathartes in the Gola Forest area has been relatively stable over the last two decades, reflecting both the efficacy of protection afforded by the Gola Forest Reserve and presumably low pressure to farm new areas in the nearby community forest. However, regular monitoring of colonies both inside and outside the reserve is required to detect any systematic impact on the birds as pressure for land increases.

This article examines the mindset and episcopal policy of George Ridding, first bishop of the new diocese of Southwell from 1884 until his death in 1904. Ridding's intellectual formation was rooted in Liberal Anglicanism, and is analysed here through his ‘Broad Church’ understanding of the Church of England as a comprehensive national Church. His commitment to this ideal is demonstrated through his episcopal charges and speeches, and through elements of the policy of diocesan management that he adopted. A brief evaluation of this policy identifies limitations, as well as continuity with the earlier movement of diocesan reform.