Until the first quarter of the seventeenth century there was a great deal of agreement about the nature of mathematical practice. Mathematicians, as well as their patrons and clients, viewed all possible aspects of their work, both theoretical and practical, as being included within their discipline. Although the mathematical sciences were a fairly recent foreign import to England, which can barely be traced back beyond the mid-sixteenth century, by the beginning of the seventeenth century there was a large and growing body of practitioners with a unified view of their subject's identity. Divisions began to appear, however, and they were often framed in terms of the proper mixture of theory and practice in mathematical education.

One early sign of the emergence of this tension is the kind of accusation made in the priority dispute between William Oughtred and Richard Delamain taking place around 1632. Their bitter conflict began over who first invented the Horizontal Quadrant, a form of sundial, and the Circles of Proportion, a logarithmic calculating device that can be considered a precursor of the slide rule, and ended in a dispute over what constituted proper mathematical practice. Oughtred accused Delamain of making his students ‘only doers of tricks, and as it were Juglers’ by teaching them the use of instruments without any theoretical foundation. Instruments, Oughtred claimed, could only be used with understanding by students who had a proper theoretical foundation. He advocated postponing their use until after the theoretical foundations of a subject had been thoroughly mastered. Delamain, on the other hand, was perfectly willing to teach practical instrumental operations without insisting upon a theoretical grounding. This paper will use the dispute between Oughtred and Delamain to investigate the breakdown of consensus over internal mathematical boundaries, the rhetoric and strategies involved in attempts to gain authority by mathematical practitioners, and the extent to which their roles were negotiated, both with other practitioners, and with their patrons and students.

These gems have life in them: their colours speak,

Say what words fail of.

In an ambitious treatise on the estimated wealth of the British Empire in the year of Waterloo, Patrick Colquhoun added to his calculations of the revenues produced by overseas property the potential profits created through exploiting natural resources. In his ‘political arithmetic’, Colquhoun recognized that an increasingly lucrative resource could be found in ‘mines and minerals’, where ‘various articles extracted from the bowels of the earth, which the new discoveries in chemistry have rendered valuable articles of commerce, have tended greatly to increase the value of the mines’. Such information, accumulated through travel, skilled techniques of identification and analysis, and collecting, proved central to regulating judgements about potential overseas investment by the government.

Practices in natural history intersected with the development of British commerce in a number of ways. Mineralogists specially trained to identify rare species of minerals scoured distant shores and collected sack-loads of specimens, seeking information about natural resources that might nourish a developing imperial economy. One such British mineralogist was John Mawe, who in 1804 received patronage from Portugal's Prince Regent to embark on ‘a voyage of commercial experiment’ to the Portuguese territory of Brazil and assess the value of the gold and diamond industries that might revitalize their ailing and isolated economy. National and individual economic interests were informed and served by the multiplication of such acts of commercial speculation, which focused on various kinds of natural resources. Mawe was very conscious that the mineral kingdom held much to be explored. Unlike botany, with Linnaean taxonomy rendering order to the kingdom, knowledge in mineralogy was far from comprehensive. Mawe lamented that ‘few have thought the knowledge of Minerals worthy of their attention, although to them we owe our national strength and riches’. Others also argued that because it addressed national interests, research and education in the earth sciences should be publicly patronized.

Generally, the mass media in Britain, as elsewhere, treat the history of science as arcane knowledge. A few iconic tales do none the less come to permeate public consciousness. How do these come to be selected from the myriad of possible narratives?

One of the most enduring and well known of stories is the discovery of penicillin, which stretched from Alexander Fleming's observation in 1928 to the award of the Nobel prize to Fleming, Howard Florey and Ernst Chain in 1945 and the subsequent dominance of American companies in its manufacture. During the 1980s, when it appeared scandalous that monoclonal antibodies discovered in Cambridge, England, had not been patented by the British government, the parallel was often made with penicillin. An alternative use was made of the story when, in July 1995, a columnist in London's Evening Standard criticized massive expenditure on medical research and claimed that most drugs were discovered by accident. He sustained his thesis by merely putting in pointed parentheses the one word, ‘penicillin’. The same year, partisans found space in the correspondence columns of the New Scientist to return enthusiastically to the debate over the proper disposition of credit between Fleming and Florey. The BBC's Money Programme broadcast a piece on how best to support inventors today in October 1996; it included film of the Science Museum's coverage of Fleming.

The story of penicillin seems therefore bound, time and time again, to great issues in British culture: pride over technological prowess, resentment over the loss of opportunity, jealousy of American success, the National Health Service and the emergence of the modern pharmaceutical industry. The appeal of the story and meaning of its associations are matched by reverence for its material relics. In high profile auctions, the sale of samples prepared by Fleming raises thousands of pounds and is previewed in the newspages and on the radio. The original plate on which Fleming observed penicillin with its sterile ring surrounding the healing penicillin is one of the most familiar of historic relics (Figure 1).

Michel Serres with Bruno Latour, Conversations on Science, Culture, and Time. Ann Arbor: University of Michigan Press, 1995. Pp. 204. ISBN 0-472-09548-X, £31.50, $44.50 (hardback); 0-472-06548-3, no price given (paperback).

Michel Serres (ed.), A History of Scientific Thought. Oxford: Blackwell, 1995. Pp. viii+760. ISBN 0-631-17739-6. £75.00, $100.00.

Michel Serres is one of the best-known philosopher-critics in France, and his name is likely to draw many readers to these two books. With sales of 50,000 copies of his La Légende des anges (1993; trans., Paris, 1995), 100,000 copies of Le Contrat naturel (1990; trans., Ann Arbor, 1995) and 300,000 copies of Le Tiers-instruit (1991; trans., forthcoming), Serres's official eminence (he was elected to the Académie Française in 1990) is more than matched by contemporary popularity. Originally trained in mathematics and logic, Serres undertook doctoral research with Gaston Bachelard – and it shows. Even at his most allusive, Serres's dexterous prose often slips into neat axiomatic and Euclidean certainties, while one can see much of both his aggressively anti-epistemological stance and his easy traffic across the science–poetics divide as an effort to distance himself from his former mentor. But, like Bachelard, Serres has a commanding range, is hugely prolific and writes – if one may say this of one of the ‘Immortals’ – with a glee and innocence that one associates with the rank amateur.

Serres, a professor of the history of science at the Sorbonne, is no amateur. ‘History of science’, he has said, ‘that's my trade’. So it may be, yet many, hearing of his forays into the history of angelology, the natural rights of trees, the iconography of Tintin and the moral status of airport terminals, are entitled to ask whether Serres is to be trusted. Put another way, should one take Serres seriously? The question is worth asking at the outset, for there is little more aggravating than intellectual energy and enthusiasm one feels with hindsight to have been misplaced. How many readers of Michel Foucault, one wonders, were shocked to find him saying in his last lectures that he admired Diogenes the Cynic, the shameless philosopher who masturbated in the Athenian public square, pour épater les bourgeois, so to speak? Maybe Foucault's oeuvre was a similar snub from a maître-penseur – a kind of masterpation, if you will.

The following list of archival material relating to the history of science acquired in 1996 and 1997 by British repositories is drawn from Accessions to Repositories, an annual publication compiled by the Historical Manuscripts Commission. It is important to note that these accessions may not have been catalogued and that access may therefore be restricted. Further inquiries should be addressed to the staff of the repositories concerned.

The Historical Manuscripts Commission seeks each year to collect information from over 250 repositories throughout the British Isles. This information is made available on the Internet via the Commission's website, http://www.hmc.gov.uk. The Commission will answer limited and specific postal and email inquiries. The information is also added to the indexes of the National Register of Archives, which are available for consultation in Quality House, Quality Court, Chancery Lane, London WC2A 1HP, or via the Internet on the address above. Alternatively, electronic users can gain access to the NRA via Telnet (telnet: public.hmc.gov.uk). Readers should be aware that the manuscript collections noted in the following digest represent only a very small part of the collected information available in the NRA.