Until recently, historians of mathematics usually agreed in refusing to consider the numerous geometrical publications of Thomas Hobbes as a contribution to the development of mathematics in the seventeenth century. From time to time, one could find statements that although Hobbes did not find new theorems he undoubtedly had profound insights into the logical foundations of mathematics, but these occasional remarks did not encourage historians to go deeper into Hobbes's mathematical thought. In the end, the general conclusion was that Hobbes's preoccupation with squaring the circle, doubling the cube (starting when the philosopher was more than forty years of age), and challenging Euclid's definitions were better ignored, at least in the history of science. In particular, his controversy with the Savilian professors Seth Ward and John Wallis was seen as a ‘deplorable affair’, liable only to damage the reputation of the protagonists.

By the early years of the twentieth century, astronomers regarded photography as one of the most valuable tools at their disposal, a technique which not only provided an accurate and reliable representation of astronomical phenomena, but also radically changed the role of the astronomical observer. Herbert Hall Turner, professor of astronomy at Oxford, wrote in 1905: ‘The wonderful exactness of the photographic record may perhaps best be characterised by saying that it has revealed the deficiencies of all our other astronomical apparatus – object-glasses and prisms, clocks, even the observer himself.’ H. C. Russell, government astronomer in Sydney, suggested that photography might in the future make the observer redundant: ‘In many cases the observer must stand aside while the sensitive photographic plate takes his place and works with the power of which he is not capable… I feel sure that in a very few years the observer will be displaced altogether.’ Such visions were not uncommon at the time, emanating from the trust invested in the photographic process after the spectacular achievements of the late nineteenth century.

Science in the twentieth century has relied on enormous financial investment for its survival. Once departed from an amateur pursuit, industry, charity and government have ploughed huge resources into it, supplying the professional occupation of science with a complex of institutional facilities – full-time posts, research laboratories, students and journals. Financial support, however, has always been a limited resource and has gone most generously to those areas of research which appear particularly novel, innovative or promising, that is to the ‘leading edges’. To secure the funds necessary to maintain their life-style, then, scientists have had to make their activities scientifically and economically attractive to the funding bodies. Historians and sociologists of twentieth-century science have tended to follow these priorities and have concentrated on the leading edges. We have studied at length the acquisition of new knowledge through research, the creation of the institutional complex and the furtherance of science through innovation, specialty and discipline formation, part and parcel of which is the gathering of the necessary funds. The competition for funds has been investigated in analyses of controversy between competing groups within a research area, which has provided important models for the social and conceptual development of science. This emphasis, however, may have missed a great deal of what happens in science.