Oxford Figures, Chapter 1: 800 years of mathematical traditions

The historical research tradition

During the seventeenth century the Oxford antiquarian interest in preserving the records of the past became subsumed in an interest in the history of mathematics itself. A number of influences came together to create a historical approach to mathematics which has characterized the Oxford tradition. Sir Henry Savile was crucial: in laying down statutes for the Chairs of geometry and astronomy, Savile gave instructions for the subjects to be taught by exegesis of the great texts of the past, principally Euclid's Elements and Ptolemy's Almagest. Another influence on the style of mathematics was the creation at this time of the Bodleian Library, by Savile's friend Sir Thomas Bodley. This, together with a smaller library attached to the Savilian Chairs, ensured the availability of many books and manuscripts for scholarly purposes.

The influence of the time is also seen in the spirit of investigation evident in the work of the Royal Society, founded in 1660 by a group of people many of whom had Oxford connections. In the activities of the Royal Society the history of a subject of concern was an essential part of how it presented itself for understanding, categorization, or analysis. Thus, when John Wallis wrote his great Treatise of algebra (1685) as a study of algebra seen through its development from earliest times, it was at once the first algebra text on this scale and the first history of mathematics written in English. The way in which Wallis presented mathematics as something intrinsically bound up with its history can be seen as a development particularly characteristic of Oxford, in which knowledge from the past is explored and built upon in order to make future progress, as much in mathematics as in any other subject.

Another way in which the Oxford historical approach to mathematics showed itself was in the production of a number of major editions of ancient mathematical texts, edited by senior University mathematicians under the auspices of the University Press. This began in the 1640s, with an edition of Arabic astronomical tables worked on by the first two Savilian Professors of astronomy. This kind of production was another consequence of Savile's insistence that his professors know about the past in order to make future progress. He recognized the extent to which astronomy, in particular, is an intrinsically historical discipline, in which records made by earlier observers are a crucial dimension of current analysis and understanding.

The tradition of major editions persisted for some time after the age of Wallis, but it was not until the nineteenth century that another Oxford mathematician showed comparable historical interest and enthusiasm. Stephen Rigaud, Savilian Professor, successively, of Geometry and Astronomy from 1810 to 1839, played a major part in the renaissance of the history of mathematics--of Newtonian studies, in particular--that was taking place in the early nineteenth century. Besides more general themes, he took pains to explore Oxford's own contributions to historical scholarship. In a paper to the Ashmolean Society in 1836, for example, Rigaud described the textual history of Archimedes' Arenarius or Sand-reckoner: this work has borne an Oxford imprint since Wallis's critical edition of 1676, incorporated by Torelli in his 1792 Oxford Archimedes, using manuscripts found in Oxford libraries from the early sixteenth century to the late eighteenth century. He pointed out, too, that one of the few English editions of this work was made by a Wadham College undergraduate, George Anderson, in 1784.

Rigaud's interest in history had been aroused by a failed attempt at the end of the eighteenth century to sustain the Oxford tradition of publishing important historical mathematical editions. In 1784 manuscripts of Thomas Harriot--perhaps the most highly regarded Oxford-educated mathematician since the Middle Ages--were rediscovered in a country house in Sussex, having been thought lost since the 1630s. An edition of the more significant papers was proposed, to be published by the University Press, and the papers were examined by Abraham Robertson, shortly to become the Savilian Professor of Geometry. He reported back that the papers were in no state for publication and would not contribute to the advancement of science. But when Rigaud took over the Savilian Chair of Astronomy and re-examined them 30 years later, he realized that Harriot's papers were indeed rich in content and full of interest; he worked on them to some effect, but his death prevented a major opus.

To bring the story up to date, interest in the Harriot papers eventually revived in the 1960s and a Thomas Harriot Seminar was founded, meeting initially in Oxford, now in Durham and Cambridge. An article published in 1969 by some of those involved described the Harriot papers as `one of the most important bodies of unpublished English scientific manuscripts, and probably the most complete collection of working observations and calculations revealing the scientific art, in one of its most original practitioners'. But the problem still remains of reducing them to order and putting them in a fit state for publication.

The history of science, as something distinct from but closely related to the history of mathematics, was pursued in various ways in twentieth-century Oxford. A relatively small area of interest tends to be buffeted in the storms of institutional politics, and it was only with considerable struggle that Robert Gunther was able to establish the Museum of the History of Science in the Old Ashmolean building, based on the scientific instrument collection of his friend Lewis Evans. Gunther's 14 volumes on early science in Oxford (1923-45) contain a considerable amount of material on which subsequent scholarship could build. In 1972 a Chair in the history of science was established at Oxford, associated with the modern history faculty.

Oxford's tradition of historical research into the history of the mathematical sciences has been extended by the award of doctoral degrees for research into the subject. The 1990s saw Julia Nicholson's thesis on the development of group theory, Eileen Magnello's on the pioneering statistician Karl Pearson, and Eleanor Robson's on mathematics in ancient Mesopotamia. Besides observing that all these degrees were gained by women, it is worth noting that each was done within a different area of the University: in the Faculty of Mathematics, the Wellcome Unit for the History of Medicine, and the Oriental Institute, respectively. Thus scholarly concerns for the history of mathematics are found throughout the University.

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