Oxford Figures, Chapter 1: 800 years of mathematical traditions

The medieval heritage

From its early years, Oxford has drawn upon mathematical influences on its ways of thinking. By comparison with the University of Paris, Oxford in the Middle Ages was more strongly influenced by a tradition of Christian Neoplatonism. In this tradition (as for Plato himself ) mathematics played an important role, as revealing God's design for the universe. An early Oxford teacher, and Chancellor of the University, was Robert Grosseteste. In what amounts to a research programme for investigating the world through mathematical, specifically geometrical, modelling, he wrote:

The usefulness of considering lines, angles and figures is the greatest, because it is impossible to understand natural philosophy without these ... For all causes of natural effects have to be expressed by means of lines, angles and figures, for otherwise it would be impossible to have knowledge of the reason concerning them.

Oxford scholars of succeeding generations would, in effect, attempt to put this programme into practice. Grosseteste's most famous admirer, the Franciscan friar Roger Bacon, went even further in proclaiming the importance of mathematics:

He who knows not mathematics cannot know the other sciences nor the things of this world ... And, what is worse, those who have no knowledge of mathematics do not perceive their own ignorance and so do not look for a cure. Conversely a knowledge of this science prepares the mind and raises it up to a well-authenticated knowledge of all things.

It was at Oxford in the next century that some of the most sophisticated mathematical discussions of the Middle Ages took place, in which mathematics was used and developed along the lines of the programme that Grosseteste and Bacon had advocated. By this time there was also a strong Aristotelian influence upon Oxford's mathematical studies.

Most of the scholars concerned with this development were Fellows of Merton College, founded in 1264. Prominent in this group was Thomas Bradwardine, who showed, in effect, how the programmatic utterances of Grosseteste and Bacon could bear real fruit in the mathematical analysis of nature: `it is mathematics which reveals every genuine truth, for it knows every hidden secret'. In the hands of Bradwardine and his fellow scholars, the mathematization of magnitudes went beyond anything thought of in Greek geometry. Members of the Merton School attempted to quantify intensities of light, heat, sound, hardness, and density, as well as magnitudes that mathematicians have still not managed to quantify effectively: knowledge, certitude, charity, and grace.

How far such developments would have gone we cannot know. Bradwardine died of bubonic plague (the `Black Death') in 1349. Many other Oxford scholars and at least a third of the population of England died of the same cause over those terrible years, and the University rapidly fell into a decline mirroring that of the country. Despite the ravages and devastation of the Black Death and other social and political miseries, teaching and learning did continue, albeit in a rather depressed state, but not for three centuries did Oxford even begin to regain the intellectual vigour of its glorious early days.

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