ABSTRACT
In antiquity, philosophy had been a living tradition. Mediaeval scholars wrote few treatises of their own but instead mainly produced commentaries on works of antiquity. In classical antiquity, therefore, mathematics included not just geometry and arithmetic but musical harmony, astronomy, statics, construction and optics. In classical antiquity, mixed mathematics represented a more modern ideal of knowledge, but there was little interest in mathematics in mediaeval Europe. Although Greek mathematics and astronomy had been further developed by the Arabs and enriched with new discoveries, little of it was taken up in Europe. In mediaeval Europe there was little appetite for advanced studies in philosophy or mathematics. The physical worldview of the Middle Ages was broadly that of Aristotle. For the Greek philosophers, reality was not dependent on divine caprice or ordained by the gods; rather it was to a great degree an independent whole.
