Hardy Grant - Greek mathematics in cultural context

The often substantial prestige and influence enjoyed by mathematics through the long history of western culture can be traced to beginnings in ancient Greece. Here arose, for example, the vision of mathematical knowledge both as uniquely certain--because attained by rigorous proof from incontestable axioms--and as potentially allowing unique insight into the cosmic order. I shall try to sketch both (i)  the development, in cultural context, of the mathematical tradition that culminated in Euclid's exemplary Elements, and (ii)  the concomitant influence of contemporary mathematics on such characteristically Greek achievements as Plato's theory of Forms, Aristotle's theory of scientific method, and the ``liberal arts'' tradition in education.