OSHER 841 - History of Infinity

Is infinity a completed object (as in: "the set of integers is infinite") or a developing object (as in: "given any finite set of integers we can produce an integer not in that set")? A related question: Is time continuous or quantized? These questions have been controversial since Plato and Aristotle, through Newton and Berkeley, to Russell and Brouwer in the twentieth century. Currently it is discernible in the classification of mathematics as analytical or digital. We will not resolve this controversy, but demonstrate how it has fueled advances in mathematics and physics over the centuries. Participants in the course need not know much mathematics beyond that taught in the 8th grade (for it is there where students first start to confront these issues). However, they should be eager to wrestle with knotty paradoxes.