Mathematical Objects and the Evolution of Rigor

ABSTRACT: In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is co-substantia1 with the operational inventions that accompany them and that determine the normativity to which they are subjected. THE HISTORICAL DEVELOPMENT AND NORMATIVITY OF MATHEMATICAL OBJECTS Mathematical experience has brought us all, at some point in our intellectual development, up against the belief that we are facing "true " knowledge. This feeling is reinforced as we come into contact with mathematical proofs, almost always during elementary geometry c1asses. Much later- if at all- we encounter a perturbing question: Of what truth does mathematics speak? The concern arises because our traditional image of "truth " refers to an apparent correspondence between intellectual constructs and the outside world that we generally call "objective reality". It is then inevitable that we ask what reality our mathematical statements conform to, what objects are predicated, and with what criteria the truthfulness of those predicates i