THE HISTORY OF MATHEMATICS The Case of Symbolic Algebra

Abstract: The adolescent’s notion of rationality often encompasses the epistemological view of mathematics as knowledge which offers absolute certainty. Several findings such as Gödel’s theorem and the construction of a strict finite arithmetic, however, provide strong arguments against that view. The static and unalterable mode of presentation of concepts in the mathematics curriculum, rather than lack of knowledge of metatheory, contributes to this misconception. I will argue that the conceptual history of mathematics provides excellent opportunities to convey the basic epistemological and ontological questions of the philosophy of mathematics in mathematics education. In particular, the emergence of the concept of an equation will be presented in a historical context. Such examples will alert students of the relativity of mathematical methods, truth, and knowledge, and will put mathematics back in the perspective of time, culture, and context. Key words: History of algebra, concept formation, absolute truth, inconsistency 1