The definition of mathematics: Philosophical and pedagogical aspects

There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of (1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning; (2) the fact that the main mathematics-related skill needed in our computerized, informationsaturated society is a proper mind-set rather than knowledge of some facts or techniques. The proposed definition of mathematics can enrich debates on its nature, in particular, connecting natural human psychological characteristics with philosophical questions of the origin of mathematics. © Springer 2005.