Abstract
This paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics. For that, an "epistemology of intuition and imagination" in the field of mathematics is outlined (suggested) emphasizing the need to adopt a dynamic conception of mathematics. In this context, intuition and imagination present themselves as forms of mathematical experience that give access, through paths that are not purely logical, to mathematical knowledge. Its epistemological and rationality characteristics, a rational of a non-logical nature, are highlighted by several examples, resources for moving the ideas involved. The epistemological study of intuition and imagination also allows highlighting its ontology, constituted of more relations than objects. From the pedagogical point of view, we discuss the formative character of philosophical studies involving intuition and imagination, mainly related to creativity in mathematics. Keywords: Mathematical knowledge; Mathematical experience; Epistemology of intuition and imagination; Creativity in mathematics.
Highlights
This paper aims to contribute to the clarification of the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing its epistemological and procedural characteristics
The aim of this paper is to clarify the role of mathematical intuition and imagination in the constitution of mathematical knowledge, evidencing their epistemological and procedural characteristics
The main subject of this study is the epistemology of intuition and imagination, it is necessarily accompanied by a discussion about the ontology of intuition and imagination, an ontology that the epigraphs of this paper, referred to the field of science and life, point to the field of mathematics
Summary
In the history of mathematics we find many examples illustrating the role of intuition and imagination in the process of elaborating knowledge. Other examples can be given, notably the case of the various geometries In this context of intuition/discovery, imagination/creation (our working hypotheses) one can argue that, regarding the study of "space", Euclidean geometry, in Euclid's own version, is on the side of intuition, while non-Euclidean geometries are on the side of imagination. To understand this distinction we must first consider what we call “geometry”, a theory (usually presented in axiomatic form), which studies geometric space and speaks of certain objects as points, lines, planes, angles, and so on. Non-Euclidean geometry models are a logical creation from the Cartesian models of Euclidean geometries
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