The extralogical face of Fermat's Last Theorem: an essay on the philosophy of mathematical practice

Abstract

For a long time, the Philosophy of Mathematics aimed to ontological and epistemological aspects of the objects of Mathematics, such an area of knowledge is usually understood, both at school and in everyday life, as a stronghold of universally and eternally true concepts, whose certainty is granted by the logical structured formalized system which is used to construct and represent it. Since last century, however, aspects of mathematical practice, such as intuition, creativity, and the use of representations going beyond the normative symbology, have been the object of study of the Philosophy of Mathematical Practice, which understands mathematics as a human action product and, therefore, social, cultural, and psychological dependent, both collectively and individually. Based on bibliographical research supported by authors who are contemporarily dedicated to this theme, considerations about the extralogical aspects in the individual process of the British mathematician Andrew Wiles that culminated in the formal and rigorous writing of the demonstration of Fermat's Last Theorem - an important proposition in the study of numbers and algebraic equations - performed 358 years after its formulation, are presented, recognizing that no demonstration of mathematical theorems, and especially not this one, can be understood depending strictly on deductive argumentation and symbolic formalism restricted analysis.