Beyond dogmatic fundamentalism in mathematics

Abstract

In this work we discuss the path from the initial stage of mathematical awareness to the understanding and critique of one’s standing beliefs as new stages of conceptual realization occur. Initial interpretation of discourse at the beginning of mathematical education passes through several stages from naive to reflexive and critical. We arrive at the concept of “initiation” into the intersubjective system at the root of mathematics and the necessity of faith in its agreements at the initial building blocks of mathematical method. There is an urgent need to reform the introduction of abstract concepts in mathematics at an earlier stage in education as they turn out not to be linked to accepted ways of teaching mathematics in a historical setting. Education in natural science suffers from lack of progression in maths curriculum and to achieve a consistent programme of development the educational progression needs to be reformed. The current state of mathematical education leaves students 500 years behind the present day and is inadequate for further progression of science.