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Michael. Gr. Voskoglou

philosophy of mathematics education

2018

33

Philosophy of Mathematics , Platonism , Mathematical Realism , Non Euclidean Geometries , Set Theory , Continuum Hypothesis , Axiom of Choice , Incompleteness Theorems , Canonical Distribution , Metaphysics of Quality

Is mathematics a discovery or an invention of the human mind? This is the question raised and investigated in the article in hands, a question that has occupied the interest of philosophers and mathematicians for centuries, at least from the Plato’s era. The development of the non Euclidean Geometries as well as some consequences of the axiomatic development of Set Theory caused two strong blows to the Platonic view that mathematics is a human discovery. A series of experimental data on the correlation of mathematics with human mind are also indicating that mathematics is a human invention. Nevertheless, many people until today are still supporting the Plato’s ideas, whereas there exist also considerations putting the truth somewhere in the middle between the above two extreme vies. However, it seems that the unique certain conclusion which could be obtained from such a discussion is that mathematics constitutes an inseparable part of the human civilization.