eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2017-08-07 5 3 95 100 10.12691/ajams-5-3-2 AJAMS2017532 article Michael Gr. Voskoglou voskoglou@teiwest.gr, mvosk@hol.gr 1 Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute of Western Greece, Patras, Greece The effectiveness of mathematics in the natural sciences was characterized by the famous Nobel prize holder E. P. Winger as being unreasonable. It is not difficult for one to understand that this characterization is related to a question that has occupied the interest of philosophers, mathematicians and other scientists at least from the Plato's era in ancient , until today: 'Is mathematics discovered or invented by humans'? In the present work in an effort to obtain a convincing explanation of the above Winger's 'enigma', the existing philosophical views about the above question are critically examined and discussed in connection with the advances in the history of mathematics that affected the human beliefs about them. http://pubs.sciepub.com/ajams/5/3/2/ajams-5-3-2.pdf philosophy of mathematics platonism mathematical realism non euclidean geometries set theory continuum hypothesis axiom of choice incompleteness theorems canonical distribution metaphysics of quality