In this article the effects of the ideas of the main schools of mathematical thought are studied on the development of mathematics education. Crucial problems that occupy nowadays the interest of those working in the field are also discussed, such as the future role of computers for the teaching and learning of mathematics. It is concluded that, although none of the existing schools of mathematical thought has succeeded in finding a solid framework for mathematics, most of the recent advances of this science were obtained through their disputations about the absolute mathematical truth. On the contrary, these disputations have created serious problems in the sensitive area of mathematics education, the most characteristic being the failure of the introduction of the “New Mathematics” to school education that distressed students and teachers for many years. The required thing for those working in this area of mathematics education is, without abandoning their persona; ideas, to search for a proper balance among the several philosophical aspects of mathematics. This will bring the required tranquillity in the area, in order to be developed smoothly for the benefit of the future generations.

philosophy of mathematics, platonism, formalism, intuitionism, logicism, mathematics education, problem-solving, mathematical modeling, computers in the teaching and learning of mathematics