We explore some aspects of the rival conceptions on the foundations of mathematics appeared during the first half of the twentieth century. We consider the conceptions respectively adopted by the four following schools of thought: the logicist school, the intuicionist school, the formalist school and the school based on the set theory foundations. We argue in favor of the great potentialities that this debate can give rise to the improvement of mathematics and physics teachings. We search connections with the quantum mechanics teaching and with the concept of meaningful learning. Some aspects of the great plurality of meanings of the term intuition are discussed.