On the Mathematics and Reality

In this article, accompanied by introducing recent backgrounds of intensifying historical concern in the relation of mathematics and reality, we try to reconsider this concern by separating the different viewpoints about the necessity and certainty of the mathematicalpropositions. The ones who consider mathematics as non-certain and non-necessary, think about this relation just as that of other sciences, either realistic or anti-realistic. On the contrary, those who I name them syntheticalists (Platonists and Kantians), are, on the one hand, somehow realist (though with a different definition), and on the otherhand, analyticalists are anti-realist. At the end, we will point to a defense of realism, founded on applicability of mathematics.