Is Mathematics Logic──On the Logicism's Foundation of Mathematics

he problem of the relation between mathematics and logic has been the focus of the mathematical philosophers for centuries. And whether the studies in the foundations of mathematics can be developed further is directly connected with the solution for it. Russell, as the representative of the logicism, pointed that mathematics can be reducible to logic, which has led to many reclaims. So we can reveal the further connection and difference between mathematics and logic by analyzing this position, and conclude that mathematics is not merely logic. Because the impredicative definitions and the axiom of infinite in set theory have been widely used in mathematics research, while which is incompatible to logic. Compared to logic, mathematics holds broader research objects and category.