Co-existence of History of Mathematics and Education of Mathematics: A Comparative Study

Education of Mathematics and History of Mathematics are both old subjects.The question is whether or not these two important subjects can help each other. Unfortunately, this idea divided mathematics society into two groups: those who believe that history of mathematics can help with Education of Mathematics and those who believe that history of mathematics not only cannot help with mathematics education but also causes some confusion. In this paper, I'll present some comparisons and draw some conclusions on how history of mathematics can make mathematics education more active and interesting.