G. Paulia, a Hungarian-American mathematician and mathematics educator, thinks that "mathematics proposed by Euclid's method seems to be a systematic deductive science; But mathematics in the process of creation looks like an experimental inductive science. " Judging from the many facts of the discovery or invention of mathematical truth, it is discovered through a lot of experiments and induction, and then its reliability and authenticity are proved by deductive reasoning. Therefore, mathematics has duality, which is not only a systematic deductive science (from the viewpoint of stereotyped mathematics), but also an experimental inductive science (from the viewpoint of mathematics in the process of creation).