In this talk, I will reveal the connection between particular representations (symbols, diagrams) and the Kantian intuition of mathematical objects. I will construct an interpretation of Kant's philosophy of mathematics that explains the requirement of pure intuitions, space and time and reveals the a priori nature of mathematics in Kant's doctrine. Kantian characterization of mathematics exposes a different reasoning model from the current method of mathematics, namely the formal sentential reasoning. I argue that by understanding this approach and by recognizing the roles of diagrams in mathematics, it is possible to realize the advantages of heterogeneous reasoning in mathematics.