In a recent PRL article, we showed that the one of the postulates of quantum mechanics is redundant, in the sense that it does not constitute a free choice in the theory. Namely, we showed that the use of the tensor product for the state of a composite system is dictated by the state and measurement postulates as well as necessary physical properties of composite systems. In this talk we will report the result and the insights we gained into the relationship between mathematics and the physics it is supposed to describe.