Consider some known physical fact, e.g. $\nabla \cdot \mathbf B = 0$ for the magnetic induction $\mathbf B$. Now, is it possible that a mathematical theorem exists, which yields a wrong prediction?
E.g. a hypothetical - correctly proven - theorem that goes: "If $\nabla\cdot\mathbf B=0$ then some new planet should be between Earth and Mars." If this theorem was right, and after deep research we were sure that no such planet exists, one obvious possibility is that the previously known fact was incorrect i.e. perhaps $\nabla \cdot \mathbf B \neq 0$ under some strange conditions. But is this the only possibility? In other words, is it possible that both the premise and the theorem were right, but the mathematically obtained prediction is not true for physics?
Please note that I picked just a silly example to make myself clear about a question regarding the relationship between mathematics and physics, but of course it is not this particular example that I am interested in. Also, I am not looking to discuss the existence of planets between Earth and Mars and, lastly, I am certainly not questioning the truth of Gauss' law.