When we study something, say math, we learn accepted axiomatic ideas. aren't those very axiomatic ideas what define math? By defining, do they not tell the precise nature of mathematics? Supposing the answer is "yes" to both questions, then allow me to ask one more question: Is "the nature of" something what that something really is? Can something only be defined by indirect observation? What really is mathematics? Could it be that, like in QM, we can only be definately sure of one thing while not the other (and unlike in QM, it does not need to be restricted to particles in this case)?