So, as to the original question, quantum mechanics cannot defy mathematics because it is mathematics. But, this does not mean it is a literally correct account of quantum physics. It can’t be. If you’ve read carefully, you’ll notice that this has some philosophically interesting consequences. read more
No, quantum physics does NOT defy logic, because it has a solid mathematical formulation behind it, just like any area of physics. What it MAY defy is the "common sense" that most people are familiar with. But "common sense" has been shown to be problematic. Einstein's Special Relativity, when it was first introduced, defied common sense at that time. read more