I've heard of mathematicians being frustrated by physicists who use fancy stuff without full understanding of the underlying principles, and sometimes they just

I've heard of mathematicians being frustrated by physicists who use fancy stuff without full understanding of the underlying principles, and sometimes they just manipulate the notation without fully justifying what that manipulation means (e.g. you may have an integral operator on some space, and you might just swap an infinite sum and that integral operator, but that requires a justification that you might omit).