“Mathematical" and "optical“ stems from design lingo and is AFAICS not an invention by the author. One can find these terms in most of design related software packages. “Mathematical” is also often described as “metrics”.

I prefer to call it “optical” and “mechanical” alignment, rather than “mathematical.”

Indeed. That's how my brain reacts to it - it keeps nagging me that thing is not properly balanced and will tear everything apart when rotating, like a washing machine does when you throw a brick inside it.