Undergraduate physics gets by with surprisingly little, if any, advanced math, so it is only natural when one realizes how inadequate one's knowledge of math actually is.

Have to disagree with this. I'm a math undergrad but a good chunk of my algebra class this semester was physics students. Additionally, the author said they have a graduate degree. As far as I know (which is not very far) modern physics makes considerable use of algebraic constructions such as tensors and lie algebras, so I'd imagine the author would be familiar with these concepts, which puts them lightyears ahead of any self-taught mathematician.

Let's just say that there was very little emphasis on Math in my Physics Masters, which in itself was very poorly taught, and leave it at that.

I don’t know, Shaum’s Outline of Tensor Calculus can bring you there in no time.

Math is being able to do logic with numbers.

I've tried creating my own math as an engineer, it's possible, but I also know every attempt I've made failed at finding something new.

My point is, we learned a lot about numbers in engineering school.

Yes but physics != engineering. You really need very minimal higher math to do engineering work. As far as I know, at my school the furthest engineers go is a course in vector calculus, ODES, baby linear algebra and simple probability. None of which would be really be considered higher math. In contrast, physics needs complex variables, Pdes and most students take at least a group theory class.

Is there something about those topics that don't follow logic?

It's not mathematics degree, fair enough.

Math,queen and servant of science..