Is "the math stuff" all the optimizations being performed e.g. vectorizing multiplication?

Not trying to sound dismissive here but the core math the post is working with is actually a pretty straightforward matrix multiplication.

The bulk of the discussion focuses on optimizing the execution of that straightforward multiplication algorithm [triple-nested for loop; O(n^3)] rather than making algorithmic/mathematic optimizations.

And again, specific questions are easier to answer. :)

Matrix multiplication isn't exactly intuitive if you've never worked with it before.