Very interesting article indeed!
>I also find it fascinating that the mathematics it takes to describe AC circuits is far more complex than for DC
Why? The math is exactly the same as for DC once you substitute complex numbers for current, voltage and impedances.
Things get more complicated in the time domain, which becomes relevant once you want to look into problems like switching HVDC on and OFF. The nonlinearities of the switching devices lead to differential equations that can only be solved numerically.