For me, the final step was easy, and I even saw it coming given the title of the puzzle. I am pretty sound on things like mythology, classical music and literature, which often helps, and sometimes my mathematical background is a bonus.
It took me much more time to sort out exactly how the across clues 14, 19 and 20 worked, but I think I have them right now. The trouble is, of course, that various alternatives look plausible but then the partition only works for one of the pair.
It seems to me that Paddock has been scrupulous in the clueing. This is an impressive puzzle, and we needed something difficult after a few rather easy weeks. I can, however, do without the across style clues for a while.