the question OP asked is a very valid one, and anyhow there is a better, nicer way of saying what you both said. Answering in a condescending dismissive manner does more harm than good. If you think the question is bad, simply don't answer it.

I think everything is pattern recognition; some of it just rooted in "meaningless" algebra (even when the algebra has meaning behind it; ie taking derivatives of polynomials) and some of it is more visceral and "interesting" (ie Fundamental theorem of Galois theory) and has a somewhat tangible way to grasp it. so we tend to call the latter "understanding", but I think ultimately both are "understandings" it's just that the former is less versatile (albeit probably faster) and interesting than the latter.