Interestingly, my experience was that your two sentences are totally contradictory. Physics and engineering was all about using memorized formulas to solve word

Interestingly, my experience was that your two sentences are totally contradictory. Physics and engineering was all about using memorized formulas to solve word problems, and mathematics was where you learned how those equations systematically fall out of some obvious assumptions. I think the real take-away is that both physics and mathematics can be taught poorly, and both can be taught well.