You speak with the wisdom of many moons, dick. Mathematical formulae are an essential aspect of engineering as you suggest. Unfortunately I, like many young engineers rely too heavily on EDA tools for this aspect. I choose develop my intuitive understanding instead. If I can solve the problem from basic understanding of the phenomena, rather than solve a complicated equation, I will do so. But then, maybe my concept of "close enough" isn't close enough.
My favorite professor once told me that in his undergraduate career he too disliked the mathematical analysis aspect, a statement that shocked me since this man was a formula g_o_d. He told me that once he had some work experience he learned the value of this aspect, and went back to school with this new attitude. I only hope that I will follow in his footsteps, and in time expand my memorization of formulae, cement my ability of mathematical manipulation, and learn not to overly rely on intuition.