Your point 1 resonates with me. Learning math has steadily increased my effectiveness as a scientist/engineer/programmer. Sometimes just knowing a mathematical concept exists and roughly what it does is enough to give you an edge in solving a problem - you can look up how to do it in detail when you need it. However, despite the fact that life continues to demonstrate to me the utility of knowing the math that I've learned, this has failed to translate into an impulse within me to actively learn more math. Pretty much at any time in the past I've felt like I knew "enough" math, and yet always see a great benefit when I learn more. You'd think this would sink in, you'd think I would start learning math for its own sake with the implicit expectation that it will very probably come in handy, but it hasn't.