> Why can't we just provide a simple real life example first and then go on explaining the details? But sometimes there is no real life example. Fundamentally

> Why can't we just provide a simple real life example first and then go on explaining the details? But sometimes there is no real life example. Fundamentally, math is abstract. Yes, mercifully, its models often have analogues in nature, making its purpose utilitarian and intuitive. But sometimes no analogue exists. As in much of modern physics, in math, often you have only abstraction. I think that's why math is difficult to learn. Without compelling illustrations based in the physical world the student must follow the concepts and proofs using the rigor of math's legal transformations, fortified only by the faith that these formalisms will sustain truth. But too often the practitioner must remain oblivious to the utility and implications of both the end and the means.