16.3, due on December 3

1. (Difficult) I still have a hard time following the math with elliptic curves.  Just adding them is important to multiplying them by a scalar, and also by a scalar factorial.  I think with some practice and if I were to look at the examples carefully (rather than skimming), I could do the arithmetic.  I also don't understand why the method in this section leads to factoring n.
2. (Reflective) The thing that amazes me is that people figured out that you could possibly factor numbers this way, and that it was faster than some other techniques.  I wonder if it happened accidentally, of if someone set out to find a new factoring technique.  I found is helpful how the book argues that using elliptic curves in some cases is similar to using other techniques we have seen (p-1 and trial division).  I don't understand the analogy, but it interesting to know there is one.
   I am curious why this technique is more effective at factoring 50-digit numbers or larger number with small prime factors, but less effective for factoring bigger numbers (with larger prime factors) than the quadratic and number field sieves.