This conclusion presents some closing thoughts discussed in the preceding chapters of this book. The book presents a rationale and set of strategies for the activity of problem generation. It suggests that although problem posing may have a life of its own, it is also a handmaiden of other aspects of mathematical activity from problem solving to greater personal understanding. The book answers how "striving" was an image that enabled us to push toward a new way of conceiving of multiplication. It points to one model for having students draw on each other's strengths. With regard to that model, it suggests many activities that might take place in an educational setting within which both creative and critical judgments can be encouraged. The book explores that the history of extending number systems uncovers a strong resistance to numbers that were called "imaginary" "irrational", "complex".