In pursuit of Hilbert's Problems

I think Hilbert's 23 problems form an organizatory framework for mathematics, that is much more organic than say the AMS classification. I believe that a book that traces the mathematics that grew from these problems can help to organize the burgeoning state mathematics is currently in.

I'm aware there is a book called "The Honours Class" that gives a history of Hilbert's problems up to their solution. However, this book is more biography than mathematics. Also, I'm interested in what happens after the problem is solved. A case study is the 17th problem, which lead to much of real algebra and real algebraic geometry today.