Is there a modern book that reviews the various fields of mathematics as they stand today? Preferably, this book/set of resources would provide some history of the motivation that led to the development of the modern subject, how these motivations evolved with time, where the "state of the art" lies today, and what connections have been discovered (or tentatively proposed) between one subject and the others.
For example, the resource may provide a blurb on the development of the Chicago school of analysis. What motivated Anton Zygmund and his group early on? At the time, which fields in mathematics would their school have been associated with?  How does their work connect with other subjects? What was the impact of their school? Which fields of mathematics is their school associated with today?

The Princeton Companion to Mathematics might be what you're looking for. It surveys an impressive number of fields in mathematics, including their historical and modern contexts, as well as describing basic definitions, theorems and open problems. And it gives mini-biographies of a whole load of important mathematicians. It's a very good reference.
