I started reading this after I found a review in some place - probably in hindu(could not find the link, though).
I have read only to some extent. But so far this book has not lived up to what my romaticized vision of what this book must be when I ordered for the book.
The book does not mention anywhere if the book is a translation from italian or not. (See http://www.maa.org/reviews/themathematicalcentury.html
- it says it indeed is a translation).
First of all I find the translation of the book quite below par. There are weird constructions that I find very hard to understand. For exmaple
Hence, in order to describe the extensions of these notions, it is imperative to obtain classification results, which are a complemnetary aspect of abstraction
What is that supposed to mean?
The content is more like a historical survey of the problems and areas in mathematics rather than a deeper discussion of various problems. In that respect the first two chapters I have read have been very useful. They provided a logical organization of various bits and pieces of mathematics I have acquired over a period of time.
As a personal anecdote: There was this job interview I attended at a large company. The team seemd to like me. So I was called in to meet the CTO. In that meeting I said that the whole of computer science is a specialized aplication of set theory - in this I had a notion of a broadish set theory, teh one discussed in teh chapter one of this book. The CTO's knowlege( though he claimed to understand "set therory") seemed to be limited to some dim notions about ven diagrams and nothing else. No. I did not get that job - he thought I was very opinionated.