The millennium problems are important mathematical problems that have, so far, eluded resolution (with the exception of the Poincaré conjecture, solved by Grigori Perelman after the book was published.) Devlin does an outstanding job of explaining what the problems are, to the extent of making them appear almost easy, and an outstanding job as well in explaining how the problems are being tackled and what the issues are. I can only wish that all math pop science books were that crystal clear. This is popular science writing at its best - informative, intelligent, and endlessly intriguing.
It is difficult to figure out for whom this book was written. It appears as if the author himself was struggling with this...unfortunately, he did not solve this problem before the book went to print. Sometimes, the author speculates whether or not a mathematical layman might be able to solve any of the problems. He does not argue why or why not. Some problems are even for him too difficult to explain, for which reason he skips a "common sense" explanation altogether and dives right into the depths of the mathematical ocean. For many problems the author does give a beginner's perspective, however, the mathematically predisposed reader does not find anything newsworthy or interesting in those paragraphs either. So, for whom was this stitched together? For the mathematical novice? She finds some basic explanations which hardly ever relate to the specifics of the problem and should be found better and more profoundly explained in any basic math book for the unitiated. For the mathematical beginner? She knows all the basic material and does not really learn much about the more complicated problems as they are not well explained. For the expert? She suffers from the previous problem for topics outside her area of expertise, and will not learn anything new on the special sections. - In short, this book disappointed me and I cannot recommend it. Why was it published in the first place? To make a quick buck on the tidal wave of mathematical literature and to promote other books by the author. The first may be, the latter I doubt. Not for me.