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Rating: 
Summary: An Approachable Guide To CMI Millenium Problems
Review: If you solve any of the seven problems proposed by the Clay Mathematics Institute, you win one million dollars and a piece of history with your name on it. Let's face it; you and I aren't going to solve these problems. But this book makes a lot of what's relevant in contemporary mathematics and physics a public information and knowledge, and that's an honorable feat. Each of the seven problems are incredibly difficult to understand on their own. Keith Devlin does an excellent job of providing a historical and mathematical background for each of these problems for the laymen, and in process, reveals how the solutions to these problems would bring an exponential leap for the human knowledge as a whole. (Devlin does an exceptional job chronicling the history of math and physics that led to Yang-Mills Theory and Mass Gap, as well as Poincare Conjecture and P vs NP) For more detailed exposition of these problems, you are better off reading the official CMI book, or checking the official website of CMI, [url]. But if you are interested in the importance of these problems and the implications the solutions to these problems can have on our lives, this book will more than suffice.
Rating:
Summary: It's Not An "Idiot's Guide to the Millenium Problems"
Review: Let's be frank: most people have a better chance of winning $1M at the state lottery than by proving any of these "millennium problems". Keith Devlin does a good job of explaining why. A little reverse psychology here and there ("...if you find the going too hard, then the wise strategy might be to give up.") just makes us want to push on toward the more difficult problems. The going isn't too hard thanks to Devlin's expository ability, but alas, I think this will be true only for aficionados of mathematics and physics. In his columns for the Mathematical Association of America, Keith has always had in mind a varied audience of readers. But how can he hope to communicate to the non-mathematician when so much meaning resides in the equations that appear throughout the book? Still, his pedagogy prevents this from becoming "The Idiot's Guide to the Millennium Problems". (I suppose it'll appear real soon.) Devlin hints at a disturbing idea. Will cutting edge problems become so abstruse some day that it will take the best minds all the fruitful years of their lives just to arrive at a position of comprehension? What then, mathematical AI?
There are some silly mistakes, perhaps caused by a looming deadline. One involves a mix-up between the relativistic precession of Mercury's orbit and the relativistic bending of light rays. A logical error appears in a footnote on pg.54, where the word "a" should replace "no". Another one appears in the caption of Fig. 5.5, where "Example" should replace "Proof". Would it be too much to ask that copy editors who are assigned technical books have a dim awareness of mathematical argumentation?
Rating: 
Summary: Pedantic
Review: This book is more pedantic than I thought it would be. Being a smallish book and a smaller audience, it is understandable that the mathematical details are trimmed down (almost excised, you might say). Still, there is too much history and not enough details. Too often the author says that it may be above the reader's level. Overall, I was disappointed, but it was not a waste.
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