
For readers passionate about mathematical puzzles, this book will be both a feast and a challenge. Joining the author on a tour de force of the history of mathematics, from the ancient to the modern and from the simple problems to the still-unsolved challenges, the reader is entertained with a fast-paced sequence of anecdotes as well as historical facts.
There are more than 40 exercises in the book that have solutions at the end, and countless open mathematical challenges that have yet to be solved by the best minds―but might trigger a flash of insight in a reader who approaches the problem with a fresh mind and solves it, not realizing that it might have remained unsolved for centuries. The range of topics spans from elementary number theory and geometry to formal logic and computer programming. A brief list of 30 references includes mainly older classical math books and a few online resources suitable for a general audience rather than a specialist.
The writing is fast paced, easy to follow and funny at times, as the author digs deeply into topics that can challenge even some experienced mathematicians. As such, the book makes for an enjoyable read, requiring the reader to occasionally put it down and take to pen and paper.
Although the book does not assume a given level of mathematical knowledge, the author ramps up very quickly from the basics to rather advanced topics, which change from chapter to chapter. Given the range of difficulty of the topics, it might not make much sense to use the book as a textbook, other than maybe for a class of very bright students who can take off from the simpler topics into the more arcane ones.
The only question left unanswered for this reviewer is how this book relates to optics. Maybe to paraphrase a saying that "all biology comes down to chemistry, all chemistry comes down to physics, and all physics comes down to math," it is because all optics comes down to math as well. And this book reflects the best that math has to offer, a range of history, anecdotes, and puzzles that amuse, challenge and stimulate the reader.
Review by Bogdan Hoanca, University of Alaska Anchorage, USA.
The opinions expressed in the book review section are those of the reviewer and do not necessarily reflect those of OPN or its publisher, Optica.