The Call Of The Primes: Surprising Patterns, Peculiar Puzzles, And Other Marvels Of Mathematics, by Owen O’Shea

This book happens to sit in an unhappy place as far as books about mathematics go. On the one hand, this book is written with an obvious love of mathematics and a desire to share that love with others. The author delights in patterns and puzzles, as he says. And if that was all there is, this would be an easy book to appreciate and to recommend to others. But, as might be expected, that is not all there is to it. Despite the author’s love of puzzles, the book is not only written in love for mathematical puzzles but also seeks to debunk the thinking of others, specifically those who have found in the golden ratio a great deal of insights, which makes the author’s writing about phi a lot more lifeless and less enjoyable than his other works, because instead of finding patterns he seeks to debunk the patterns that others have found in them. This is bad enough, but given the author’s desire to debunk what the author thinks to have been made up, the author runs into problems of hypocrisy given that he makes up a correspondent with a suitably romantic Chinese background who gets the last word in every chapter as a means of trying to one-up the author and present in epistolatory form what was missed in a more developed fashion in the chapters. It would have been better to integrate material more organically than to have a fake Chinese amateur math expert present his comments and additions to the work as if it was someone else other than the author trying to squeeze more material in.

This hints at a broader aspect of this book that leaves it in a sort of uncanny valley as far as I am concerned as a reader. This is a book that appears to be written to lay readers of mathematics, those outside of formal mathematics study. The author himself comes from a recreational mathematics background and works for Ireland’s department of defense in an unspecified position (perhaps cryptography or something related to signals intelligence, one may hope). Yet this book is not written for the reader who has a basic knowledge in mathematics, but someone who is pretty proficient with regards to numbers, just an amateur and not a professional. Indeed, the author’s ideal audience, paradoxically enough, is the precise same audience as the imaginary character he writes about, someone who has studied in mathematics or engineering or a related field where knowledge and skill with numbers is important, but not someone who is a professional in the field, as the author nowhere wishes to uphold to professional norms of conduct (which would preclude the use of imaginary interlocutors as the author uses in, or other forms of subterfuge in one’s presentation). It is unclear just how many people would appreciate this book, having read it, as they would likely find the book above their level of mathematics while also below their level of character and morals, which is a dangerous place for a book to find itself.

In terms of its contents, this book is about 300 pages long and it is divided into sixteen chapters. The book begins with an acknowledgement and introduction. After that the author discusses the Lo Shu and other magic squares–which perhaps puts the book in a bad spot to begin by hinting at areas of divination (1). This is followed by the author’s discussion of prime numbers (2), as well as Pythagorean triples (3). This is followed by a discussion of deceptive puzzles in probability theory like the Monte Hall problem (4). Two chapters on sequences follow, namely the Fibonacci sequence (5) and then the lesser-known Lucas sequence (6). A dissatisfying chapter on Phi (7) comes before two chapters that explore notable square roots, namely i (8) and the square root of 2 (9), both of which had serious effects in the history of mathematics. This is followed by chapters on the square (10) and triangular (11) numbers. Finally, after all this while, the author gets around to talking in detail about pi (12) and e (13), two of the best known transcendental numbers. By this point the book is almost over, though, and the author then continues on to write about Pascal’s triangle (14), before ending the main materials of the book with chapters on some strange and remarkable coincidences to the author (15) as well as some beautiful mathematics equations (16). The book then ends with notes, a select bibliography, and an index.