Pythagoras' Revenge
A Mathematical Mystery

by Arturo Sangalli

A certain ambiguity

A mathematical mystery.

Pythagoras - a mystic, a philosopher, a brilliant mathematician, a secretive religious leader - who lived 2500 years ago, left no written work and still his name is remembered today as it is sure to be remembered yet for many generations to come. Who did not hear of the Pythagorean theorem, a theorem that fascinated young children, mature mathematicians and grown-ups from all walks of life, the US presidents included? A theorem that gathered more proofs that any other known to the mankind. Such a man left no written works, or so we learn from history books. But what if? What if a man like that were to write a book? What mystery, what message to the future generations would it contain? Just try to don Pythagoras' hat and put on his shoes, i.e., sandals. This probably what the author Arturo Sangalli did when devising a plot that spans 2500 years of history. I had no chance to follow my own advice as it occurred to me only after I finished reading the book. I can only attest that the author's fantasy and imagination never led him astray.

A math Ph.D. and a freelance science author, Sangalli weaves a story in which mathematics plays an integral part. The plot is clever and consistently riveting - I could not predict a single turn of events from one chapter to the next. Nonetheless, the chain of events is imminently plausible, except perhaps for the part where a young professor of mathematics appears unaware of Sam Loyd's 15. To his credit, he finds an elegant solution to the puzzle.

Mathematics is very accessible and in good taste, from the famous Pythagorean theorem and the incommensurability of the square root of 2 of 2500 years standing through the halting problem, the question of randomness and computer security that came to the forefront of mathematical research in the second half of the twentieth century. One need not be a mathematician to understand and appreciate the mathematical pieces. Along the way, the reader learns a little about Babylonian and ancient Chinese and Indian mathematics and about the role Arab scholars played in preserving the works of Greek mathematicians. The story of Pythagoras and his sect serves as a background and the frame for the whole novel. The author's prose is excellent and the book as a pleasure to read.

The book is intended for a broad audience, especially for those who usually shun mathematics but enjoy a good mystery. I heartily congratulate both the author and the Princeton University Press for producing a high quality book that intertwines mathematical ideas into a compelling work of fiction.

(On a separate page the author, Arturo Sangalli, reflects on his attempt to educate (mathematically) through fiction.)

Pythagoras' Revenge - A Mathematical Mystery, A. Sangalli, Princeton University Press, 2009

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