One of the greatest accomplishments in the history of cryptography occurred in 1940 when a Swedish mathematician broke the German code used for strategic military communications. This story has all the elements of a classic thriller: a desperate wartime situation; a moody and secretive mathematical genius with a talent for cryptography; and, a stunning mathematical feat, mysterious to this day. Arne Beurling, the man who inherited Einstein's office at Princeton's Institute for Advanced Study, was the figure who played this role at a crucial moment in world history. Though the cracking of the code from the Geheimschreiber (G-Schreiber) device is every bit as impressive as the breaking of the Enigma code by the Poles and English, this secret has been kept for over 50 years!Through the eyes of a former head of Sweden's signal intelligence organization, Bengt Beckman, the reader will learn about the events leading up to the breakthrough and make the acquaintance of not only a remarkable mathematician, but also a remarkable human being. Arne Beurling was a leading international figure who achieved beautiful results in mathematical analysis. By the arrival of World War II, he was one of the most powerful and original mathematicians in the world and widely considered a genius. During his military service, he demonstrated a flair for code and was well known within Swedish cryptology circles. The natural choice of the Swedish intelligence service was to place Beurling at the center of the group charged with breaking the G-Schreiber code. His single-handed effort 'broke the unbreakable'. Using only teleprinter tapes and cipher text, he deciphered the code that the Germans believed impossible to crack - in two weeks! The feat, in a word, was astonishing.Many wonder how he did it. But Beurling took his secret to the grave, retorting when asked, 'A magician does not reveal his secrets'. The author, Bengt Beckman, for many years was the head of the cryptanalysis department of the Swedish signal intelligence agency. In writing this book, he made extensive use of its archives. He also interviewed many people who participated in the Swedish wartime intelligence effort. He describes in detail Beurling's attack on the G-Schreiber system as well as attacks on several other wartime crypto systems, noting high points from the history of Swedish cryptology. The book will appeal to a broad audience of readers, from historians and biography buffs to mathematicians to anyone with a passing interest in cryptology and cryptanalysis. This English edition has been translated by Kjell-Ove Widman, Director of Sweden's Mittag-Leffler Institute. Also on cryptography and available from the AMS is Cryptography: An Introduction.