Upon the receipt of the book *Alan Turing: The Enigma*, an amusing anecdote jumped immediately to mind. In high school, one of the more formal English teachers advised us not to go on a book selection hunt with a ruler! He was**,** of course, referring to choosing the shortest book, i.e., one with the least number of pages. This rather large volume on Alan Turing, the cryptanalysis and mathematical genius who did much to define the modern computer, comprises 664 pages, and with postscript, notes and indices runs to 736! As such, it is certainly the most complete work done to date on this complex man, a mixture of equal parts genius, runner and an oblivious observer of the norms of early twentieth century Britain.

The book is divided into eight chapters, each enclosing one to six years of Turing’s life.

The first four are placed under the heading “The Logical” and the last four under “The Physical.”

The first chapter sets the tone by telling the reader almost more than he would wish to know about Turing’s ancestors, stretching back several hundred years. The record becomes more detailed when we get to his parents in the latter part of the 19th century. A detailed and repetitive theme that occurs during this period is the snobbery and stifling conformity of British, Irish and French culture in the post-Victorian era. Another theme shaping the society around them was the vast uncertainty that existed as the niceties of religion and polite society were gradually replaced with the cold calculation of scientific progress. But even this held elements of uncertainty. Turing’s father was a civil servant working with the railroads in India and his mother the product of Anglo-Irish landed gentry. The family bounced between England and India as the father’s work demanded, but many times left the children with friends in England to spare Alan the harsh Indian weather. At this point, two traits emerged which were to distinguish Alan Turing’s life throughout adulthood. His genius and extremely creative problem solving abilities and his ability to ignore the harsher realities of the world around him.

It was in the very early years at public school that Alan Turing displayed his love of mathematics and science but mostly disinterest in everything else. He was threatened with possible expulsion on more than one occasion but managed to impress his teachers after taking a prize for doing well in examinations. His headmaster commented that “He owes his place and prize entirely to mathematics and science, but he shewed improvement on the literary side. If he goes on as he is doing now, he should do very well.”

Such was the early life of an enigmatic young man. Love chemistry, astronomy and mathematics, and fake the rest!

In the third chapter that takes the reader to September of 1939, it was like reuniting with an old friend. One of the most pleasing chapters within the book *A Beautiful Mind* was about the years that John Nash spent at Princeton as a graduate student. The stories of his professors and interactions with fellow students, as well as the advanced mathematics that he dealt with (to say nothing about the rivalries/jealousies) were exciting, as well as enlightening. The same can be said for Alan Turing’s time at Princeton. He arrived to work on his Ph.D. under Alonzo Church and, in the interim, interacted with a constellation of mathematical greats (J. v. Neumann, Weyl, Courant, Hardy, Einstein and Lefschetz). He also bemoaned the fact that Gödel, Kleene, Rosser and Bernays all had left the previous year. He received his doctorate in due course, but it was quite telling that he had also had courses in cryptanalysis, as this was then the mechanical implementation to abstract mathematics and logic. Enter the second world war…

With his extensive knowledge of mathematics and logic, plus a growing knowledge of cryptanalysis, he was a natural to be recruited to the British code breaking teams at Bletchley Park, where the government code and cryptanalysis school did much of its work. He not only mastered the logic behind the German enigma machines but also developed methods for physically (after mathematically) determining the cam settings on the wheels used in these machines. Towards the end of the war, he also helped develop a secure voice scrambler. He repeatedly used probability and statistics to optimize the code breaking algorithms that he, and others, developed, and he wrote two papers on the subjects.

Sadly, his post-war years were dominated by the uproar concerning his sexual orientation, which was considered deviant and unnatural behavior at the time. Although his death due to cyanide ingestion was labeled a suicide, alternate theories exist (accidental inhalation). In spite of a late pardon by the government, the world of computation still gives Turing the honor due his genius in numeric and electronic computation.

Though long and detailed, the book is a fascinating read and one of the most detailed, given the scarcity of original materials.

**Availability**

*Alan Turing: The Enigma*. by Andrew Hodges. Princeton University Press, Princeton, NJ. (1983; preface copyright 2014). $84.99 (HC), $9.83 (Pbk)

*John Wass is a statistician based in Chicago, IL. He may be reached at **[email protected]**.*