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Alan Turing: The Enigma

Andrew Hodges
Princeton University Press
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The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
Katherine Safford-Ramus
, on

This book is an incredibly detailed and meticulously researched biography of Alan Turing. Reading it is a melancholy experience, since you know from the outset that the ending is a tragic one and that knowledge overshadows you throughout. While the author divides the text into two parts, it actually reads like a play in four acts.

Cover of the Centenary EditionThe first act documents Turing’s childhood and school years. A considerable literature exists that describes the public school experience in Britain in the twentieth century; Turing’s time spent therein seems typical. His failure to comprehend and adhere to expected social norms became visible but did not seem to cause insurmountable difficulties. One comes away from this part of the book with a sense that Turing was, in modern terms, the kid who exists on the fringe of the group, tolerated but never completely accepted. At times I found this section of the book slow going because of the level of detail. The quantity of available documents is, to a modern reader, astounding. I pondered the task of future biographers, who will lack print sources because so much communication today is oral or electronic.

Act Two is the war years. Again, much has been written about the contributions of the team at Bletchley Park to the success of the Allied victory in World War II. Hodges shines the spotlight on Turing and the abstract mathematics that he brought to play in the task of deciphering the mechanics of the German encoding machine. For me this the most riveting section of the book, caught up in the tension of the period where the happy ending was not at all apparent to the team. Instructors in modern algebra courses would benefit from reading about Turing’s application of group theory to cryptography. It offers an opportunity to emphasize the intriguing links between abstraction and applications that surface repeatedly in the field of mathematics.

What I term “Act Three” begins during the war but continues after the end of the conflict when the practical role of Turing’s universal machine emerges. This part of the book contains a wealth of information about the infancy of computer science and its strong connection to mathematics. I worked in systems analysis during the adolescence of computer science in the 1970s, when many of the project team members had been mathematics majors in college. With each generation of coding languages, that connection becomes more tenuous, somewhat like the experience of immigrant families to their homeland. Hodges brings the reader back to those early days, to the competition between countries and system designers and, of course, to the seminal work of Alan Turing.

The final act is a tragedy. Turing is adrift. The intensity of the war effort is gone and, due to secrecy provisions, he cannot disclose the fact that he was a pivotal player in the decryption work. His design for a computer has strong competitors who appear to be pulling ahead in the race. It is his personal life, however, that is his downfall. Turing’s failure to comprehend and defer to the powerful social and political norms of Britain in the 1950s resulted in his arrest and trial, with both professional and personal consequences. Turing died at the age of forty-one, was cremated, and his ashes scattered. Hodges closes the book with the statement “There is no memorial.” Thanks to Andrew Hodges the last sentence is false. This book is Turing’s memorial, and one that does justice to the subject.

Katherine Safford-Ramus is a Professor of Mathematics at Saint Peter’s University, Jersey City, New Jersey. Her research focuses on adults learning mathematics. Her second love is history, particularly the home front during World War II, and she peppers her mathematics lectures with tidbits from math history.

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