Preface

Summary

In his autobiography, A Mathematician's Apology, the number theorist and pacifist G. H. Hardy wrote

… both Gauss and lesser mathematicians may be justified in rejoicing that there is one science [number theory] at any rate … whose very remoteness from ordinary human activities should keep it gentle and clean.

Hardy's book was published in 1940, toward the end of his career. If he had postponed his judgment for another 30 years, he might have come to a different conclusion, for number theory became the basis for an important technology long associated with war: cryptography, the use of secret codes.

Cryptography has been in use for at least several thousand years. It is listed in the Kama Sutra as one of the 64 arts to be mastered by women. One well-known elementary cryptosystem is attributed to Julius Caesar. Numerous anecdotes attest to the importance of cryptography in war and diplomacy over the years – and to that of cryptanalysis, the cracking of codes. For example, Britain's interception and deciphering of the Zimmerman telegram, a message from Germany's foreign minister to the government of Mexico (via the ambassador), helped speed the United States' entry into World War I, for the message promised Texas, New Mexico, and Arizona to Mexico in return for its help against the United States.