The art of math in war: cryptology throughout World War 2

From the American Revolution to the Cold War, American history has often been taught by looking from one battle to the next. These landmarks in our history are incredibly important and have affected the citizens of this country socially, economically, and politically for years in the past and likely for years to come. Now, alternatively, the mathematics that has been highlighted in the American education system is just the basics—enough to build upon for the students who would like to go further, but not so much as to overwhelm those who will never use math past algebra. Due to this lack of depth in our mathematics education, these two incredibly important aspects of our history—math and war—have rarely been connected in any meaningful way for most people learning one or both of these subjects. This overlap, however, is an incredible part of the history of the United States, especially as it relates to World War 2 within the realm of cryptology. From the Enigma machine and its decoding to the information surrounding D-Day, mathematics played a vital role in World War 2 and through these incredible mathematicians and the work that they did, our country has been able to continue progressing in these fields and others to become the advanced nation we are today.