Saving Bombers in WWII: The Genius of Mathematician Abraham Wald

Abraham Wald’s Early Years

In the 1930s, Reich’s expansionist policies not only grew Germany’s territory but also intensified the persecution of Jews. Amidst this turmoil, a Hungarian-born mathematician named Abraham Wald stood out. He was a brilliant scholar, holding a Ph.D. in mathematics from the University of Vienna. However, as the Reich’s aggression escalated, Wald, a Jew, was forced to flee from his home in Romania. His academic prowess opened a door of hope when he was offered a position in the United States. This move not only saved him and his family from the horrors of persecution but also set the stage for his significant contributions to the Allied war effort during World War II.

Abraham Wald

Joining the War Effort

Upon arriving in America, Wald joined Columbia University’s statistical research group. This team of mathematicians and statisticians was pivotal in assisting the military with complex problems during World War II. They contributed to various military advancements, from developing accurate bomb sights to aiding in the creation of the atom bomb. Despite being considered an “enemy alien” due to his Eastern European origins, Wald dedicated his skills to defeating the Axis powers, driven by his personal experiences with the Reich’s tyranny.

B-17E U.S. Air Force

Identifying the Problem

The American Navy and Army Air Corps were losing bombers and crews at an unsustainable rate. To address this, they analyzed returning planes, documenting bullet holes to determine where additional armor might be beneficial. The goal was to balance the plane’s weight with necessary armor, ensuring operational effectiveness without compromising safety. The military sought Wald’s expertise to optimize armor distribution without affecting the aircraft’s performance.

The damaged portions of returning planes show locations where they can sustain damage and still return home; those hit in other places presumedly do not survive. (Image shows hypothetical data.) Photo: Martin Grandjean (vector), McGeddon (picture), Cameron Moll (concept)

The Twist of Logic

Wald identified a critical flaw in the military’s approach: survivorship bias. This bias focused on the aircraft that returned safely, neglecting those lost in combat. The military’s analysis was skewed, emphasizing the reinforcement of parts that were least vulnerable. Wald proposed that armor should be placed in areas with fewer bullet holes, as these were likely the spots that, when hit, led to fatal outcomes. His analysis included the likelihood of a plane being downed based on where it was hit, leading to a revolutionary approach in armor distribution.

The Impact of Wald’s Work

Wald’s recommendations were swiftly implemented, with immediate effects. Armor was strategically placed on the most vulnerable parts of the planes, notably the engines. This adjustment led to a significant decrease in casualties and aircraft losses, allowing the military to concentrate on other strategic aspects of the war. Wald’s contribution was not just a mathematical triumph but a lifesaving intervention that had a profound impact on the war’s dynamics.

Abraham Wald’s essays and findings continued to be influential long after the war. Tragically, Wald and his wife died in a plane crash in 1950. His story from a persecuted scholar to a key figure in the American war effort underscores the profound impact one individual can have on history.

Boeing B-17 Superfortress
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