This article is a case study that describes the natural and human history of the gaze heuristic. The gaze heuristic is an interception heuristic that utilizes a single input (deviation from a constant angle of approach) repeatedly as a task is performed. Its architecture, advantages, and limitations are described in detail. A history of the gaze heuristic is then presented. In natural history, the gaze heuristic is the only known technique used by predators to intercept prey. In human history the gaze heuristic was discovered accidentally by Royal Air Force (RAF) fighter command just prior to World War II. As it was never discovered by the Luftwaffe, the technique conferred a decisive advantage upon the RAF throughout the war. After the end of the war in America, German technology was combined with the British heuristic to create the Sidewinder AIM9 missile, the most successful autonomous weapon ever built. There are no plans to withdraw it or replace its guiding gaze heuristic. The case study demonstrates that the gaze heuristic is a specific heuristic type that takes a single best input at the best time (take the best2). Its use is an adaptively rational response to specific, rapidly evolving decision environments that has allowed those animals/humans/machines who use it to survive, prosper, and multiply relative to those who do not.