Innovation Comes from Unexpected Places (or Neglected Ones)
In 1966 a Russian scientist named Pyotr Ufimtsev wrote a paper called "Method of Edge Waves in the Physical Theory of Diffraction," which described the mathematics required to develop aircraft that could evade radar. The paper was extremely technically dense, and employed a set of formulas originally developed a hundred years earlier by Scottish physicist James Clerk Maxwell to reach its conclusions. Even if you understood the impact of what Ufimtsev was saying, you had to read almost the entire 40 pages before getting to the zinger.
Nine years later the US Airforce Foreign Technology Division finally translated it from its original Russian, and it was picked up by a bright engineer in Lockheed's Skunkworks (the same group that went on to develop the SR-71 Blackbird, and which earlier had created the U2 spy plane). He happened to have just started working on the Skunkworks' first real stealthy aircraft, and so was primed for unorthodox thinking on how to reduce the radar "signature" of a plane.
So the theories of a Russian scientist were ignored by the Russians themselves, and later picked up by an American to build aircraft created to avoid Russian radar. The end result was that the Stealth F-117 fighter (66 feet long, 43 foot wingspan, and weighing over 50,000 lbs) appeared to be the size of a 1/8" ball bearing to radar.
As I've noted before, it's often a fine line between stupid and clever, and the Skunkworks group was consistently successful at separating the two. Not always at first, but they learned quickly with small teams and rapidly iterated prototypes. They had short deadlines, small budgets and large goals, which tended to force open-ness to unorthodox thinking. There was no sense of "not invented here" at the Skunkworks; they would take ideas from wherever and whomever in order to get done what they needed.
(For more on the history of the Skunkworks, Ben Rich's book tells it engagingly from the perspective of being Kelly Johnson's right hand man and successor as director of the Skunkworks.)