The Development of Radar and Chaos Theory

Mathematician Mary Cartwright and her colleague JE Littlewood made an important discovery while trying to work out problems engineers were having in getting radar to work:

"The whole development of radar in World War Two depended on high power amplifiers, and it was a matter of life and death to have amplifiers that did what they were supposed to do. The soldiers were plagued with amplifiers that misbehaved, and blamed the manufacturers for their erratic behaviour. Cartwright and Littlewood discovered that the manufacturers were not to blame. The equation itself was to blame."

In other words, odd things happened when some sorts of values were fed into the standard equation they were using to predict the amplifiers' performance. Cartwright and Littlewood were able to show that as the wavelength of radio waves shortens, their performance ceases to be regular and periodic, and becomes unstable and unpredictable. This work helped explain some perplexing phenomena engineers were encountering.
Cartwright herself was always somewhat diffident when asked to assess the lasting importance of her war work. She and Littlewood had provided a scientific explanation for some peculiar features of the behaviour of radio waves, but they did not in the end supply the answer in time. They simply succeeded in directing the engineers' attention away from faulty equipment towards practical ways of compensating for the electrical "noise" - or erratic fluctuations - being produced.
So while Cartwright and Littlewood were producing significant results on the stability of solutions to the equation describing the oscillation of radio waves, the engineers working on radar systems decided they could not wait for precise mathematical results. Instead, once it had been identified, they worked around the problem, by keeping the equipment within predictable ranges.

The whole story is pretty interesting.