Mary Cartwright Stumbled Onto Chaos Theory While Helping Britain Build Better Radar

In 1938, the British Department of Scientific and Industrial Research wrote to the London Mathematical Society with an unusual request. The military's new radar systems were producing erratic outputs that the engineers couldn't explain — not at full strength, not consistently, just enough to be a problem. The Society was asked whether any pure mathematicians knew anything about van der Pol-type nonlinear differential equations, which seemed to model the behavior. Cambridge's Mary Cartwright responded: she had been working on exactly that problem.

Through the war years, Cartwright collaborated with the Cambridge analyst John Edensor Littlewood on what they kept calling "a small monster." The forced van der Pol equation governs an oscillator with a kick of external energy. At low forcing they found neat periodic behavior. At higher forcing they found, in Cartwright's own working journals, an explosion of solution structure — long-period orbits, sensitive dependence on initial conditions, infinitely many distinct periodic solutions interleaved in any small region of phase space. Littlewood later wrote: "Suddenly the whole vista of the dramatic fine structure of solutions stared us in the face."

The result, published as a series of dense papers in the late 1940s, was effectively the first detailed demonstration of what would eventually be named chaotic dynamics — twenty years before Edward Lorenz, working independently on weather prediction, found the same kind of behavior in his own equations and brought "the butterfly effect" into popular vocabulary. Cartwright was elected Fellow of the Royal Society in 1947 — the first woman ever for mathematics — became Mistress of Girton College in 1948, and was made a Dame in 1969. She lived until 1998. Modern dynamical-systems courses still cite her work, and the term Cartwright-Littlewood theorem persists.