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Mary Lucy Cartwright: The Inspired Mathematician Behind Chaos Theory

4 min read
08_19_2021
Mary Lucy Cartwright (1900–1998) was a British mathematician who contributed to important advances in function theory and differential equations. Alongside John Littlewood, she was one of the first mathematicians to study what would later be known as Chaos Theory.

Cartwright studied mathematics at St Hugh’s College, Oxford, graduating in 1923 with a first-class degree — the first woman to do so. She did a stint as a teacher before returning to Oxford in 1928 for a Ph.D. She went on to publish a seminal article, “From Nonlinear Oscillations to Topological Dynamics,” in the Journal of the London Mathematical Society in 1931. She also worked on cluster sets in the theory of functions of one complex variable, the results of which would later be known as Cartwright’s Theorem.

At the outbreak of World War II, the British Department of Scientific and Industrial Research’s Radio Research Board asked Cartwright to help solve problems with its new top-secret radar technology. Drawing on their expertise in nonlinear differential equations, she and long-term colleague John Littlewood studied solutions of the Van der Pol equation, including a factor known as “sinusoidal forcing” and its role in the erratic behavior of high-frequency radio waves.

Exploring the Butterfly Effect

The duo published their results when the war ended, but they went relatively unnoticed. It was only in the 1960s that mathematicians, including Edward Lorenz, came across their findings and built them into the foundations of chaos theory. Heavily explored during the 1980s, the theory is based on the premise that complex systems — like weather patterns and water flows — sometimes reside in chaos, generating energy but without any predictability or direction. Today, its applications range from weather prediction to market research, crowd management and heartbeat inequalities.

“It has been said that something as small as the flutter of a butterfly’s wing can cause a typhoon halfway around the world.”

Their findings also influenced catastrophe theory – studying and classifying how the appearance or disappearance of a fixed point causes a system to abruptly change its state.

Cartwright became Girton’s Head of School in 1949 and was promoted to Reader in the Theory of Functions at Girton in 1959, although she continued to write papers on mathematical research subjects into the late 1980s.

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