At about this time, in 1808, the French Academy of Sciences announced a contest to explain the "underlying mathematical law" of a German physicist's study on the vibration of elastic surfaces. Sophie was fascinated and set out to explain the law underlying Chladni's study. The Academy set a two-year deadline, and in 1811 Sophie submitted the only entry in the contest. Her lack of formal education was evident in the anonymous paper she submitted, and thus she was not awarded the prize. Lagrange corrected her errors and two years later she again entered the contest which had been extended. She received honorable mention this time. It was in 1816, when she entered for the third time and won with her paper Memoir on the Vibrations of Elastic Plates. After winning the contest, Sophie continued her work on the theory of elasticity publishing several more memoirs. Her work in the theory of elasticity would prove to be very important to the field.