The foundational work of Sophie Germain (1778-1831) on Fermat's Last Theorem, a problem unsolved in mathematics into the late 20th century, stood unmatched for over one hundred years. Though published by a mentor of hers, Adrien-Marie Legendre, it is still referred to in textbooks as Germain's Theorem.

Germain worked alone, which was to her credit, yet contributed in a fundamental way to her limited development as a theorist. Her famed attempt to provide the mystery of Chladni figures with a pure mathematical model was made with no competition or collaboration. The three contests held by the Paris Academie Royale des Sciences from 1811 to 1816, regarding acoustics and elasticity of vibrating plates, never had more than one entry--hers. Each time she offered a new breakthrough: a fundamental hypothesis, an experimentally disprovable claim, and a treatment of curved and planar surfaces. However, even her final prizewinning paper was not published until...