Chladni plate vibration resisted mathematical solution even for Germain and Lagrange

Evidence

Napoleon’s contest came to a close with a single entry from Sophie Germain (1776–1831), a talented mathematician and number theorist, after whom the Germain prime numbers are named (figure 15.8). However, the vibration of Chladni plates was a problem for analysis, Laplace’s field. Germain was out of her element. She did not win the contest. The judges, including Laplace and the equally celebrated Joseph Louis Lagrange (1736–1813), correctly pointed out that she had not solved the problem. They noted that the differential equation she arrived at did not have certain properties it needed, even though they did not know what the correct equation was. — Eric J. Heller, Why You Hear What You Hear- An…, 1391