Adrien-Marie Legendre is famous for laying the groundwork of
many different mathematical problems in such disparate fields as
statistics, number theory, and differential equations. He invented
the statistical tool known as the least squares method and almost
single-handedly solved elliptic functions and elliptic integrals.
Additionally, he solved what is now known as the Legendre equation;
an equation that arises in electrostatic theory and quantum
mechanics, among other places, and whose solutions are called the
Legendre polynomials.