Gaston Darboux

Finishing first in the nationwide entrance examinations for both École Polytechnique and École Normale Supérieure in 1861, Darboux chose the ENS. Appointed professor of geometry at the Sorbonne in 1880, he trained generations of mathematical giants including Élie Cartan.

His monumental Leçons sur la théorie générale des surfaces (1887–1896) synthesized differential equations, kinematics, and geometric surfaces, creating modern differential geometry and the moving frame method. As Permanent Secretary of the Académie des Sciences from 1900 to 1917, he directed French scientific mobilization.