Ernest Vessiot's father was a school teacher, then later he was appointed inspector general of primary schools. Vessiot therefore came from an academic background. He attended the lycée at Marseilles, then sat the entrance examination for the École Normale Supérieure in Paris.
In the entrance examination Vessiot was placed second to Hadamard and thereafter he studied in the same class as Hadamard. After graduating from the École Normale Supérieure, Vessiot accepted a teaching post at Lyon in 1887.
In 1892 he submitted his doctoral dissertation on groups of linear transformations, in particular studying the action of these groups on the independent solutions of a differential equation.
After the award of his doctorate, Vessiot taught in a number of places, Lille, Toulouse, Lyon and finally Paris in 1910. He was appointed to the prestigious post of Director of the École Normale Supérieure in Paris and he continued to hold this post until he retired in 1935. In his role of director he supervised the construction of new physical laboratories at the École Normale Supérieure.
Vessiot applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.
Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Académie des Sciences in 1943.
Article by: J J O'Connor and E F Robertson