**Ernest Vessiot** was a French mathematician who worked on the integrability of ordinary differential equations.

- The historian Camille Jullian (1859-1933) was a pupil in Alexandre Vessiot's class and wrote about his outstanding qualities as both a teacher and as a person.
- These qualities meant that Ernest was brought up in an academic environment in which there was a kind and understanding encouragement to hard work.
- Ernest's secondary education was at the lycée in Marseilles where his performance was outstanding and he obtained his baccalaureate in 1883.
- In the entrance examination Vessiot was placed second to Jacques Hadamard and thereafter he studied in the same class as Hadamard.
- Vessiot also took Paul Appell's course on rational mechanics.
- Vessiot was awarded his bachelor's degree in mathematics and physics in 1886.
- Vessiot accepted a teaching post at the Lycée Ampère in Lyon in 1887 and began teaching there after his return from Germany.
- This school, originally a Jesuit establishment, had been founded in 1519 and given several different names before being named the Lycée de Lyon in 1848 and then the Lycée Ampère in the year that Vessiot began teaching there.
- However, school teaching was only part of Vessiot's work for at the same time he was undertaking research for his doctorate advised by Émile Picard.
- After the award of his doctorate, Vessiot taught in a number of universities.
- Vessiot published a second edition in 1919.
- The first edition ran to 326 pages but with the additions that Vessiot made to the second edition it was 376 pages.
- Vessiot taught for thirteen years in the Faculty of Science Lyon before gaining an appointment in Paris in 1910.
- As we mentioned above, Vessiot applied continuous groups to the study of differential equations.
- One must never forget that Vessiot was an unusual Frenchman at that time, perfectly aware of the work of Lie who, in turn, at the end of his life, considered Vessiot to be his heir.
- As a consequence, Vessiot knew the theory of Lie groups and, when he wrote his thesis in 1892 on what is now called the Picard-Vessiot theory of linear ODEs, he knew about Lie's latest research on pseudogroups.
- Hence, in Vessiot's mind, the Picard-Vessiot theory of linear ODEs could be considered only as an intermediate step towards the achievement of the classical Galois theory, namely the Galois theory for systems of PDEs ...
- However, Painlevé's hopes for Vessiot's future happiness did not materialise.
- However, we have moved ahead and we should return to saying something of Vessiot's career after his appointment to the Faculty of Science in Paris in 1910.
- However, Vessiot was also an outstanding lecturer, renowned for the clarity and rigour of his lectures.
- Vessiot spent the last 25 years of his career in Paris, concentrating on his role as a lecturer and as an examiner.

Born 8 March 1865, Marseilles, France. Died 17 October 1952, La Bauche, Savoie, France.

View full biography at MacTutor

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive