Dumas then went to Berlin for some months, where he attended lectures by Georg Frobenius, Hermann Schwarz and Kurt Hensel. He returned to Paris, and in 1904 he was awarded a doctorate for his thesis Sur les fonctions à caractère algébrique dans le voisinage d'un point donné Ⓣ . Two years later he habilitated at the Polytechnic in Zürich, with the paper Sur quelques cas d'irréductibilité des polynômes à coefficients rationnels Ⓣ. In both of these papers he used new notions introduced by Hensel . Dumas taught higher mathematics as a Privatdozent at the Polytechnic; he was promoted to Titularprofessor in 1913.
In the same year he was appointed to a professorship in mathematics at the Engineering School of the University of Lausanne. He became an ordinary professor in 1916. Dumas stayed at his alma mater until he retired in 1942, teaching mainly differential and integral calculus to future engineers and mathematicians. Among his students was Georges de Rham, who became Dumas's assistant in the mid-1920s. Dumas's own research interests would be classed 'as classical algebraic geometry (over the complex field)'  today. He was also very interested in Poincaré's work. His mathematical papers cover various topics in algebra, analysis and geometry, and include Note relative aux abaques à alignement Ⓣ (1906), Sur les singularités des surfaces Ⓣ (1912), and his lectures Notes de calcul différentiel et integral Ⓣ (1925). In addition, Dumas wrote a couple of papers on technical education in the French-speaking part of Switzerland.
Dumas joined the organising committee of the first International Congress of Mathematicians at the preliminary meeting in July 1896, as the French-speaking secretary. He is mentioned by name only a couple of times, when specific jobs were given to him: He wrote the letter to Greenhill, inviting him again to attend the congress , and finalised the congress programme with Geiser, Franel and Hirsch on 2 August. Rudio and Franel, the two general secretaries at the congress, also had their personal secretaries, Hirsch and Dumas. It can be assumed that Dumas, as the native French speaker, was Franel's secretary. Dumas did not give a talk at the congress, but he was among the signatories of the invitations. Dumas attended more ICMs than most of his colleagues on the organising ccommittee. Representing the University of Lausanne, he attended the 1920 ICM in Strasbourg, the 1928 ICM in Bologna, and the 1932 ICM in Zürich. He gave a talk in Bologna, entitled Sur les singularités des surfaces Ⓣ, in section II-B (geometry). Dumas also served on the organising committee of the 1932 congress in Zürich.
Dumas became a member of the Swiss Mathematical Society (Schweizerische Mathematische Gesellschaft: SMG) when it was founded in 1910. He gave a number of talks at the society's annual meetings and served as secretary-treasurer from 1920-1922. From 1922-1924 and again from 1930-1931 he was president of the SMG. In 1944 he was made an honorary member of the society. In 1923 he co-founded the so-called Colloque mathématique des Universités romandes Ⓣ, later renamed as Cercle mathématique de Lausanne Ⓣ. This was a 'very rigorous group'  that organised lectures and meetings until the 1980s. Furthermore, Dumas was a member of the Euler-Kommission from 1919- 1943. He was awarded an honorary doctorate from the University of Lausanne when he retired in 1942.
Apart from mathematics and education, Dumas also had a strong interest in literature and philosophy.
Article by: Stefanie Eminger, University of St Andrews