[5][6] His PhD thesis, entitled Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel.

Right after World War II he put many efforts to improve the cooperation between French and German mathematicians and restore the flow of exchanges of ideas and students.

After 1945 he started his own seminar in Paris, which deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation.

The number of his official students was small, but includes Joséphine Guidy Wandja (the first African woman to gain a PhD in mathematics),[42][43] Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.

Motivated by the solution to the Cousin problems, he worked on sheaf cohomology and coherent sheaves and proved two powerful results, Cartan's theorems A and B.

Among his major contributions, he worked on cohomology operations and homology of the Eilenberg–MacLane spaces,[44] he introduced the notion of Steenrod algebra,[45] and, together with Jean-Pierre Serre, developed the method of "killing homotopy groups".

[46][47] His 1956 book with Samuel Eilenberg on homological algebra[48] was an important text, treating the subject with a moderate level of abstraction with the help of category theory.