[1] After the war, he completed his studies and in 1948 he defended his PhD thesis, entitled Propriétés topologiques des variétés feuilletées [Topological properties of foliated manifolds] and supervised by Charles Ehresmann.

[1][3] There, in 1965 he created with Jean Leray and Pierre Lelong the series of meeting Rencontres entre Mathématiciens et Physiciens Théoriciens.

[1][3] Reeb was the founder of the topological theory of foliations, a geometric structure on smooth manifolds which partition them in smaller pieces.

[6] One of its first significant result, Reeb stability theorem, describes the local structure foliations around a compact leaf with finite holonomy group.

Towards the end of his career, Reeb become a supporter of the theory of non-standard analysis by Abraham Robinson, coining the slogan "The naïve integers don't fill up