From 1913 to 1921 he studied at the Gheorghe Lazăr High School in Bucharest, after which he attended University of Cluj, graduating in 1924.

[1] He obtained his Ph.D. in mathematics in 1929, with thesis Sur les fonctions polygènes d'une variable complexe written under the direction of Émile Picard[1][2] and defended before a jury that also included Édouard Goursat and Gaston Julia.

[3] After returning to Romania, he was appointed assistant the University of Cluj in 1930; he was promoted to lecturer in 1934 and named professor in 1942.

In his best-known work,[6] he established in 1961 the following foundational result regarding the writhe of a knot: take a ribbon in three-dimensional space, let

[12] The topological interpretation of helicity in terms of the Gauss linking number and its limiting form has been called the "Călugăreanu invariant" by Keith Moffatt and Renzo L.