[2] He obtained his Ph.D. degree in mathematics in 1905, with thesis On the continuity of complex variable functions written under the direction of Henri Poincaré.

[3] After returning to Romania, Pompeiu was named Professor of Mechanics at the University of Iași.

Pompeiu's contributions were mainly in the field of mathematical analysis, complex functions theory, and rational mechanics.

In an article published in 1929, he posed a challenging conjecture in integral geometry, now widely known as the Pompeiu problem.

Among his contributions to real analysis there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set.