He researched and taught widely in the fields of mathematics and the physical sciences, working not only in his native Catalonia, but also in the rest of Spain and in South America.
He held professorships in the universities of Zaragoza, Barcelona and Madrid, specializing in physical and mathematical sciences and publishing numerous articles about those subjects.
In 1909, while at the Academy of Sciences and Arts of Barcelona, he produced an important work entitled Emisión de radiaciones por cuerpos fijos o en movimiento.
The theories of quanta and relativity captivated him, and he invited such figures as Jacques Hadamard) (1921), Hermann Weyl (1921), Arnold Sommerfeld (1922), Tullio Levi-Civita (1922) and Albert Einstein (1923) to Barcelona.
Einstein's Spanish visit, between 22 and 28 February 1923, was a notable success, organized by Terradas, the Catalan Government, the Mancomunitat, and Rafael Campalans.
In 1942 he created the Spanish Instituto Nacional de Técnica Aeroespacial / INTA (National Institute of the Aerospace Technology), that after Terrade's death received his name.
In (1910) he published "Discrete elements of matter and radiation", "Corrientes marinas" (1941) and, to gain entry to the Royal Academy of the Spanish Language, the volume "Neologismos, arcanismos in plàtica de ingenieros" (1946).