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.
He lectured at several universities in South America: in Buenos Aires and Rio de la Plata (Uruguay) from 1936 to 39. Terradas was the first professor to hold the chair in Differential Equation when it was first established in Madrid in 1932.