The Portuguese Society of Mathematics was founded in December 1940 by a group of mathematicians who had two main aims. On the one hand, they wished to introduce to Portugal those areas of research that were of interest in other countries at the time. On the other, they wished to publicise these new areas and to revitalise Portuguese Mathematics by capturing the interest of university and pre-university youth.

In this talk we will contextualize the coming of age of this generation of mathematicians, known in Portugal as "the 40s generation". We will analyze several aspects of their work, including the journal Portugaliae Mathematica, the Mathematics Gazette, the foundation of the Portuguese Society of Mathematics and its first years of activities. Our analysis is only made for the period 1936-1945, a crucial period of change in what concerns mathematical activity as an institutionalised practice. Concerning mathematical developments, this is the most interesting period of this age in Portugal, and it coincides with the stay in this country of António Monteiro after his return from Paris, where he completed his PhD under the supervision of Maurice Fréchet. Monteiro is the decisive figure of this time and the one behind most of the important mathematical innovations in Portugal in the first half of the 20th century.