[7] During the 1939–1940 academic year, he won an "Istituto Nazionale di Alta Matematica" scholarship and went in Rome to the institute:[8] there he followed the courses held by Francesco Severi, Mauro Picone, Luigi Fantappiè, Giulio Krall and Leonida Tonelli.
[12] Nonetheless, in desperate conditions, he was able to lead his men to the Italian coasts with a rubber dinghy, and was awarded a Silver Medal of Military Valor for this act.
[16] It was also necessary to organize courses and exams for the numerous war veterans coming back from the front and for new students, with more than a half of the teaching personnel blocked beyond the Gothic Line:[15] and in performing all those task Cafiero, jointly with few others and working as an adjunct professor of "Esercitazioni di Matematiche", was an outstanding collaborator of Renato Caccioppoli and Carlo Miranda.
[27][29] In particular, he established a seminar on abstract measure theory open to assistant professors and to graduate students as well, and this was felt as true scientific revolution:[29] he held the chair of mathematical analysis for three years.
[35]Come Andreotti anche Stampacchia non poté venire subito a Pisa e così io fui felice di avere con me un altro valoroso allievo di Renato Caccioppoli, Federico Cafiero, che restò a Pisa poco tempo, ma vi lasciò una forte traccia e formò il suo valido continuatore Giorgio Letta.