Then he served as an instructor at Engineering department of the University of Rome and as consultant for Istituto Nazionale per le Applicazioni del Calcolo (INAC), directed by Mauro Picone, his mathematics teacher.

Subsequently, when he returned to Rome, Salvadori was a convinced critic of the regime of Benito Mussolini,[1] and was aware of the risks for his mother's family.

[citation needed] It was difficult to leave Italy but in late 1938, he received a grant to study the first television experiments in the United States – his teacher and friend Enrico Fermi was an influential member of the examining commission.

While in the U.S., Salvadori stored some goods in a safe deposit box and left the key with Raymond D. Mindlin, whom he had met in New York a few months before, after a conference about the activities of Picone's institute.

[4] In the United States, Salvadori first worked for the Lionel Train Company until 1940, developing time and motion studies that so impressed the president that he was made an offer to become CEO, which he turned down.

As he reached retirement age, Salvadori began volunteering to work with under-privileged minority students from inner-city New York public schools.

Developing a hands-on method of teaching kids about the built environment, he was able to reach out to thousands of students and teachers, giving them an appreciation of the usefulness of mathematics and science.

[1] As a structural engineer, Salvadori became known for the design of thin concrete shells as he strove to create great architecture in all of his projects, including the concrete structural system for the CBS Building in Manhattan, designed by Eero Saarinen, and the seashell-inspired restaurant building at the hotel La Concha, in San Juan, Puerto Rico.