After his mother's unexpected death when he was twelve, he spent two years at the Montana Knabeninstitut, a boys' boarding school near Zürich in Switzerland, where he was mentored by Save Bercovici, who interested him in mathematics.

[citation needed] Persuaded by his father that he could not make a living as a mathematician, he entered the University of Buenos Aires, where he studied engineering.

After graduating in civil engineering in 1947, he got a job in the research laboratory of the geophysical division of the state-owned oil company, the YPF (Yacimientos Petrolíferos Fiscales).

[citation needed] While still working at YPF, Calderón became acquainted with the mathematicians at the University of Buenos Aires: Julio Rey Pastor, the first professor in the Institute of Mathematics, his assistant Alberto González Domínguez (who became his mentor and friend), Luis Santaló and Manuel Balanzat.

At the YPF Lab Calderón studied the possibility of determining the conductivity of a body by making electrical measurements at the boundary; he did not publish his results until 1980, in his short Brazilian paper.

Also, Calderón insisted that the focus should be on algebras of singular integral operators with non-smooth kernels to solve actual problems arising in physics and engineering, where lack of smoothness is a natural feature.

[8] Work by Calderón in interpolation theory opened up a new area of research,[16] see also the Commentary by Charles Fefferman and Elias M. Stein,[8] and in ergodic theory, his basic paper[17] (see also the Commentary by Donald L. Burkholder,[8] and[18]) formulated a transference principle that reduced the proof of maximal inequalities for abstract dynamical systems to the case of the dynamical system on the integers, on the reals or, more generally, on the acting group.

Calderón together with his mentor and collaborator Zygmund, maintained close ties with Argentina and Spain, and through their doctoral students and their visits, strongly influenced the development of mathematics in these countries.