as his assistant. Zygmund invited Calderón to work with him, and in 1949 Calderón arrived in Chicago with a Rockefeller Fellowship. He was encouraged by Marshall Stone to obtain a doctorate, and with three recently published papers as dissertation, Calderón obtained his PhD in mathematics under Zygmund's supervision in 1950. The collaboration reached fruition in the Calderón-Zygmund theory of singular integrals, and lasted more than three decades. The memoir of 1952 was influential for the Chicago School of hard analysis. The Calderón-Zygmund decomposition lemma, invented to prove the weak-type continuity of singular integrals of integrable functions, became a standard tool in analysis and probability theory. The Calderón-Zygmund Seminar at the University of Chicago ran for decades. Calderón contributed to the theory of differential equations, with his proof of uniqueness in the Cauchy problem using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary (the "method of the Calderón projector"), and the role played by algebras of singular integrals, through the work of Calderón's student R. Seeley, in the initial proof of the Atiyah-Singer index theorem, see also the Commentary by Paul Malliavin. The development of pseudo-differential operators by Kohn-Nirenberg and Hörmander also owed much to Calderón and his collaborators, R. Vaillancourt and J. Alvarez-Alonso. 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. It led to what is now known as the "Calderón program", with major parts: Calderón's study of the Cauchy integral on Lipschitz curves, and his proof of the boundedness of the "first commutator". These papers stimulated research by other mathematicians in the following decades; see also the later paper by the Calderón brothers and the Commentary by Y. Meyer. Work by Calderón in interpolation theory opened up a new area of research, see also the Commentary by Charles Fefferman and Elias M. Stein, and in ergodic theory, his basic paper (see also the Commentary by Donald L. Burkholder, and) 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. Career In his academic career, Calderón taught at many different universities, but primarily at the University of Chicago