I began my graduate studies in mathematics in the early 1950s and wrote my Ph.D. thesis under the direction of Antoni Zygmund. The graduate program offered by the University of Chicago was excellent. But I really learned most by attending and participating in the legendary “Zygmund seminar”. It was there that I learned the various topics in harmonic analysis that formed the basis of what is now known as the “Calderón–Zygmund School”. Alberto Calderón had received his Ph.D. at the University of Chicago before I started my studies with Zygmund and had left to join the faculty at Ohio State University and, a short time later, at MIT. I felt his presence at the University of Chicago, however, in practically every session of the Zygmund seminar. He had made important contributions in each topic we discussed: interpolation of operators, potential theory and the boundary behavior of harmonic functions, ergodic theory, and, of course, singular integrals. I was surrounded by not only a remarkable faculty but also by a large number of very talented graduate student colleagues who have by now made important contributions in mathematics. I could not help, however, having a feeling of great awe for this individual who was capable of making so many important contributions in such a large number of topics. As I stated above, he was an ever present participant of the Zygmund seminar.
I first met Alberto shortly before I finished my thesis in the mid-1950s. He visited the University of Chicago, and after presenting a beautiful talk on singular integrals and their connection with partial differential equations, Zygmund, the young group that was working with him, and Alberto met in Zygmund’s office and discussed various topics in harmonic analysis. I remember vividly the impressions Alberto made on me. He had unique insights and ways of looking into the various subjects we discussed and in a very friendly, open, and generous way shared this knowledge with us. I began to realize what was his main strength: he made special efforts to reduce each concept he considered to clear, simple components, and from this understanding he was able to arrive at methods for solving a problem that often were applicable to many other fields in mathematics. His considerable contributions in analysis are being described elsewhere in these Notices; I will not try to give such a description. I do want to emphasize, however, this important feature that is ever present in his research: The methods he discovered often go way beyond the results he obtained. Ideas he used in his study of the interpolation of operators have had an important impact in fields that seem totally different. One of the important equations that characterize wavelets, for example, is really a discrete version of what is known as the “Calderón Reproducing Formula”.
Since this first meeting I have had several opportunities to be with Alberto, and on each occasion all the feelings I described above were strengthened. I was asked by the mathematics department of the University of Chicago to give the “Zygmund lectures”, and I presented them in March of this year. Recently I became interested in the mathematical theory of wavelets and chose this topic for the three lectures I gave. Alberto attended these lectures and expressed an interest in the subject; in particular, he asked me to send him what I had written. I was very excited at the prospect of establishing an area of common interest with him. I obtained a copy of a book on wavelets I had recently coauthored withand put it together with a collection of papers I thought might interest Alberto, but then I heard the sad news of his passing away. Along with many others, I will miss him very much.