When I arrived at the University of Maryland in 1957, it was one of the most important centers for partial differential equations in the whole world.
Most of the activity took place in the Institute for Fluid Dynamics and Applied Mathematics, which was situated on the third floor of the present Mathematics Building, while the Department of Mathematics occupied the first and the second floor. The fourth floor is a later addition.
Many of the mathematicians at the Institute had a joint appointment in the Department, and did teach a course. Some, who originally came to the Institute, switched to the Department.
Two of those are still with us, though both are emeriti now. One of them, Karl Stellmacher, gave a negative solution to a celebrated problem of Hadamard whether the only partial differential operators which exhibit Huygens' phenomenon are those which can be obtained by a change of variables from the wave operator. Among Avron Douglis' numerous publications, there is one written in collaboration with Shmuel Agmon and Louis Nirenberg which is one of the most often quoted papers in the history of mathematics.
The first generation of member of the Institute was recruited by Monroe Martin, it first director, and by Alexander Weinstein, who has outstanding contributions to eigenvalues and to singular partial differential operators. Unfortunately Weinstein had a difficult personality, and some of those who came because of him, left because of him.
In the early 1960's New York State created five Einstein chairs in science, each endowed with the then enormous sum of one hundred thousand dollars. Two of the five Einstein professors came from Maryland: Joaquin Diaz and Elliot Montroll. Diaz died at a relatively young age, and Montroll returned later from Rochester to Maryland. Among the other mathematicians who were at the Institute, let me mention Hans Weinberger, who left for Minnesota and was the first director of the Institute for Mathematics and Applications there, and J. H. Bramble, L. Payne and G. S. S. Ludford, who all went to Cornell. Between 1953 and 1960, the great Hungarian-Swedish mathematician Marcel Riesz spent at least one semester each year at the Institute.
For young mathematicians working in partial differential equations it was customary to spend a year or two, or at least a few months, at the Institute. Among the visitors, let me list Shmuel Agmon, Lars Garding, Lars Hormander, Jacques-Louis Lions (who came wiht his then two-year old son Pierre-Louis, now a world-class mathematician in his own right), Jaak Peetre, Carlo Pucci, Wolfgang Walter.
Another distinguished member of the Institute was J. M Burgers, the "father of magnetohydrodynamics." A young colleague, who lectured recently on the Burgers equation, was surprised when I told him that Burgers spent the last thirty years or so of his life at Maryland.
The Martin-Marietta Company originally wanted to found an "Institute for Fluid Dynamics," and it was only at the insistence of Weinstein that "and Applied Mathematics" was added to its name. At one of the unfortunate reorganizations it was renamed "Institute for Physical Science and Technology" and no one seems to have protested that mathematics was left out, in spite of the fact that to this day a lot of very important mathematical activity takes place there. However, during the mid-sixties the Department started to play an increasingly important role in the mathematical life of the University.