Richard Courant came to New York University in 1934 as a visiting professor, having left his position as director of the Mathematics Institute at the University of Göttingen in Germany. In 1935, he was invited to build up the Department of Mathematics at the Graduate School of Arts and Sciences. In 1937, Courant was joined by Kurt O. Friedrichs and James J. Stoker. Together with a few of the faculty members already in the department, they formed a closely knit research group.

During World War II, under the sponsorship of the Office of Scientific Research and Development, this team became the nucleus of an expanded group that undertook mathematically challenging problems arising from various war projects. However, in contrast to most other ad hoc assembled teams, this group did not abandon basic research and advanced instruction.

After the war, support from the Office of Naval Research and other government agencies maintained the group and encouraged its growth. The name Institute for Mathematics and Mechanics was adopted in 1946.

In that same year, Morris Kline organized an effort focused on mathematical problems of electromagnetic wave propagation. This project gave rise to the Institute's Division of Wave Propagation and Applied Mathematics.

The Atomic Energy Commission installed a state-of-the-art electronic computer at New York University in 1952. This led to the creation of the Courant Mathematics and Computing Laboratory, which has functioned for many years under the auspices of the U.S. Department of Energy.

A research project on plasma fusion was initiated by Harold Grad in 1954. Its present-day descendant is the Division of Magnetofluid Dynamics, led by Harold Weitzner.

Paul R. Garabedian's research on transonic flow, shockless airfoils, and plasma physics led to the creation of the Division of Computational Fluid Dynamics in 1978.

James J. Stoker succeeded Courant as director in 1958 and served until 1966. During this period, the Institute acquired a large measure of autonomy within the University framework. It became the Courant Institute of Mathematical Sciences and in 1965 moved to a newly constructed building named in honor of Warren Weaver.

Our computer science program began in the 1960s under the leadership of Max Goldstein and Jacob T. Schwartz. The program ultimately became a separate department with its own graduate and undergraduate programs. Rapid development continued through the 1980s, with new leadership from Olof B. Widlund and others. This led to a variety of research activities including programming languages, computer graphics, parallel architectures, and theory.

The growth of computer science was naturally accompanied by new demands for space. The Courant Institute presently occupies several floors of a nearby building at 60 Fifth Avenue, in addition to its home in Warren Weaver Hall.

The Institute has grown immensely over the years. The research divisions still exist, but they do not begin to capture the remarkable diversity of the Institute's research activity.

Since Stoker stepped down in 1966, the Institute's directors have been Kurt O. Friedrichs, Jürgen Moser, Louis Nirenberg, Peter D. Lax, S. R. Srinivasa Varadhan, Cathleen S. Morawetz, Henry P. McKeanDavid W. McLaughlin, Charles M. Newman, Leslie Greengard, and Gerard Ben Arous. The current director is Russ Caflisch.