New York University's Courant Institute of Mathematical Sciences is a leading center for research and education in mathematics and computer science. For seventy-five years, we have contributed to U.S. and international science and engineering by promoting an integrated view of mathematics and computation. Our research activities are broad, covering many areas of mathematics and computer science, as well as the application of these disciplines to problems in the biological, physical, and economic sciences. As computer science, mathematics, and their applications evolve, so does the Courant Institute. In mathematics, we currently offer great depth in analysis, partial differential equations, probability, geometry, topology, and number theory. In computer science our strengths include machine learning and its applications to computer vision and natural language processing, theoretical computer science and cryptography, computer graphics and systems. Perhaps our most unique feature is an emphasis on the interplay of disciplines at the boundary between mathematics and computer science, particularly in the areas of scientific computing, machine learning and data analysis, computer graphics and computational geometry. The Courant Institute has played a central role in the development of applied mathematics, analysis, and computer science. Our faculty has received numerous national and international awards in recognition of their extraordinary research accomplishments. We are equally proud of our former students and postdoctoral associates who now provide leadership at universities, government laboratories, and private industry throughout the world.