VI.83 Richard Courant

b. Lublinitz, Silesia (then part of Germany, now Poland), 1888; d. New York, 1972

Mathematical physics; partial differential equations; minimal surfaces; compressible flow; shock waves

The long and eventful life of Courant was full of high achievements: in mathematical research, the applications of mathematics, as a teacher of many future mathematicians, as a writer of superb books on mathematics, and as an organizer and administrator of large institutions. The fact that Courant—an outsider in his native Germany and a refugee in the United States—could accomplish these things is a testament to his personality as well as to his scientific outlook.

Born in Lublinitz, Courant completed his high school training in Breslau, living on his own and supporting himself by tutoring. His older Breslau friends, Hellinger and Toeplitz, went on to Göttingen, then the mecca of mathematics, and in due course Courant followed them. There he was taken on as an assistant to HILBERT [VI.63], and he began a close friendship with Harald Bohr, which was later extended to Harald’s brother Niels.

Under Hilbert’s direction, Courant wrote his dissertation on the use of DIRICHLET’S PRINCIPLE [IV.12 §3.5] (on minimizing energy) for constructing conformal maps. Courant also used Dirichlet’s principle in several further mathematical studies.

During World War I Courant was drafted into the army as an officer; he fought on the western front and was seriously wounded. After returning to academic life he turned his energies to mathematics and proved some remarkable results: an isoperimetric inequality for the lowest frequency of a vibrating membrane; and the Courant max-min principle for the EIGENVALUES [I.3 §4.3] of a SELF-ADJOINT OPERATOR [III.50 §3.2], so useful in studying the distribution of eigenvalues of the operators of mathematical physics.

In 1920 Courant was named as KLEIN’s [VI.57] successor as professor in Göttingen; the appointment was pushed through by Klein and Hilbert, who saw, correctly, that he shared their vision of the relationship between mathematics and science, that he would strike a balance between research and education, and that he had the administrative energy and wisdom to push his mission to fruition.

Courant became close friends with the publisher Ferdinand Springer. One of the fruits of this relationship was the famous “Grundlehren” series of monographs, affectionately known as the “Yellow Peril.” The third volume in this series is Courant’s exposition of RIEMANN’s [VI.49] geometric view of the theory of analytic functions, combined with Hurwitz’s lectures on ELLIPTIC FUNCTIONS [V.31]. In 1924 the first volume of Courant-Hilbert on Mathematical Physics appeared; it contained, presciently, much of the mathematics needed for Schrödinger’s version of quantum mechanics. His influential calculus book appeared in 1927. His research did not languish; in 1928 he published, jointly with his students Friedrichs and Lewy, the basic paper on the difference equations of mathematical physics.

Under Courant’s leadership, Göttingen, where the lively international atmosphere had been destroyed by World War I, became once again an important center for mathematics, as well as physics: the list of visitors reads like a Who’s Who of mathematics. This was totally shattered when Hitler took over the government: Jewish professors, Courant among the first, were dismissed unceremoniously and had to flee or face annihilation. Courant and his family found refuge in New York, where he was invited to build a Graduate School of Mathematics at New York University (NYU). Without any foundation to build on, Courant succeeded in this task, with the help of his former student Friedrichs and of the American James Stoker, who shared Courant’s scientific ideals. Courant found New York a reservoir of talent, and attracted students such as Max Shiffman, and later Harold Grad, Joe Keller, Martin Kruskal, Cathleen Morawetz, Louis Nirenberg, and others, including the writer of this article.

In 1936, in a burst of creativity, Courant obtained several basic results about MINIMAL SURFACES [III.94 §3.1] using Dirichlet’s principle. In 1937 he finished the second volume of Courant–Hilbert. The immensely successful popular book he wrote jointly with Herb Robbins, What Is Mathematics?, appeared in 1940. In 1942 when federal financing for scientific research became available, Courant’s group embarked on an ambitious study of supersonic flow and shock waves.

Federal support did not stop after the war; this enabled Courant to vastly expand the scale of research and graduate instruction at NYU. The research combined, at a high intellectual level, theoretical mathematics with applications such as fluid dynamics, statistical mechanics, the theory of elasticity, meteorology, the numerical solution of partial differential equations, and other topics. Nothing like this had been attempted before at a university in the United States. The institute created by Courant, eventually named after him, is flourishing today and has served as a model for other centers around the world.

Courant hated the Nazis, but did not condemn all Germans; after the war he helped to rebuild mathematics in Germany and was instrumental in inviting talented young German mathematicians and physicists to the United States.

Courant received much help from friends of his youth, many of whom became leaders in their fields, as well as from science administrators in government and industry who admired his vision of mathematics and the gallant spirit that was demonstrated by his willingness to fight against seemingly insuperable odds.

Further Reading

Reid, C. 1976. Courant in Göttingen and New York: The Story of an Improbable Mathematician. New York: Springer.

Peter D. Lax