**Richard Courant** (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book *What is Mathematics?*, co-written with Herbert Robbins.

## Life and career

Courant was born in Lublinitz, in the Prussian Province of Silesia. His parents were Siegmund Courant and Martha Courant née Freund of Oels. Edith Stein was Richard's cousin on the paternal side. During his youth his parents moved often, including to Glatz, then to Breslau and in 1905 to Berlin. He stayed in Breslau and entered the university there, then continued his studies at the University of Zürich and the University of Göttingen. He became David Hilbert's assistant in Göttingen and obtained his doctorate there in 1910. He was obliged to serve in World War I, but was wounded shortly after enlisting and therefore dismissed from the military. He continued his research in Göttingen and then engaged a two-year period at the University of Münster as professor of mathematics. There he founded the Mathematical Institute, which he headed as director from 1928 until 1933.

Courant left Germany in 1933, earlier than many Jewish escapees. He did not lose his position due to being Jewish, as his previous service as a front-line soldier exempted him; however, his public membership in the social-democratic left was reason enough (for the Nazis) for dismissal.^{[1]}

In 1936, after one year at Cambridge, Courant accepted a professorship at New York University in New York City. There he founded an institute for graduate studies in applied mathematics. The Courant Institute of Mathematical Sciences (as it was renamed in 1964) is now one of the most respected research centers in applied mathematics.

Courant and David Hilbert authored the influential textbook *Methoden der mathematischen Physik* which, with its revised editions, is still current and widely used since its publication in 1924. With Herbert Robbins he coauthored a popular overview of higher mathematics, intended for the general public, titled *What is Mathematics?*.

Courant's name is also attached to the finite element method,^{[2]} with his numerical treatment of the plain torsion problem for multiply-connected domains, published in 1943.^{[3]} This method is now one of the ways to solve partial differential equations numerically. Courant is a namesake of the Courant–Friedrichs–Lewy condition and the Courant minimax principle.

Courant died in New Rochelle, New York.^{[4]}

## Perspective on mathematics

Commenting upon his analysis of experimental results from in-laboratory soap film formations, Courant believed that the existence of a physical solution does not obviate mathematical proof. Here is a quote from Courant on his mathematical perspective:

Empirical evidence can never establish mathematical existence--nor can the mathematician's demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful.

^{[5]}

## Personal life

In 1919 Courant married Nerina (Nina) Runge (1891-1991), a daughter of the Göttingen professor for Applied Mathematics, Carl Runge (of Runge-Kutta fame).

Richard and Nerina had four children: Ernest, a particle physicist and innovator in particle accelerators; Gertrude (1922-2014), a PhD biologist and wife of the mathematician Jürgen Moser (1928–1999); Hans, a physicist who participated in the Manhattan Project; and Leonore (known as "Lori," 1928-2015), a professional violist and wife of the mathematician Jerome Berkowitz (1928–1998).

## Publications

- Courant, R. (1937),
*Differential and Integral Calculus*, Vol. I, translated by McShane, E. J. (2nd ed.), New York: Interscience, ISBN 4-87187-838-4

- Courant, R. (1936),
*Differential and Integral Calculus*, Vol. II, translated by McShane, E. J., New York: Interscience, ISBN 4-87187-835-X

- Courant, Richard; John, Fritz (1965),
*Introduction to Calculus and Analysis*, Vol. I, New York: Interscience, ISBN 3-540-65058-X

- Courant, Richard; John, Fritz (1974),
*Introduction to Calculus and Analysis*, Vol. II/1, New York: Interscience, ISBN 3-540-66569-2

- Courant, Richard; John, Fritz (1974),
*Introduction to Calculus and Analysis*, Vol. II/2, New York: Interscience, ISBN 3-540-66570-6

- Courant, Richard; Hilbert, David (1953), Methods of Mathematical Physics, Vol. I (2nd ed.), New York: Interscience, ISBN 0-471-50447-5, MR 0065391 (archive) (translated from German:
*Methoden der mathematischen Physik I*, 2nd ed, 1931)^{[6]}

- Courant, Richard; Hilbert, David (1962), Methods of Mathematical Physics, Vol. II, New York: Interscience, doi:10.1002/9783527617234, ISBN 0-471-50439-4, MR 0140802 (translated from German:
*Methoden der mathematischen Physik II*, 1937)^{[7]}

- Courant, R.; Friedrichs, K. O. (1948),
*Supersonic Flow and Shock Waves*, New York: Interscience^{[8]}

- Courant, Richard; Robbins, Herbert (1941),
*What is Mathematics?*, Oxford University Press

## References

**^**http://www-irma.u-strasbg.fr/~schappa/GoeNS.pdf**^**Giuseppe Pelosi (2007). "The finite-element method, Part I: R. L. Courant: Historical Corner". doi:10.1109/MAP.2007.376627. Missing or empty`|url=`

(help)**^**Courant, Richard (1943). "Variational methods for the solution of problems of equilibrium and vibrations".*Bulletin of the American Mathematical Society*. doi:10.1090/s0002-9904-1943-07818-4.**^**NY Times Obituary "Dr. Richard Courant Dies at 84; Influential Mathematics Scholar; Organizer and Ex. Direcgor of Institute at N.Y.U. Aided Research and Teaching"**^***The Parsimonious Universe*, Stefan Hildebrandt & Anthony Tromba, Springer-Verlag, 1996, page 148**^**Tamarkin, J. D. (1932). "Review: Methoden der mathematischen Physik, Bd. I, zweite verbesserte Auflage, by R. Courant and D. Hilbert".*Bull. Amer. Math. Soc.***38**(1): 21–22. doi:10.1090/S0002-9904-1932-05311-3.**^**Weyl, Hermann (1938). "Review: Methoden der mathematischen Physik, Vol. 2, by R. Courant and D. Hilbert".*Bull. Amer. Math. Soc.***44**(9): 602–604. doi:10.1090/S0002-9904-1938-06791-2.**^**Lin, C. C. (1951). "Review:*Supersonic flow and shock waves*, by R. Courant and K. O. Friedrichs".*Bull. Amer. Math. Soc.***57**(1, Part 1): 85–87. doi:10.1090/s0002-9904-1951-09457-4.

## Sources

- Medawar, Jean; Pyke, David (2012).
*Hitler's Gift: The True Story of the Scientists Expelled by the Nazi Regime*. New York: Arcade Publishing. ISBN 978-1-61145-709-4.

## External links

Wikiquote has quotations related to: Richard Courant |

- Richard Courant at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Richard Courant",
*MacTutor History of Mathematics archive*, University of St Andrews . - Biographical memoir – by Peter Lax
- Oral History interview transcript with Richard Courant 9 May 1962, American Institute of Physics, Niels Bohr Library and Archives
- National Academy of Sciences Biographical Memoir
- 2015 Video Interview with Hans Courant by Atomic Heritage Foundation Voices of the Manhattan Project