Richard Courant (January 8, 1888 – January 27, 1972) was a German-Americanmathematician. He is best known by the general public for the bookWhat is Mathematics?, co-written withHerbert Robbins. His research focused on the areas ofreal analysis,mathematical physics, thecalculus of variations andpartial differential equations. He wrote textbooks widely used by generations of students of physics and mathematics. He is also known for founding theinstitute now bearing his name.

Richard Courant
Courant in 1969
Born	(1888-01-08)January 8, 1888 Lublinitz,German Empire (nowLubliniec,Poland)
Died	January 27, 1972(1972-01-27) (aged 84) New Rochelle, New York, United States
Citizenship	Germany United States
Alma mater	University of Zurich University of Göttingen
Known for	Courant number Courant minimax principle Courant–Friedrichs–Lewy condition Courant's nodal domain theorem[1] Methoden der mathematischen Physik
Scientific career
Fields	Mathematics
Institutions	University of Göttingen University of Münster University of Cambridge New York University
Thesis	On the application of Dirichlet's principle to the problems of conformal mapping (1910)
Doctoral advisor	David Hilbert
Doctoral students	Leifur Ásgeirsson Herbert Busemann William Feller Kurt Friedrichs Harold Grad Fritz John Joseph Keller Edgar Krahn Martin Kruskal Anneli Lax Hans Lewy Otto Neugebauer Franz Rellich

Courant was born inLublinitz, in thePrussianProvince of Silesia (now in Poland). His parents were Siegmund Courant and Martha Freund ofOels.Edith Stein was Richard's cousin on the maternal side. During his youth his parents moved often, including toGlatz, then toBreslau and in 1905 toBerlin. He stayed in Breslau and entered theuniversity there, then continued his studies at theUniversity of Zürich and theUniversity of Göttingen. He becameDavid Hilbert's assistant in Göttingen and obtained his doctorate there in 1910. He was obliged to serve inWorld War I, but was wounded shortly after enlisting and therefore dismissed from the military. Courant left theUniversity of Münster in 1921 to take overErich Hecke's position at theUniversity of Göttingen.^[2] There he founded the Mathematical Institute, which he headed as director from 1928 until 1933.

Courant leftGermany in 1933, earlier than many Jewish escapees. He did not lose his position due to beingJewish, as his previous service as a front-line soldier exempted him; however, his public membership in thesocial-democratic left was reason enough (for the Nazis) for dismissal.^[3]

In 1936, after one year atCambridge, Courant accepted a professorship atNew York University in New York City. There he founded an institute for graduate studies inapplied mathematics. TheCourant Institute of Mathematical Sciences (as it was renamed in 1964) is now one of the most respected research centers in applied mathematics.^[4]

Courant andDavid Hilbert authored the influentialtextbookMethoden der mathematischen Physik, which, with its revised editions, is still current and widely used since its publication in 1924. WithHerbert Robbins he coauthored a popular overview of higher mathematics, intended for the general public, titledWhat is Mathematics?. WithFritz John he also coauthored the two-volume workIntroduction to Calculus and Analysis, first published in 1965.^[5]

Courant's name is also attached to thefinite element method,^[6] with his numerical treatment of the plain torsion problem for multiply-connected domains, published in 1943.^[7]This method is now one of the ways to solvepartial differential equationsnumerically. Courant is a namesake of theCourant–Friedrichs–Lewy condition and theCourant minimax principle.

Courant was an elected member of both theAmerican Philosophical Society (1953) and the United StatesNational Academy of Sciences (1955).^[8][9] In 1965, theMathematical Association of America recognized his contributions to Mathematics with their Award for Distinguished Service to Mathematics.^[10][11]

Courant died of astroke inNew Rochelle, New York on January 27, 1972, aged 84.^[12]

Commenting upon his analysis of experimental results from in-laboratory soap film formations, Courant explained why the existence of a physical solution does not obviatemathematical 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.^[13]

In 1912, Courant marriedNelly Neumann, who had earned her doctorate at Breslau insynthetic geometry in 1909. They lived together in Göttingen until they were divorced in 1916. She was later murdered by the Nazis in 1942 for being Jewish.^[14]

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

Richard and Nerina had four children:Ernest, aparticle physicist and innovator in particle accelerators; Gertrude (1922–2014), a biologist and wife of the mathematicianJürgen Moser (1928–1999);Hans (1924-2019),^[15][16] a physicist who participated in theManhattan Project; and Leonore (known as "Lori," 1928–2015), a professional violist and wife of the mathematician Jerome Berkowitz (1928–1998) and subsequently wife of mathematicianPeter Lax until her death.^[17]

• Courant, R. (1937),Differential and Integral Calculus, vol. I, translated by McShane, E. J. (2nd ed.), New York: Interscience,ISBN 978-4-87187-838-8

• Courant, R. (1936),Differential and Integral Calculus, vol. II, translated by McShane, E. J., New York: Interscience,ISBN 978-4-87187-835-7

• Courant, Richard; John, Fritz (1965),Introduction to Calculus and Analysis, vol. I, New York: Interscience,ISBN 978-3-540-65058-4

• Courant, Richard; John, Fritz (1974),Introduction to Calculus and Analysis, vol. II/1, New York: Interscience,ISBN 978-3-540-66569-4

• Courant, Richard; John, Fritz (1974),Introduction to Calculus and Analysis, vol. II/2, New York: Interscience,ISBN 978-3-540-66570-0

• Courant, Richard;Hilbert, David (1953),Methods of Mathematical Physics, vol. I (2nd ed.), New York: Interscience,ISBN 978-0-471-50447-4,MR 0065391 (archive) (translated from German:Methoden der mathematischen Physik I, 2nd ed, 1931)^[18]

• Courant, Richard;Hilbert, David (1962),Methods of Mathematical Physics, vol. II, New York: Interscience,doi:10.1002/9783527617234,ISBN 978-0-471-50439-9,MR 0140802 (translated from German:Methoden der mathematischen Physik II, 1937)^[19]

• Courant, R.;Friedrichs, K. O. (1948),Supersonic Flow and Shock Waves, New York: Interscience^[20]

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

• Reid, Constance (1976).Courant in Göttingen and New York. The Story of an Improbable Mathematician. New York, Heidelberg, Berlin: Springer-Verlag.ISBN 978-0-387-90194-7.

• 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.

• Richard Courant at theMathematics Genealogy Project
• O'Connor, John J.;Robertson, Edmund F.,"Richard Courant",MacTutor History of Mathematics Archive,University of St Andrews
• Oral History interview transcript with Richard Courant on 9 May 1962, American Institute of Physics, Niels Bohr Library & Archives
• National Academy of Sciences Biographical Memoir
• 2015 Video Interview with Hans Courant by Atomic Heritage Foundation Voices of the Manhattan Project
• US News Rankings of Applied Mathematics Programs