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Richard Courant

richard courant, richard courant what is mathematics pdf
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


  • 1 Life and career
  • 2 Perspective on mathematics
  • 3 Personal life
  • 4 Publications
  • 5 References
  • 6 Sources
  • 7 External links

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

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 With Fritz John he also coauthored the two-volume work Introduction to Calculus and Analysis, first published in 1965

Courant's name is also attached to the finite element method, with his numerical treatment of the plain torsion problem for multiply-connected domains, published in 1943 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

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

Personal life

In 1912 Courant married Nelly Neumann, who had earned her doctorate at Breslau in Symplectic 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 cite: https://jwaorg/encyclopedia/article/neumann-nelly

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


  • 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
  • Courant, Richard; Hilbert, David 1962, Methods of Mathematical Physics, Vol II, New York: Interscience, doi:101002/9783527617234, ISBN 0-471-50439-4, MR 0140802  translated from German: Methoden der mathematischen Physik II, 1937
  • Courant, R; Friedrichs, K O 1948, Supersonic Flow and Shock Waves, New York: Interscience 
  • Courant, Richard; Robbins, Herbert 1941, What is Mathematics, Oxford University Press 


  1. ^ Schappacher, Norbert 1991 "Edmund Landau's Göttingen: From the Life and Death of a Great Mathematical Center" PDF The Mathematical Intelligencer 13 4: 12–18 doi:101007/bf03028334 
  2. ^ Giuseppe Pelosi 2007 "The finite-element method, Part I: R L Courant: Historical Corner" doi:101109/MAP2007376627  Missing or empty |url= help
  3. ^ Courant, Richard 1943 "Variational methods for the solution of problems of equilibrium and vibrations" Bulletin of the American Mathematical Society 49: 1–24 doi:101090/s0002-9904-1943-07818-4 
  4. ^ NY Times Obituary "Dr Richard Courant Dies at 84; Influential Mathematics Scholar; Organizer and Ex Direcgor of Institute at NYU Aided Research and Teaching"
  5. ^ The Parsimonious Universe, Stefan Hildebrandt & Anthony Tromba, Springer-Verlag, 1996, page 148
  6. ^ 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:101090/S0002-9904-1932-05311-3 
  7. ^ 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:101090/S0002-9904-1938-06791-2 
  8. ^ 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:101090/s0002-9904-1951-09457-4 


  • Reid, Constance 1976 Courant in Göttingen and New York The Story of an Improbable Mathematician New York, Heidelberg, Berlin: Springer-Verlag ISBN 0-387-90194-9 
  • 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

  • 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

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