# Mathematician:Richard Courant

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## Contents

## Mathematician

German mathematician best known for his writings.

Made considerable contributions to the field numerical analysis.

Founded the series of books *Grundlehren der mathematischen Wissenschaften* (Foundations, or "basic teachings", of Mathematical Sciences), subtitled *Comprehensive Studies in Mathematics*, in higher mathematics in $1920$ for Springer-Verlag.

## Nationality

German

## History

- Born: 8 Jan 1888, Lublinitz, Germany (now Lubliniec, Poland)
- 1892: Moved with family to Glatz
- 1897: Moved with family to Breslau, attended the König-Wilhelm Gymnasium
- 1902: Took up tutoring in order to support himself
- 1904: Parents left Breslau and moved to Berlin
- 1905: Left school to attend classes in mathematics and physics at the University of Breslau
- 1906: Passed the university entrance examinations
- Spring 1907: Spent a semester at Zurich
- 1 November 1907: Began studies at Göttingen
- 1908 Became David Hilbert's assistant
- 1910: Obtained doctorate from Göttingen under Hilbert's supervision
- Late 1910: Start of military service
- 1911: Returned to Göttingen to complete habilitation, again under Hilbert
- Summer 1912: Married Nelly Neumann
- 1914: Drafted into army
- 27 September 1915: Wounded and received leave
- 1915: Divorced Nelly
- December 1918: Returned to Göttingen to teach
- 22 January 1919: Married Nerina Runge, daughter of Carl Runge
- Spring 1920: Replaced Wilhelm Killing at the chair of mathematics at Münster
- 1922: Founded the university's Mathematics Institute
- 1932: Visited the major universities in the USA to lecture there
- 5 May 1933: Expelled from Göttingen by Nazi regime, went to Istanbul then Cambridge
- 1934: Went to New York
- June 1935: Offered a permanent position at New York
- 1936: Offered a professorship at New York University.
- 1936-39: Used his position to help other professors who had also been expelled from Germany
- 1953-58: Director of his new Institute of Mathematical Sciences at New York University
- 19 November 1971: Suffered a stroke
- Died: 27 Jan 1972, New Rochelle, New York, USA

## Theorems and Definitions

- Courant-Friedrichs-Lewy Condition (with Kurt Friedrichs and Hans Lewy)
- Courant Number
- Courant Minimax Principle
- Contributed towards the Finite Element Method.

## Publications

- 1910:
*Über die Anwendung des Dirichletschen Prinzipes auf die Probleme der konformen Abbildung*(On the application of Dirichlet's principle to the problems of conformal mappings): PhD thesis - 23 February 1912:
*On existence proofs in mathematics*(inaugural lecture) - 1922:
*Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen*(with Adolf Hurwitz) - 1924:
*Methods of Mathematical Physics*(with David Hilbert): ISBN 0471504475 - 1928:
*Über die partiellen Differenzengleichungen der mathematischen Physik*(*Math. Ann.***Vol. 100**,*no. 1*: 32 – 74) (with Kurt Friedrichs and Hans Lewy) - 1934:
*Differential and Integral Calculus, Volume 1*(translated by E.J. McShane) - 1937:
*Differential and Integral Calculus, Volume 1, 2nd ed.*(translated by E.J. McShane) - 1941:
*What is mathematics?*(with Herbert Robbins)

## Notable Quotes

*Just as deduction should be supplemented by intuition, so the impulse to progressive generalisation must be tempered and balanced by respect and love for colourful detail. The individual problem should not be degraded to the rank of special illustration of lofty general theories. In fact, general theories emerge from consideration of the specific, and they are meaningless if they do not serve to clarify and order the more particularised substance below. The interplay between generality and individuality, deduction and construction, logic and imagination -- this is the profound essence of live mathematics. Any one or another of these aspects of mathematics can be at the centre of a given achievement. In a far-reaching development all of them will be involved. Generally speaking, such a development will start from the "concrete" ground, then discard ballast by abstraction and rise to the lofty layers of thin air where navigation and observation are easy. After this flight comes the critical test of landing and reaching specific goals in the newly surveyed low plains of individual "reality". In brief, the flight into abstract generality must start from and return to the concrete and specific.*- -- Epigraph to in 1972: George F. Simmons:
*Differential Equations*

- -- Epigraph to in 1972: George F. Simmons:

## Sources

- John J. O'Connor and Edmund F. Robertson: "Richard Courant": MacTutor History of Mathematics archive

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): Preface