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Carl David Tolmé Runge

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Carl David Tolmé Runge

Carl Runge
Carl David Tolmé Runge
Born (1856-08-30)30 August 1856
Bremen, German Confederation
Died 3 January 1927(1927-01-03) (aged 70)
Göttingen, Weimar Republic
Residence Germany
Citizenship German
Fields Mathematics
Institutions University of Hanover (1886–1904)
Georg-August University of Göttingen (1904–1925)
Alma mater Berlin University
Doctoral advisor Karl Weierstrass
Ernst Kummer
Doctoral students Max Born
Friedrich Adolf Willers
Hermann König
Known for Runge–Kutta method
Runge's phenomenon
Laplace–Runge–Lenz vector

Carl David Tolmé Runge (German: ; 1856–1927) was a German mathematician, physicist, and spectroscopist.

He was co-developer and co-eponym of the Runge–Kutta method (German pronunciation: [ˈʀʊŋə ˈkʊta]), in the field of what is today known as numerical analysis.


He spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864).

In 1880, he received his Ph.D. in mathematics at Berlin, where he studied under Karl Weierstrass. In 1886, he became a professor at the Technische Hochschule Hannover in Hanover, Germany.

His interests included mathematics, spectroscopy, geodesy, and astrophysics. In addition to pure mathematics, he did a great deal of experimental work studying spectral lines of various elements (together with Heinrich Kayser), and was very interested in the application of this work to astronomical spectroscopy.

In 1904, on the initiative of Georg-August University of Göttingen, which he accepted. There he remained until his retirement in 1925.

His son, Wilhelm Runge, was an early developer of radar. His daughter, Nerina (Nina) Runge, married the mathematician Richard Courant.


The crater Runge on the Moon is named after him.

See also


  • Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen Curven (PhD dissertation, Friese, 1880)
  • Analytische Geometrie der Ebene (B.G. Teubner, Leipzig, 1908)
  • Graphical methods; a course of lectures delivered in Columbia university, New York, October, 1909, to January, 1910 (Columbia University Press, New York, 1912)
  • Carl Runge und Hermann König Vorlesungen über numerisches Rechnen (Springer, Heidelberg, 1924)
  • Graphische Methoden (Teubner, 1928)


  • Iris Runge: Carl Runge und sein wissenschaftliches Werk, Vandenhoeck & Ruprecht, Göttingen 1949.

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