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Carl David Tolmé Runge (German pronunciation: [ˈʁʊŋə]; 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist.

He was co-developer and co-eponym of the Runge–Kutta method (pronounced [ˌʀʊŋəˈkʊta]), 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 in Hannover, 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 Felix Klein he received a call to the Georg-August University of Göttingen, which he accepted. There he remained until his retirement in 1925

Carl David Tolmé Runge


The crater Runge on the Moon is named after him.

See also

* Runge's phenomenon
* Runge's method for diophantine equations.


* 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)


* Paschen F (1929). "Carl Runge". Astrophysical Journal 69: 317–321. doi:10.1086/143192. http://adsabs.harvard.edu//full/seri/ApJ../0069//0000317.000.html.
* Iris Runge: Carl Runge und sein wissenschaftliches Werk, Vandenhoeck & Ruprecht, Göttingen 1949.

External links

* O'Connor, John J.; Robertson, Edmund F., "Carl David Tolmé Runge", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Runge.html .
* Biography
* Carl David Tolmé Runge at the Mathematics Genealogy Project


Mathematics Encyclopedia

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