Carl Runge

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Carl Runge
Carl David Tolmé Runge
Born(1856-08-30)30 August 1856
Died3 January 1927(1927-01-03) (aged 70)
Alma materBerlin University
Known forRunge–Kutta method
Runge's phenomenon
Runge's theorem
Laplace–Runge–Lenz vector
Schumann–Runge bands
Scientific career
InstitutionsLeibniz University Hannover (1886–1904)
University of Göttingen (1904–1925)
Doctoral advisorKarl Weierstrass
Ernst Kummer
Doctoral studentsMax Born
Friedrich Adolf Willers
Hermann König

Carl David Tolmé Runge (German: [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 (German pronunciation: [ˈʀʊŋə ˈkʊta]), in the field of what is today known as numerical analysis.

Life and work[edit]

Runge spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. His mother was Fanny Schwartz Tolmé.[1] 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 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 University of Göttingen, which he accepted. There he remained until his retirement in 1925.


His daughter Iris also became a mathematician and his son Wilhelm was an early developer of radar. Another of his daughters, Nerina (Nina), married the mathematician Richard Courant.


The crater Runge on the Moon is named after him. The Schumann–Runge bands of molecular oxygen are named after him and Victor Schumann.

See also[edit]



  • Paschen F (1929). "Carl Runge". Astrophysical Journal. 69: 317–321. Bibcode:1929ApJ....69..317P. doi:10.1086/143192.
  • Iris Runge: Carl Runge und sein wissenschaftliches Werk, Vandenhoeck & Ruprecht, Göttingen 1949.


  1. ^ Tobies, Renate (5 January 2012). Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Springer Science & Business Media. p. 439. ISBN 978-3-0348-0251-2.
  2. ^ Swift, Elijah (1923). "Book Review: Praxis der Gleichungen". Bulletin of the American Mathematical Society. 29 (7): 327–328. doi:10.1090/S0002-9904-1923-03742-7. ISSN 0002-9904.
  3. ^ Bôcher, Maxime (1909). "Book Review: Analytische Geometrie der Ebene". Bulletin of the American Mathematical Society. 16 (1): 30–33. doi:10.1090/S0002-9904-1909-01851-8. ISSN 0002-9904.
  4. ^ Gronwall, T. H. (1916). "Book Review: Graphische Methoden". Bulletin of the American Mathematical Society. 22 (8): 407–408. doi:10.1090/S0002-9904-1916-02812-6. ISSN 0002-9904.

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