# Carl David Tolmé Runge

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

Carl Runge | |
---|---|

Born | |

Died | 3 January 1927 70) | (aged

Residence | Germany |

Citizenship | German |

Alma mater | Berlin University |

Known for | Runge–Kutta method Runge's phenomenon Laplace–Runge–Lenz vector |

Scientific career | |

Fields | Mathematics Physics |

Institutions | Leibniz University Hannover (1886–1904) University of Göttingen (1904–1925) |

Doctoral advisor | Karl Weierstrass Ernst Kummer |

Doctoral students | Max Born Friedrich Adolf Willers Hermann König |

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.

## Biography

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 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.

### Family

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.

## Honors

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

- Runge-Kutta numerical method for the approximate solutions of ordinary differential equations
- Runge's phenomenon
- Runge's method for diophantine equations.
- Laplace–Runge–Lenz vector
- Runge's theorem

## Works

- 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)
- Vector Analysis (Goettingen, 1919)

## Bibliography

- 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.

## External links

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