Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

, and spectroscopist. He was co-developer and co-

eponym An eponym is a noun after which or for which someone or something is, or is believed to be, named. Adjectives derived from the word ''eponym'' include ''eponymous'' and ''eponymic''. Eponyms are commonly used for time periods, places, innovati ...

of the Runge–Kutta method (), in the field of what is today known as

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

Life and work

Runge spent the first few years of his life in

Havana Havana (; ) is the capital and largest city of Cuba. The heart of La Habana Province, Havana is the country's main port and commercial center. The family later moved to

Bremen Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (, ), is the capital of the States of Germany, German state of the Bremen (state), Free Hanseatic City of Bremen (), a two-city-state consisting of the c ...

, where his father died early (in 1864). In 1880, he received his Ph.D. in mathematics at

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

, where he studied under

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school t ...

. In 1886, he became a professor at the Technische Hochschule Hannover in

Hanover Hanover ( ; ; ) is the capital and largest city of the States of Germany, German state of Lower Saxony. Its population of 535,932 (2021) makes it the List of cities in Germany by population, 13th-largest city in Germany as well as the fourth-l ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

. His interests included mathematics,

spectroscopy Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Spectro ...

geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...

, and

astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...

. In addition to pure mathematics, he did experimental work studying

spectral line A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission (electromagnetic radiation), emission or absorption (electromagnetic radiation), absorption of light in a narrow frequency ...

s of various elements (together with Heinrich Kayser), and was very interested in the application of this work to

astronomical spectroscopy Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the electromagnetic spectrum, spectrum of electromagnetic radiation, including Visible light astronomy, visible light, Ultraviolet astronomy, ultr ...

. In 1904, on the initiative of

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

he received a call to the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, 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 Richard Courant (January 8, 1888 – January 27, 1972) was a German-American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

Honors

The

crater A crater is a landform consisting of a hole or depression (geology), depression on a planetary surface, usually caused either by an object hitting the surface, or by geological activity on the planet. A crater has classically been described ...

Runge on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

is named after him. The Schumann–Runge bands of molecular oxygen are named after him and

Victor Schumann Victor Schumann (21 December 1841 – 1 September 1913) was a physicist and spectroscopist who in 1893 discovered the vacuum ultraviolet. Schumann studied the extreme ultraviolet region of the electromagnetic spectrum. For this, he used a Pr ...

Works

Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen Curven
(PhD dissertation, Friese, 1880)
Praxis der Gleichungen
(G.J. Göschen, Leipzig, 1900) *
Praxis der Gleichungen, zweite, verbesserte Auflage
(W. de Gruyter, Berlin, 1921)
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) * Graphische Methoden (Teubner, 1912) *
Graphische Methoden, dritte Auflage
(Teubner, 1928)
Vektoranalysis
(S. Hirzel, Leipzig, 1919) *
Vector Analysis
(Methuen & Co., London, 1923); translated from 1919 German original by H. Levy * Carl Runge und Hermann König
Vorlesungen über numerisches Rechnen
(Springer, Heidelberg, 1924)

Bibliography

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

References

External links

*
Biography
* {{DEFAULTSORT:Runge, Carl 1856 births 1927 deaths Academic staff of the University of Göttingen 19th-century German mathematicians 19th-century German physicists Numerical analysts Scientists from Bremen (city) German spectroscopists Academic staff of Leibniz University Hannover Humboldt University of Berlin alumni 20th-century German mathematicians 20th-century German physicists Presidents of the German Mathematical Society