**Carl Runge** worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements.

- Carl was the third of his parents' four sons.
- Although Carl was born in Bremen, he spent his early years in Havana.
- Three of Carl's four older siblings eventually settled in England.
- Carl attended the Lyceum in Bremen and, in 1875, passed the examinations required for university entrance.
- Runge's career as a student of literature was, however, short lived for after six weeks of the course he changed to mathematics and physics.
- Runge attended courses with fellow student Max Planck and they became close friends, remaining so for the rest of their lives.
- In the autumn of 1877 Planck and Runge both went to Berlin but Runge turned to pure mathematics after attending Karl Weierstrass's lectures.
- Although Runge had committed himself to the study of pure mathematics he did not lose his initial interest in philosophy.
- Paulsen had just been appointed as an extraordinary professor at Berlin and Runge rated him extremely highly.
- Now, although Weierstrass was his advisor, he had not suggested the topic of Runge's thesis; rather this had come out of discussions he had with other students in the Mathematischer Verein in which he was actively engaged.
- Runge then worked on a procedure for the numerical solution of algebraic equations in which the roots were expressed as infinite series of rational functions of the coefficients.
- There were three standard methods for the numerical solution of such equations, namely by Newton, Bernoulli and Gräffe, and the method found by Runge had all three of the standard methods as special cases.
- Runge had published little at this stage in his career but after visiting Mittag-Leffler in Stockholm in September 1884 he was persuaded by Mittag-Leffler to write up the results he had produced.
- Fortunately this did not prove to be an obstacle for long for in March 1886 Runge obtained a chair at the Technische Hochschule at Hannover.
- Runge's home at Hannover ...
- Runge was a man of affairs and of great personal charm.
- Within a year of taking up the professorship at Hannover, Runge had moved away from pure mathematics to study the wavelengths of the spectral lines of elements other than hydrogen.
- Kayser and Runge published seven joint papers in the Proceedings of the Berlin Academy of Science over a period of seven years.
- Runge did a great deal of experimental work and published a great quantity of results.
- Runge continued his work on spectroscopy alone for six months but then persuaded Friedrich Paschen to join him.
- Runge visited England in 1895 and became friendly with Lord Rayleigh.
- At this stage Runge continued his work with Julius Precht who had previously held the Extraordinary Chair of Theoretical Physics at Heidelberg.
- It is interesting to consider why Runge remained so long at the Technische Hochschule at Hannover while others were appointed to more prestigious chairs.
- The reason almost certainly is that Runge did not fit in.
- Physicists, however, considered Runge a mathematician and would have not considered him entirely suitable for a chair of physics at one of the leading institutions.
- It is worth remarking at this point that Runge always considered himself a mathematician.
- At Göttingen, Runge became highly involved in teaching and undertook less research.
- Runge reached the retirement age of 68 in 1923 but he continued to run his Institute until his successor, Gustav Herglotz, arrived in 1925.

Born 30 August 1856, Bremen, Germany. Died 3 January 1927, Göttingen, Germany.

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Analysis, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive