Ferdinand von Lindemann
Ferdinand von Lindemann | |
|---|---|
 Carl Louis Ferdinand von Lindemann | |
| Born | 12 April 1852 |
| Died | 6 March 1939 (aged 86) Munich, Germany |
| Alma mater | Friedrich-Alexander-Universität Erlangen-Nürnberg |
| Known for |
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| Scientific career | |
| Fields | Mathematics |
| Institutions | |
| Doctoral advisor | C. Felix Klein[1] |
| Doctoral students |
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Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician who proved in 1882 that π (pi) is a transcendental number, meaning it is not a root of any nonzero polynomial with rational coefficients.
Life and education
Lindemann was born in Hanover, the capital of the Kingdom of Hanover. His father, Ferdinand Lindemann, taught modern languages at a gymnasium in Hanover. His mother, Emilie Crusius, was the daughter of the gymnasium's headmaster. The family later moved to Schwerin, where young Ferdinand attended school.
He studied mathematics at Göttingen, Erlangen, and Munich. At Erlangen he received a doctorate, supervised by Felix Klein,[1] on non-Euclidean geometry. Lindemann subsequently taught in Würzburg and at the University of Freiburg. During his time in Freiburg, Lindemann devised his proof that π is a transcendental number (see the Lindemann–Weierstrass theorem). After his time in Freiburg, Lindemann transferred to the University of Königsberg. While a professor in Königsberg, Lindemann acted as supervisor for the doctoral theses of the mathematicians David Hilbert, Hermann Minkowski, and Arnold Sommerfeld.[2]
Transcendence proof
In 1882, Lindemann published the result for which he is best known, the transcendence of π.[3] His methods were similar to those used nine years earlier by Charles Hermite to show that e, the base of natural logarithms, is transcendental, and the works of Joseph Liouville from the 1840s establishing the existence of transcendental numbers.[4]: 127 Before the publication of Lindemann's proof, Johann Heinrich Lambert had already shown that π is irrational in 1768.[4]: 119
References
- ^ a b Ferdinand von Lindemann at the Mathematics Genealogy Project
- ^ "Ferdinand von Lindemann - Biography". Maths History. Retrieved 2022-08-06.
- ^ Lindemann, F. (1882). "Ueber die Zahl π*)". Mathematische Annalen (in German). 20 (2): 213–225. doi:10.1007/BF01446522. ISSN 0025-5831. Retrieved 2026-04-12.
- ^ a b Dunham, William (2005). The Calculus Gallery. Princeton University Press. ISBN 978-0-691-13626-4.
External links
Media related to Ferdinand von Lindemann at Wikimedia Commons- O'Connor, John J.; Robertson, Edmund F., "Ferdinand von Lindemann", MacTutor History of Mathematics Archive, University of St Andrews
- Ferdinand von Lindemann at the Mathematics Genealogy Project
- Lindemann, F. "Über die Zahl π", Mathematische Annalen 20 (1882): pp. 213–225.