The Online Encyclopedia and Dictionary






Ferdinand von Lindemann

Carl Louis Ferdinand von Lindemann (April 12, 1852 - March 6 1939) was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i.e., it is not a zero of any polynomial with rational coefficients.

Early life and education

Lindemann was born in Hannover, Germany. His father, Ferdinand Lindemann, taught modern languages at a Gymnasium in Hannover. 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, on non-Euclidean geometry.

Transcendence proof

In 1882, he published the result for which he is best known, the transcendence of π. His methods were similar to those used nine years earlier by Charles Hermite to show that e, the base of natural logarithms, is transcendental. Before the publication of Lindemann's proof, it was known that if π is transcendental, then the ancient and celebrated problem of squaring the circle by straightedge and compass could not be solved.


While a professor at the University of Königsberg, Lindemann acted as supervisor for the doctoral thesis of David Hilbert.

See also Lindemann-Weierstrass theorem.

Last updated: 10-29-2005 02:13:46