Lindemann, Ferdinand von

▪ German mathematician

born April 12, 1852, Hannover, Hanover [Germany]

died March 1, 1939, Munich, Germany

      German mathematician who is mainly remembered for having proved that the number π (pi) is transcendental—i.e., it does not satisfy any algebraic equation with rational coefficients. This proof established that the classical Greek construction problem of squaring the circle (constructing a square with an area equal to that of a given circle) by compass and straightedge is insoluble.

      Beginning in 1870 Lindemann studied at the University of Göttingen (Göttingen, University of), the University of Munich (Munich, University of), and the University of Erlangen, where he received his doctorate in 1873. Following postgraduate studies he taught at the University of Freiburg (Freiburg, Albert Ludwig University of) from 1877 to 1883.

      Lindemann's proof that π is transcendental was made possible by fundamental methods developed by the French mathematician Charles Hermite (Hermite, Charles) during the 1870s. In particular Hermite's proof of the transcendence of e, the base for natural logarithms (logarithm), was the first time that a number was shown to be transcendental. Lindemann visited Hermite in Paris and learned firsthand of this famous result. Building on Hermite's work, Lindemann published his proof in an article entitled “Über die Zahl π” (1882; “Concerning the Number π”).

      Lindemann's sudden fame led to his appointment in 1883 as professor of mathematics at the University of Königsberg (Königsberg, Albertus University of), Germany (now Kaliningrad, Russia), and 10 years later to a distinguished professorship at the University of Munich. His work in mathematics was primarily in geometry. In Königsberg he headed a distinguished community of young mathematicians that included Adolf Hurwitz (1859–1919), David Hilbert (Hilbert, David) (1862–1943), and Hermann Minkowski (Minkowski, Hermann) (1864–1909).

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