Доклад: Carl Louis Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann
Born: 12 April 1852 in Hannover, Hanover (now Germany)
Died: 6 March 1939 in Munich, Germany
Ferdinand von Lindemann was the first to prove that p is transcendental, that is, p is not the root of any algebraic
equation with rational coefficients.
His father, also named Ferdinand Lindemann, was a
modern language teacher at the Gymnasium in Hannover at the time of his birth.
His mother was Emilie Crusius, the daughter of the headmaster of the Gymnasium.
When Ferdinand (the subject of this biography) was two years old his father was
appointed as director of a gasworks in Schwerin. The family moved to that town
where Ferdinand spent his childhood years and he attended school in Schwerin.
As was the standard practice of students in Germany in
the second half of the 19th century, Lindemann moved from one university to
another. He began his studies in Göttingen in 1870 and there he was much
influenced by Clebsch. He was fortunate to be taught by Clebsch for he had only
been appointed to Göttingen in 1868 and sadly he died in 1872. Later
Lindemann was able to make use of the lecture notes he had taken attending
Clebsch's geometry lectures when he edited and revised these note for
publication in 1876.
Lindemann also studied at Erlangen and at Munich. At
Erlangen he studied for his doctorate and, under Klein's direction, he wrote a
dissertation on nonEuclidean line geometry and its connection with nonEuclidean
kinematics and statics. The degree was awarded in 1873 for the dissertation
Uber unendlich kleine Bewegungen und über Kraftsysteme bei allgemeiner
projektivischer Massbestimmung.
After the award of his doctorate Lindemann set off to
visit important mathematical centres in England and France. In England he made
visits to Oxford, Cambridge and London, while in France he spent time at Paris
where he was influenced by Chasles, Bertrand, Jordan and Hermite. Returning to
Germany Lindemann worked for his habilitation. This was awarded by the
University of Würzburg in 1877 and later that year he was appointed as
extraordinary professor at the University of Freiburg. He was promoted to
ordinary professor at Freiburg in 1879.
Lindemann became professor at the University of
Königsberg in 1883. Hurwitz and Hilbert both joined the staff at
Königsberg while he was there. While in Königsberg he married
Elizabeth Küssner, an actress, and daughter of a local school teacher. In
1893 Lindemann accepted a chair at the University of Munich where he was to
remain for the rest of his career.
Lindemann's main work was in geometry and analysis. He
is famed for his proof that is transcendental. The problem of squaring the
circle, namely constructing a square with the same area as a given circle using
ruler and compasses alone, had been one of the classical problems of Greek
mathematics. In 1873, the year in which Lindemann was awarded his doctorate,
Hermite published his proof that e is transcendental. Shortly after this
Lindemann visited Hermite in Paris and discussed the methods which he had used
in his proof. Using methods similar to those of Hermite, Lindemann established
in 1882 that p was
also transcendental.
In fact his proof is based on the proof that e is
transcendental together with the fact that e^{<font}face=symbol>pi
= 1. Many historians of science regret that Hermite, despite doing most of the
hard work, failed to make the final step to prove the result concerning which
would have brought him fame outside the world of mathematics. This fame was
instead heaped on Lindemann but many feel that he was a mathematician clearly
inferior to Hermite who, by good luck, stumbled on a famous result. Although
there is some truth in this, it is still true that many people make their own
luck and in Lindemann's case one has to give him much credit for spotting the
trick which Hermite had failed to see.
Lambert had
proved in 1761 that p was
irrational but this was not enough to prove the impossibility of squaring the
circle with ruler and compass since certain algebraic numbers can be
constructed with ruler and compass. Lindemann's proof that p is transcendental finally
established that squaring the circle with ruler and compasses is insoluble. He
published his proof in the paper über die Zahl in 1882.
Physics was also an area of interest for Lindemann. He
worked on the theory of the electron, and came into conflict with Arnold
Sommerfeld on this subject. Eckert, in [4], looks at Lindemann's contributions
to physics, using manuscript materials, including correspondence with
Sommerfeld.
Another research interest of Lindemann was the history
of mathematics. He also undertook, in collaboration with his wife, translating
work. In particular they translated and revised some of Poincaré's writings.
Lindemann was elected to the Bavarian Academy of
Sciences in 1894 as an associate member, becoming a full member in the
following year. He given an honorary degree by the University of St Andrews in
1912.
Wussing writes in [1]:
Lindemann was one of the founders of the modern German
educational system. He emphasised the development of the seminar and in his
lectures communicated the latest research results. He also supervised more than
sixty doctoral students, including David Hilbert.
Hilbert was
Lindemann's doctoral student in Königsberg. Another of his doctoral
students was Oskar Perron who studied under him in Munich.
J J O'Connor and E F Robertson
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