Carl Louis Ferdinand von Lindemann
Quick Info
Born
12 April 1852
Hannover, Hanover (now Germany)
Died
6 March 1939
Munich, Germany
Summary
Ferdinand von Lindemann
was the first to prove that π is transcendental, i.e. π is not the root of any algebraic equation with rational coefficients.
Biography
Ferdinand von Lindemann
's 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
19
th
century, Lindemann moved from one university to another. He began his studies in Gottingen 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 Gottingen 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
non-Euclidean
line geometry and its connection with non-Euclidean kinematics and statics. The degree was awarded in
1873
for the dissertation
Uber unendlich kleine Bewegungen und uber 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 Wurzburg 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 Konigsberg in
1883
.
Hurwitz
and
Hilbert
both joined the staff at Konigsberg while he was there. While in Konigsberg he married Elizabeth Kussner, 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 π is
transcendental
, that is, π is not the root of any algebraic equation with
rational
coefficients. 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 π was also transcendental.
In fact his proof is based on the proof that
e
is transcendental together with the fact that
e
i
π
=
?
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 π 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 π is transcendental finally established that squaring the circle with ruler and compasses is insoluble. He published his proof in the paper
Uber die Zahl π
ⓣ
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
Poincare
'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 Konigsberg. Another of his doctoral students was
Oskar Perron
who studied under him in Munich.
- R V Jones, H Wussing, Biography in
Dictionary of Scientific Biography
(
New York
1970
-
1990)
. See
THIS LINK
.
- Biography in
Encyclopaedia Britannica.
http://www.britannica.com/biography/Ferdinand-von-Lindemann
- C Caratheodory, Nekrolog auf Ferdinand von Lindemann,
Sitzungsberichte der mathematisch Abteilung der Bayrischen Akademie der Wissenschaften zu Munich
1
(1940)
,
61
-
63
.
- M Eckert, Mathematik auf Abwegen : Ferdinand Lindemann und die Elektronentheorie,
Centaurus
39
(2)
(1997)
,
121
-
140
.
- R Fritsch, The transcendence of π has been known for about a century - but who was the man who discovered it?,
Resultate Math.
7
(2)
(1984)
,
164
-
183
.
- R C Gupta, Lindemann's discovery of the transcendence of π : a centenary tribute,
Ganita-Bharati. Bulletin of the Indian Society for the History of Mathematics
4
(3
-
4)
(1982)
,
102
-
108
.
- F von Lindemanns
70
Geburtstag,
Jahresberichte der Deutschen Mathematiker-Vereinigung
31
(1922)
,
24
-
30
.
- M Waldschmidt, Les debuts de la theorie des nombres transcendants, in
La recherche de la verite
(
Paris,
1999)
,
73
-
96
.
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)
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)
Written by
J J O'Connor and E F Robertson
Last Update March 2001