|
In 1872, upon appointment, at the young age of twenty-three, to full prores
sorship on the Philosophical Faculty and Sinate of the University of Erlangen,
Felix Klein (1849-1925) preaented, according to custom, both an oral speech
introducing himself to his new faculty associates and a written paper exhibiting
research interests in his field of mathematics. The speech was aimed at a wide
university audience and expressed klein's pedagogical view of the unity of all
knowledge and the ideal that a complete education should not be neglected
|
because
of special studies. The written work, which was passed out at the time
of the speech, was designed for
his departmental colleagus. Thus, the two
ters and his serious commitment to mathematical research.
The written paper, based upon work by himself and Sophus Lie (1842-
1899) in group theory, set forth a remarable definition of "a geometry" that
served to codify essentially all the existing geometries of the time and pointed
the way to codify essentially all the existing geometries of the time and pointed
the way to new and fruitful avenues of geometrical research. It has become
known as the Erlanger Programm, and it appeared right at the time when group
theory was invading almost every domain of mathematics, and some mathema
ticians were beginning to feel that all mathematics is nothing but some aspect of
group theory. This programm can be regarded as perhaps Klein's single most
important mathematical accomplishment.
Felix Klein was born in Dusseldorf in 1849. He studied at Bonn, Got
tingen, and Berlin, and served as assistant to Julius Plucker Bonn. His first
professorial position was at the University of Erlangen (1872-1875), where his
inaugural paper set forth the geometric program described above. He then
taught at Munich, Leipzig University (1872-1875), and Gottingen University
(1886-1913), officiating as department head at the altter institution. Hi was
deitor of the Mathematische Annalen and founder of the great mathematical
Encyklopadie. He was aa lucid expositor, an inspiring teacher, and a gifted
lecturer. Hi died at Gottingen in 1925.
During klein's tenure as department head at Gottingen University, that
institution became a mecca for mathematics students from all over the worle. A
remarkable number of top-flight mathematicians studied at the university or
served there as worthy successors to Garss, Dirichlet, and Riemann, making
the Gottingen school of mathematics one of the most famous of modern times.
 |