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Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician and professor at the University of Bonn from 1864. Peter Gustav Dirichlet was his teacher. He supervised the early work of Felix Klein. While
Lipschitz gave his name to the Lipschitz
continuity
condition, he worked in a broad range of areas. These
included number theory, algebras with involution, mathematical
analysis, differential
geometry and classical
mechanics. He wrote: Lehrbuch der
Analysis (two
volumes, Bonn 1877, 1880); Wissenschaft
und
Staat (Bonn,
1874); Untersuchungen
über
die Summen von Quadraten (Bonn,
1886); Bedeutung der
theoretischen Mechanik (Berlin,
1876). Rudolf
Lipschitz's father was a
landowner and Rudolf was born at his father's estate at Bönkein
which
was near Königsberg. He began his university studies at a young
age, entering the University of Königsberg and studying there
under Franz Neumann. Following the custom of that time to study at
different universities, Lipschitz went from Königsberg to Berlin
where he studied under Dirichlet. This was not a particularly easy time
for Lipschitz whose health was rather poor and caused him to take a
year away from his studies to recover. However, he completed his
doctoral studies with the award of a doctorate on 9 August 1853. There was no immediate university teaching
post for Lipschitz who spent four years teaching at the Gymnasium in
Königsberg and at the Gymnasium in Elbing. In 1857, however,
Lipschitz became a Privatdozent at the University of Berlin. In this
same year he married Ida Pascha, the daughter of one of the landowners
with an estate near to his father's. Then in 1862 he became an
extraordinary professor at Breslau. During
his two years in Breslau, Lipschitz
wrote two not very important papers. Jointly with Heinrich
Schröter and M Frankenheim, he
founded a seminar in mathematics and mathematical physics. He was
nominated an ordinary professor by the University of Bonn and he left
Breslau at Easter 1864. The University of Bonn was where Lipschitz
spent the rest of his career. This was not because he did not have the
opportunity to move. Quite the reverse, after Clebsch died in November 1872, he
was offered his chair at Göttingen in the following year.
Lipschitz was quite happy at Bonn, however, and he turned down the
offer from Göttingen. Klein received his doctorate from
the University of Bonn in 1868. He was supervised by Plücker, and examined by
Lipschitz. Perhaps if Klein had still been in
Göttingen when Lipschitz was offered the chair there, he may have
been more inclined to accept. Perhaps the most remarkable fact about Lipschitz's work was the widely different topics on which he contributed :-
He worked on quadratic differential forms and mechanics. Lipschitz mechanical interpretation of Riemann's differential geometry would prove to be a vital step in the road towards Einstein's special theory of relativity. Lipschitz showed that :-
Lipschitz's work on the Hamilton-Jacobi method for integrating the
equations of motion of a general dynamical system led to important
applications in celestial mechanics. Lipschitz is remembered for the 'Lipschitz
condition', an inequality that guarantees a unique solution to the differential
equation y'
= f (x, y). Peano gave an existence theorem
for this differential equation, giving conditions which guarantee at
least one solution. His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras. In fact Lipschitz rediscovered Clifford algebras and was the first to apply them to represent rotations of Euclidean spaces, thus introducing the spin groups Spin(n). |