Paul Finsler
Encyclopedia
Paul Finsler in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
) was a German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
and Swiss mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Finsler did his undergraduate studies at the Technische Hochschule Stuttgart
University of Stuttgart
The University of Stuttgart is a university located in Stuttgart, Germany. It was founded in 1829 and is organized in 10 faculties....
, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory
Constantin Carathéodory
Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
. He studied for his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
at the University of Cologne
University of Cologne
The University of Cologne is one of the oldest universities in Europe and, with over 44,000 students, one of the largest universities in Germany. The university is part of the Deutsche Forschungsgemeinschaft, an association of Germany's leading research universities...
, receiving it in 1922. He joined the faculty of the University of Zurich
University of Zurich
The University of Zurich , located in the city of Zurich, is the largest university in Switzerland, with over 25,000 students. It was founded in 1833 from the existing colleges of theology, law, medicine and a new faculty of philosophy....
in 1927, and was promoted to ordinary professor there in 1944.
Finsler's thesis work concerned differential geometry, and Finsler spaces
Finsler manifold
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold together with the structure of an intrinsic quasimetric space in which the length of any rectifiable curve is given by the length functional...
were named after him by Élie Cartan
Élie Cartan
Élie Joseph Cartan was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications...
in 1934. The Hadwiger–Finsler inequality
Hadwiger–Finsler inequality
In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler...
, a relation between the side lengths and area of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger
Hugo Hadwiger
Hugo Hadwiger was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.-Biography:...
. Finsler is also known for his work on the foundations of mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
, developing a non-well-founded set theory
Non-well-founded set theory
Non-well-founded set theories are variants of axiomatic set theory which allow sets to contain themselves and otherwise violate the rule of well-foundedness...
with which he hoped to resolve the contradictions implied by Russell's paradox
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...
.