Paul Finsler (born 11 April 1894, in

Heilbronn Heilbronn () is a List of cities and towns in Germany, city in northern Baden-Württemberg, Germany, surrounded by Heilbronn (district), Heilbronn District. From the late Middle Ages on, it developed into an important trading centre. At the begi ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

, died 29 April 1970 in

Zurich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

) was a German and Swiss

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, where he received his Ph.D. in 1919 under the supervision of

Constantin Carathéodory Constantin Carathéodory (; 13 September 1873 – 2 February 1950) was a Greeks, Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, ...

. He studied for his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

at the

University of Cologne The University of Cologne () is a university in Cologne, Germany. It was established in 1388. It closed in 1798 before being re-established in 1919. It is now one of the largest universities in Germany with around 45,187 students. The Universit ...

, receiving it in 1922. He joined the faculty of the

University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...

in 1927, and was promoted to

ordinary professor Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

there in 1944. Finsler's thesis work concerned

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, and Finsler spaces were named after him by

Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...

in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a

triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

in the

Euclidean plane In mathematics, a Euclidean plane is a Euclidean space of Two-dimensional space, dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position (geometry), position of eac ...

, is named after Finsler and his co-author

Hugo Hadwiger Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss people, Swiss mathematician, known for his work in geometry, combinatorics, and cryptography. Biography Although born in Karlsruhe, Ge ...

, as is the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex. Finsler is also known for his work on the

foundations of mathematics Foundations of mathematics are the mathematical logic, logical and mathematics, mathematical framework that allows the development of mathematics without generating consistency, self-contradictory theories, and to have reliable concepts of theo ...

, developing a

non-well-founded set theory Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axio ...

with which he hoped to resolve the contradictions implied by

Russell's paradox In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains ...

Publications

* (Reprinted by Birkhäuser (1951)) * * * * *Finsler: ''Aufsätze zur Mengenlehre.'' (ed. G. Unger) 1975. *

Publications

References

Further reading