Paul Finsler

Paul Finsler (11 April 1894 – 29 April 1970) was a German and Swiss mathematician.^[1]

Paul Finsler
Finsler (from a group portrait) at the International Mathematical Congress, Zürich, 1932
Born	(1894-04-11)11 April 1894 Heilbronn, Germany
Died	29 April 1970(1970-04-29) (aged 76) Zurich, Switzerland
Alma mater	University of Göttingen
Known for	Finsler manifold Finsler's lemma Finsler–Hadwiger theorem Hadwiger–Finsler inequality Non-well-founded set theory
Scientific career
Fields	Mathematics
Institutions	University of Zurich
Academic advisors	Constantin Carathéodory

Born in Heilbronn, Germany, Finsler did his undergraduate studies at the Technische Hochschule Stuttgart,^[1] and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory.^[2] He studied for his habilitation at the University of Cologne, receiving it in 1922.^[1] He joined the faculty of the University of Zurich in 1927, and was promoted to ordinary professor there in 1944.^[1] He died on 29 April 1970.

Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934.^[1] The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger, as is the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex.^[3] Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox.^[1][4]

Publications

• Finsler, Paul (1918), Über Kurven und Flächen in allgemeinen Räumen, Dissertation, Göttingen, JFM 46.1131.02 (Reprinted by Birkhäuser (1951))^[5]
• Finsler, Paul (1926). "Gibt es Widersprüche in der Mathematik?". Jahresbericht der Deutschen Mathematiker-Vereinigung. 34: 143–154.
• Finsler, Paul (1926). "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. doi:10.1007/bf01283861. S2CID 121054124.
• Finsler, Paul (1926). "Über die Grundlegung der Mengenlehre. Erster Teil". Mathematische Zeitschrift. 25: 683–713. doi:10.1007/bf01283862. Finsler, Paul (1963). "Über die Grundlegung der Mengenlehre. Zweiter Teil". Commentarii Mathematici Helvetici. 38 (1): 172–218. doi:10.1007/bf02566915. S2CID 124928448.
• Finsler, P. (1933). "Die Existenz der Zahlenreihe und des Kontinuums". Commentarii Mathematici Helvetici. 5: 88–94. doi:10.1007/BF01297507. S2CID 120768947.
• Finsler: Aufsätze zur Mengenlehre. (ed. G. Unger) 1975.
• Booth, David; Ziegler, Renatus, eds. (1996). Finsler Set Theory: Platonism and Circularity. "Translation of Paul Finsler's papers on set theory with introductory comments". Birkhäuser Basel. doi:10.1007/978-3-0348-9031-1. ISBN 978-3-0348-9876-8.