Paul Finsler

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Prof. Finsler at the International Mathematical Congress, Zürich 1932.

Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician.[1]

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]

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]


  • Finsler, Paul (1918), Über Kurven und Flächen in allgemeinen Räumen, Dissertation, Göttingen, JFM 46.1131.02 (Reprinted by Birkhäuser (1951))[5]
  • "Gibt es Widersprüche in der Mathematik? (Antrittsvorlesung Köln 1923)". Jahresbericht DMV. 34. 1926.
  • "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. 1926. doi:10.1007/bf01283861.
  • "Über die Grundlegung der Mengenlehre. Erster Teil". Mathematische Zeitschrift. 25: 683–713. 1926. doi:10.1007/bf01283862. "Über die Grundlegung der Mengenlehre. Zweiter Teil". Commentarii Mathematici Helvetici (CMH). 38 (1): 172–218. 1963. doi:10.1007/bf02566915.
  • Die Existenz der Zahlenreihe und des Kontinuums. CMH 1933.
  • 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.


  1. ^ a b c d e f O'Connor, John J.; Robertson, Edmund F., "Paul Finsler", MacTutor History of Mathematics archive, University of St Andrews.
  2. ^ Paul Finsler at the Mathematics Genealogy Project.
  3. ^ Finsler, Paul; Hadwiger, Hugo (1937), "Einige Relationen im Dreieck", Commentarii Mathematici Helvetici, 10 (1): 316–326, doi:10.1007/BF01214300.
  4. ^ Breger, Herbert (1992), "A restoration that failed: Paul Finsler's theory of sets", in Gillies, Donald, Revolutions in Mathematics, Oxford University Press, pp. 249–264.
  5. ^ Busemann, H. (1952). "Review: Über Kurven und Flächen in allgemeinen Räumen, by P. Finsler". Bull. Amer. Math. Soc. 58 (1): 102. doi:10.1090/s0002-9904-1952-09572-0.

Further reading[edit]

  • Burckhardt, J. J. (1980), Die Mathematik an der Universität Zurich 1916-1950 unter den Professoren R. Fueter, A. Speiser und P. Finsler, Basel.