Paul Finsler

Paul Finsler
Prof. Finsler 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

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]

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.

References

1. 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, S2CID 122841127.
4. Breger, Herbert (1992), "A restoration that failed: Paul Finsler's theory of sets", in Gillies, Donald (ed.), 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

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