Paul Finsler

{{Infobox scientist

| name = Paul Finsler

| image = FinslerPaul Zurich1932.tif

| image_size =

| caption = Prof. Finsler at the International Mathematical Congress, Zürich 1932.

| birth_date = {{birth date|1894|4|11|df=y}}

| birth_place = Heilbronn, Germany

| death_date = {{death date and age|1970|4|29|1894|4|11|df=y}}

| death_place = Zurich, Switzerland

| resting_place =

| citizenship =

| field = Mathematics

| work_institutions = University of Zurich

| alma_mater = University of Göttingen

| academic_advisors = Constantin Carathéodory

| doctoral_students =

| known_for = Finsler manifold
Finsler's lemma
Finsler–Hadwiger theorem
{{no wrap|Hadwiger–Finsler inequality}}
Non-well-founded set theory

| influences =

| influenced =

| prizes =

| footnotes =

| signature =

}}

Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician.{{MacTutor|id=Finsler|title=Paul Finsler}}

Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory.{{mathgenealogy|name=Paul Finsler|id=52428}}. He studied for his habilitation at the University of Cologne, receiving it in 1922. He joined the faculty of the University of Zurich in 1927, and was promoted to ordinary professor there in 1944.

Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. 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.{{citation

| last1 = Finsler | first1 = Paul

| last2 = Hadwiger | first2 = Hugo | author2-link = Hugo Hadwiger

| doi = 10.1007/BF01214300

| issue = 1

| journal = Commentarii Mathematici Helvetici

| pages = 316–326

| title = Einige Relationen im Dreieck

| volume = 10

| year = 1937| s2cid = 122841127

}}. 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.{{citation

| last = Breger | first = Herbert

| contribution = A restoration that failed: Paul Finsler's theory of sets

| editor-last = Gillies | editor-first = Donald

| pages = 249–264

| publisher = Oxford University Press

| title = Revolutions in Mathematics

| year = 1992| title-link = Revolutions in Mathematics

}}.

Publications

{{Citation | last1=Finsler | first1=Paul | title=Über Kurven und Flächen in allgemeinen Räumen | publisher=Göttingen | series=Dissertation | jfm=46.1131.02 | year=1918 | url=https://catalog.hathitrust.org/Record/007896148}} (Reprinted by Birkhäuser (1951)){{cite journal|author=Busemann, H.|authorlink=Herbert Busemann|title=Review: Über Kurven und Flächen in allgemeinen Räumen, by P. Finsler|journal=Bull. Amer. Math. Soc.|year=1952|volume=58|issue=1|page=102|url=https://www.ams.org/journals/bull/1952-58-01/S0002-9904-1952-09572-0/|doi=10.1090/s0002-9904-1952-09572-0|doi-access=free}}
{{cite journal | last1=Finsler | first1=Paul|url=https://eudml.org/doc/145712 |title=Gibt es Widersprüche in der Mathematik? |journal=Jahresbericht der Deutschen Mathematiker-Vereinigung|volume=34|pages=143–154|year=1926}}
{{cite journal|url=http://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002369001|title=Formale Beweise und die Entscheidbarkeit|journal=Mathematische Zeitschrift|year=1926|volume=25|pages=676–682|doi=10.1007/bf01283861|last1=Finsler|first1=Paul|s2cid=121054124}}
{{cite journal|title=Über die Grundlegung der Mengenlehre. Erster Teil.|url=http://eudml.org/doc/167904|journal=Mathematische Zeitschrift|volume=25|year=1926|pages=683–713|doi=10.1007/bf01283862|last1=Finsler|first1=Paul}} {{cite journal|title=Über die Grundlegung der Mengenlehre. Zweiter Teil.|journal=Commentarii Mathematici Helvetici |volume=38|issue=1|year=1963|pages=172–218|doi=10.1007/bf02566915|last1 = Finsler|first1 = Paul|s2cid=124928448 }}
{{cite journal |doi=10.1007/BF01297507|title = Die Existenz der Zahlenreihe und des Kontinuums|journal = Commentarii Mathematici Helvetici|volume = 5|pages = 88–94|year = 1933|last1 = Finsler|first1 = P.|s2cid = 120768947}}
Finsler: Aufsätze zur Mengenlehre. (ed. G. Unger) 1975.
{{cite book |editor-last1=Booth|editor-first=David |editor-last2=Ziegler|editor-first2=Renatus|date=1996 |title=Finsler Set Theory: Platonism and Circularity. "Translation of Paul Finsler's papers on set theory with introductory comments"|publisher=Birkhäuser Basel |doi=10.1007/978-3-0348-9031-1 |isbn=978-3-0348-9876-8}}

Paul Finsler

Publications

References

Further reading