View source for Wilhelm Blaschke

{{short description|Austrian mathematician (1885–1962)}}
{{Expand German|topic=bio|Wilhelm Blaschke|date=December 2009}}
{{Infobox scientist
| name              = Wilhelm Blaschke
| image             = Wilhelm Blaschke.jpg
| image_size        = 
| caption           = 
| birth_date        = {{birth date|1885|09|13|df=y}}
| birth_place       = [[Graz]], [[Austria-Hungary]]
| death_date        = {{death date and age|1962|03|17|1885|09|13|df=y}}
| death_place       = [[Hamburg]], [[West Germany]]
| nationality       = Austrian
| fields            = [[Mathematics]]
| workplaces        = [[University of Hamburg]]
| alma_mater        = [[University of Vienna]]
| doctoral_advisor  = [[Wilhelm Wirtinger]]
| doctoral_students = [[Shiing-Shen Chern]]<br>[[Luis Santaló]]<br>[[Emanuel Sperner]]<br>[[Gerhard Thomsen]]
| notable_students  = [[Alberto Dou Mas de Xaxàs]]
| known_for         = [[Blaschke product]]<br>[[Blaschke selection theorem]]<br>[[Blaschke–Santaló inequality]]
| awards            = 
}}
'''Wilhelm Johann Eugen Blaschke''' (13 September 1885 – 17 March 1962) was an [[Austria]]n [[mathematician]] working in the fields of [[differential geometry|differential]] and [[integral geometry]].

==Education and career==
Blaschke was the son of mathematician Josef Blaschke, who taught geometry at the Landes Oberrealschule in [[Graz]].
After studying for two years at the Technische Hochschule in Graz, he went to the [[University of Vienna]], and completed a doctorate in 1908 under the supervision of [[Wilhelm Wirtinger]].<ref name=mt>{{MacTutor Biography|id=Blaschke|mode=cs1}}</ref> His dissertation was ''Über eine besondere Art von Kurven vierter Klasse''.<ref name=mg/>

After completing his doctorate he spent several years visiting mathematicians at the major universities in Italy and Germany. He spent two years each in positions in Prague, Leipzig, Göttingen, and Tübingen until, in 1919, he took the professorship at the [[University of Hamburg]] that he would keep for the rest of his career.<ref name=mt/> His students at Hamburg included [[Shiing-Shen Chern]], [[Luis Santaló]], and [[Emanuel Sperner]].<ref name=mg>{{MathGenealogy |id=18601}}</ref>

In 1933 Blaschke signed the ''[[Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State]]''.<ref name=behnke/><ref name="Klee52">[[Ernst Klee]]: ''Das Personenlexikon zum Dritten Reich. Wer war was vor und nach 1945''. Fischer Taschenbuch Verlag, Zweite aktualisierte Auflage, Frankfurt am Main 2005, S. 52.</ref> However, he defended [[Kurt Reidemeister]] against the Nazis and, in the early 1930s, campaigned against [[Ludwig Bieberbach]] for leadership of the [[German Mathematical Society]], arguing that the society should remain international and apolitical in opposition to Bieberbach's wish to "enforce Nazi policies on German mathematics and race". However, by 1936 he was supporting Nazi policies, called himself "a Nazi at Heart", and was described by colleagues as "Mussolinetto" for his fascist beliefs.<ref name=mt/> He officially joined the [[Nazi Party]] in 1937.<ref name=behnke>''Heinrich Behnke (1898-1979): zwischen Mathematik und deren Didaktik'', Uta Hartmann, 2009 {{isbn|9783631588604}}</ref>

After the war, Blaschke was removed from his position at the University of Hamburg for his Nazi affiliation, but after an appeal his professorship was restored in 1946.<ref name=mt/> He remained at the university until his retirement in 1953.<ref name=mt/>

==Publications==
In 1916 Blaschke published one of the first books devoted to [[convex set]]s: ''Circle and Sphere'' (''Kreis und Kugel''). Drawing on dozens of sources, Blaschke made a thorough review of the subject with citations within the text to attribute [[credit (creative arts)|credit]] in a classical area of mathematics.

*[https://archive.org/details/kreisundkugel00blasgoog ''Kreis und Kugel''], Leipzig, Veit 1916;<ref>{{cite journal|author=Groß, Wilhelm|author-link=Wilhelm Gross|title=Kreis und Kugel: von Dr. Wilhelm Blaschke. Veit & Comp., Leipzig 1916, 169 S. 650 Mark|journal=Monatshefte für Mathematik und Physik|volume=28|year=1917|page=A4|doi=10.1007/BF01698249}}</ref> 3rd edn. Berlin, de Gruyter 1956
*[http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABN4015 ''Vorlesungen über Differentialgeometrie''], 3 vols., Springer, Grundlehren der mathematischen Wissenschaften 1921-1929 (vol. 1, Elementare Differentialgeometrie;<ref>{{cite journal|author=Bliss, G. A.|authorlink=Gilbert Ames Bliss|title=Blaschke on Differential Geometry|journal=Bull. Amer. Math. Soc.|year=1923|volume=29|issue=7|pages=322–325|url=http://www.ams.org/journals/bull/1923-29-07/S0002-9904-1923-03737-3/| doi = 10.1090/S0002-9904-1923-03737-3 |doi-access=free}}</ref> vol. 2, Affine Differentialgeometrie; vol. 3, Differentialgeometrie der Kreise und Kugeln, 1929)
*with G. Bol: ''Geometrie der Gewebe''. Berlin: Springer 1938<ref>{{cite journal|author=Walker, R. J.|title=Review: W. Blaschke and G. Bol, ''Geometrie der Gewebe''|journal=Bull. Amer. Math. Soc.|year=1939|volume=45|issue=9|pages=652–653|url=http://www.ams.org/journals/bull/1939-45-09/S0002-9904-1939-07052-3|doi=10.1090/s0002-9904-1939-07052-3|doi-access=free}}</ref>
*''Ebene Kinematik''. Leipzig: B.G. Teubner 1938,<ref>{{cite journal|author=Synge, J. L.|authorlink=John Lighton Synge|title=Review: W. Blaschke, ''Eben Kinematik''|journal=Bull. Amer. Math. Soc.|year=1939|volume=45|issue=11|pages=814–815|url=http://www.ams.org/journals/bull/1939-45-11/S0002-9904-1939-07071-7/|doi=10.1090/s0002-9904-1939-07071-7|doi-access=free}}</ref> 2nd expanded edn. with Hans Robert Müller, Oldenbourg, München 1956
*''Nicht-Euklidische Geometrie und Mechanik I, II, III''. Leipzig: B.G.Teubner (1942)
*''Zur Bewegungsgeometrie auf der Kugel.'' In: ''Sitzungsberichte der Heidelberger Akademie der Wissenschaften'' (1948)
*''Einführung in die Differentialgeometrie''. Springer 1950,<ref>{{cite journal|author=Allendoerfer, Carl B.|title=Review, W. Blaschke, ''Einführung in die Differentialgeometrie''|journal=Bull. Amer. Math. Soc.|year=1951|volume=57|issue=1, Part 1|pages=84–85|url=http://www.ams.org/journals/bull/1951-57-01/S0002-9904-1951-09454-9/|doi=10.1090/s0002-9904-1951-09454-9|doi-access=free}}</ref> 2nd expanded edn. with H. Reichardt 1960
*with Kurt Leichtweiß: ''Elementare Differentialgeometrie''. Berlin: Springer (5th edn. 1973)
*''Reden und Reisen eines Geometers''. Berlin : [[VEB Deutscher Verlag der Wissenschaften]] (1961; 2nd expanded edn.)
*''Mathematik und Leben'', Wiesbaden, Steiner 1951
*''Griechische und anschauliche Geometrie'', Oldenbourg 1953
*''Projektive Geometrie'', 3rd edn, Birkhäuser 1954
*''Analytische Geometrie'', 2nd edn., Birkhäuser 1954
*''Einführung in die Geometrie der Waben'', Birkhäuser 1955<ref>{{cite journal|author=Hsiung, C. C.|authorlink=Chuan-Chih Hsiung|title=Review: W. Blaschke, ''Einführung in die Geometrie der Waben''|journal=Bull. Amer. Math. Soc.|year=1957|volume=63|issue=3|pages=203–204|url=http://www.ams.org/journals/bull/1957-63-03/S0002-9904-1957-10104-9/|doi=10.1090/s0002-9904-1957-10104-9|doi-access=free}}</ref>
*''Vorlesungen über Integralgeometrie'', VEB, Berlin 1955
*''Reden und Reisen eines Geometers'', 1957
*''Kinematik und Quaternionen''. Berlin: [[VEB Deutscher Verlag der Wissenschaften]] (1960)
*''Gesammelte Werke'', Thales-Verlag, Essen 1982 vol. 1 {{isbn|3889082017}};<ref>{{cite journal|title=review of ''Gesammelte Werke, Band I'' by Wilhelm Blaschke, edited by W. Burau, S. S. Chern et al.|author=Willmore, Tom|journal=Proceedings of the Edinburgh Mathematical Society|volume=27|issue=3|date=October 1984|pages=347–349|doi=10.1017/S0013091500022549}}</ref> 1985 vol. 2 {{isbn|3889082025}}; 1985 vol. 3 {{isbn|3889082033}}

==Eponyms==
Blaschke's name has been lent as an [[eponym]] to a number of mathematical theorems and concepts:
*[[Blaschke selection theorem]]
*[[Blaschke–Lebesgue theorem]]
*[[Blaschke product]]
*[[Blaschke sum]]
*[[Blaschke condition]]
*[[Hilbert%27s_fourth_problem#Blaschke–Busemann_measure|Blaschke–Busemann measure]]
*[[Blaschke–Santaló inequality]]
*[[Blaschke conjecture]]: "The only [[Wiedersehen manifold]]s in any dimension are the standard Euclidean spheres."

==See also==
*[[Affine differential geometry]]
*[[Affine geometry of curves]]
*[[Body of constant brightness]]
*[[Web (differential geometry)]]
*[[Pestov–Ionin theorem]]

==References==
{{reflist}}

==External links==
* {{PM20|FID=pe/001869}}

{{Authority control}}

{{DEFAULTSORT:Blaschke, Wilhelm}}
[[Category:Nazi Party members]]
[[Category:1885 births]]
[[Category:1962 deaths]]
[[Category:Differential geometers]]
[[Category:Scientists from Graz]]
[[Category:People from the Duchy of Styria]]
[[Category:Academic staff of the University of Greifswald]]
[[Category:Austrian expatriates in Germany]]
[[Category:Mathematicians from Austria-Hungary]]
[[Category:20th-century Austrian mathematicians]]
[[Category:Members of the German Academy of Sciences at Berlin]]
[[Category:University of Vienna alumni]]
[[Category:Academic staff of the University of Hamburg]]
[[Category:Austrian Nazis]]