Wilhelm Johann Eugen Blaschke (13 September 1885 – 17 March 1962) was an

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in the fields of differential and

integral geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformation ...

Education and career

Blaschke was the son of mathematician Josef Blaschke, who taught geometry at the Landes Oberrealschule in

Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...

. After studying for two years at the Technische Hochschule in Graz, he went to the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...

, and completed a doctorate in 1908 under the supervision of

Wilhelm Wirtinger Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory. Biography He was born at Ybbs on the Danube and studied at the Unive ...

. His dissertation was ''Über eine besondere Art von Kurven vierter Klasse''. 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 The University of Hamburg (german: link=no, Universität Hamburg, also referred to as UHH) is a public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('' Allgemeines Vor ...

that he would keep for the rest of his career. His students at Hamburg included

Shiing-Shen Chern Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...

Luis Santaló Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician. He graduated from the University of Madrid and he studied at the University of Hamburg, where he received his Ph.D. in 1936. His advisor was Wilhe ...

, and

Emanuel Sperner Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at ...

. 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 Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat officially translated into English as the Vow of allegiance of the Professors of the German Universities and High-Schools to Ad ...

''.

Ernst Klee Ernst Klee (15 March 1942, Frankfurt – 18 May 2013, Frankfurt) was a German journalist and author. As a writer on Germany's history, he was best known for his exposure and documentation of medical crimes in Nazi Germany, much of which was concer ...

: ''Das Personenlexikon zum Dritten Reich. Wer war was vor und nach 1945''. Fischer Taschenbuch Verlag, Zweite aktualisierte Auflage, Frankfurt am Main 2005, S. 52. However, he defended

Kurt Reidemeister Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götting ...

against the Nazis and, in the early 1930s, campaigned against

Ludwig Bieberbach Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi. Biography Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate ...

for leadership of the

German Mathematical Society The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathe ...

, 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. He officially joined the

Nazi Party The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that crea ...

in 1937.''Heinrich Behnke (1898-1979): zwischen Mathematik und deren Didaktik'', Uta Hartmann, 2009 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. He remained at the university until his retirement in 1953.

Publications

In 1916 Blaschke published one of the first books devoted to

convex set In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex r ...

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 Credit (from Latin verb ''credit'', meaning "one believes") is the trust which allows one party to provide money or resources to another party wherein the second party does not reimburse the first party immediately (thereby generating a debt) ...

in a classical area of mathematics.
''Kreis und Kugel''
Leipzig, Veit 1916; 3rd edn. Berlin, de Gruyter 1956
''Vorlesungen über Differentialgeometrie''
3 vols., Springer, Grundlehren der mathematischen Wissenschaften 1921-1929 (vol. 1, Elementare Differentialgeometrie; vol. 2, Affine Differentialgeometrie; vol. 3, Differentialgeometrie der Kreise und Kugeln, 1929) *with G. Bol: ''Geometrie der Gewebe''. Berlin: Springer 1938 *''Ebene Kinematik''. Leipzig: B.G. Teubner 1938, 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, 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 (DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/). Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "un ...

(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 *''Vorlesungen über Integralgeometrie'', VEB, Berlin 1955 *''Reden und Reisen eines Geometers'', 1957 *''Kinematik und Quaternionen''. Berlin:

(1960) *''Gesammelte Werke'', Thales, Essen 1985

Namesake

A number of mathematical theorems and concepts is associated with the name of Blaschke. *

Blaschke selection theorem The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence \ of convex sets contained in a bounded set, the theorem guarantees the existence of a subsequence \ and a co ...

Blaschke–Lebesgue theorem In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form that every curve of a given width has area at least as large as the Reuleaux triangle, it is ...

Blaschke product In complex analysis, the Blaschke product is a bounded analytic function in the open unit disc constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers :''a''0, ''a''1, ... inside the unit disc, with the property ...

Blaschke sum In convex geometry and the geometry of convex polytopes, the Blaschke sum of two polytopes is a polytope that has a facet parallel to each facet of the two given polytopes, with the same measure. When both polytopes have parallel facets, the meas ...

Blaschke condition In complex analysis, the Blaschke product is a bounded analytic function in the open unit disc constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers :''a''0, ''a''1, ... inside the unit disc, with the propert ...

* Blaschke–Busemann measure * Blaschke–Santaló inequality *

Blaschke conjecture In mathematics—specifically, in Riemannian geometry—a Wiedersehen pair is a pair of distinct points ''x'' and ''y'' on a (usually, but not necessarily, two-dimensional) compact Riemannian manifold (''M'', ''g'') such that every g ...

: "The only Wiedersehen manifolds in any dimension are the standard Euclidean spheres."

References

External links

* {{DEFAULTSORT:Blaschke, Wilhelm Nazi Party members 1885 births 1962 deaths Differential geometers Scientists from Graz People from the Duchy of Styria University of Greifswald faculty Austrian expatriates in Germany Austro-Hungarian mathematicians 20th-century Austrian mathematicians Members of the German Academy of Sciences at Berlin University of Vienna alumni University of Hamburg faculty

Education and career

Publications

Namesake

See also

References

External links