Background

Wilhelm Johann Eugen Blaschke was born on September 13, 1885, in Graz, Austria. Blaschke’s father, Josef Blaschke (1852-1917), was a professor of descriptive geometry at the Landes Oberrealschule at Graz.

Education

Blaschke began his studies at the Technische Hochschule of Graz and earned his doctorate from the University of Vienna in 1908. For more than a decade afterward, he traveled through Europe, seeking contact with many of the leading geometers of his day. He spent some months in Pisa with Luigi Bianchi and a semester in Göttingen, drawn there by Felix Klein, David Hilbert, and Carl Runge.

Career

After receiving his doctorate degree in 1908, Blaschke worked at Bonn with Eduard Study, whose main fields of research were geometry, kinematics, and the theory of invariants. Blaschke became Privatdozent at Bonn in 1910, but in the following year, he went to the University of Greifswald to join Friedrich Engel, with whom he shared an admiration for the great Norwegian mathematician Sophus Lie.

In 1913 Blaschke accepted an extraordinary professorship at the Deutsche Technische Hochschule in Prague, and in 1915 he moved to Leipzig, where he became a close friend of Gustav Herglotz. Two years later he was made full professor at the University of Königsberg. After a short stay at Tübingen, Blaschke was called in 1919 to the full professorship of mathematics at the University of Hamburg, a position he retained until his retirement in 1953. He also held visiting professorships at Johns Hopkins University, at the University of Chicago, at the University of Istanbul, and at the Humboldt University in Berlin, and lectured at universities all over the world.

At Hamburg, Blaschke succeeded within a few years in gaining worldwide recognition for the department of mathematics of the newly founded university, for he was able to attract to Hamburg such well-known mathematicians as Erich Hecke, Emil Artin, and Helmut Hasse. Very soon Hamburg became a center of great mathematical activity and productivity, testimony to which is given by the Abhandlungen aus dem mathematischen Seminar der Universität Hamburg and the Hamburger Mathematische Einzelschriften, both founded by Blaschke.

Blaschke made “kinematic mapping” (discovered independently in 1911 by Josef Grünwald), which established a mapping between the group of isometries (motions) in the plane and the threedimensional point space, a central tool in kinematics; and in an abstract turn given to it by Kurt Reidemeister, it proved very useful in the axiomatic foundation of several geometries. In Kreis und Kugel (1916), Blaschke investigated the isoperimetric properties of convex bodies, characterizing circles and spheres as figures of minimal properties. In this, he was following methods suggested by Steiner, who had been criticized by Dirichlet for omitting an existence proof. This was first remedied by Weierstrass by means of the calculus of variation, but Blaschke supplied the necessary existence proofs in a fashion closer to the spirit of Steiner.

Blaschke’s books on differential geometry soon gained worldwide recognition. The three-volume Vorlesungen (1921-1929) put into practice Felix Klein’s “Erlangen Program” for differential geometry: Volume I was devoted to classical geometry, Volume II to affine differential geometry (a subject developed by Blaschke and his pupils), and Volume III to the differential geometry of circles and spheres, controlled by the transformation groups of Moebius, Laguerre, and Sophus Lie.

Furthermore, Blaschke originated topological differential geometry, which studies invariants of differentiable mappings; he collected the results in his books Geometrie der Gewebe (1938) and Einführung in die Geometrie der Waben (1955). In 1950 Blaschke gave a new, concise exposition of differential geometry based on ideas of E. Cartan.

Inspired by Gustav Herglotz and by some classical problems of geometrical probability (Buffon’s needle problem, Crofton’s formulas), Blaschke began, about 1935, a series of papers on integral geometry. Because of its relations to convex bodies and kinematics, this field of research was especially to his liking; and many of his students continued his work in this area - Hadwiger, Wu, Chem, and Santalo.

Achievements

• Blaschke major achievements mostly centered around his research on differential and integral geometry and kinematics. Blaschke discovered kinematic mapping, which later became important to the axiomatic foundations of various geometries, and established it as a fundamental technique in kinematics. He also originated topological differential geometry, the study of invariant differentiable mappings. His more important works include Kreis und Kugel (1916; “Circle and Sphere”); Vorlesungen über Differentialgeometrie, 3 vol. (1921–29; “Lectures on Differential Geometry”); Vorlesungen über Integralgeometrie, 2 vol. (1935–37; “Lectures on Integral Geometry”); Grundlagen von Einsteins Relativitatstheorie (1921–23; “Foundations of Einstein’s Theory of Relativity”); and Analytische Geometrie (1948; “Analytical Geometry”).
  
  Blaschke received honorary doctorates from the universities of Sofia, Padua, and Greifswald, and the Karlsruhe Technische Hochschule. He was elected corresponding or honorary member of about a dozen European scientific academies.

Works

More photos

• book

  • Vorlesungen Uber Differentialgeometrie Und Geometrische Grundlagen Von Einsteins Relativitatstheorie, Von Wilhelm Blaschke

    (Vol. 2)

    1921
  • Kreis Und Kugel 1916
  • Vorlesungen Über Differentialgeometrie I: Elementare Differentialgeometrie 1929
  • Vorlesungen über Höhere Geometrie 1937
  • Mathematik Und Leben 1950

Politics

Anschluss, a political union of Austria with Germany, had long been supported by Austrian Social Democrats. It was a process that Blaschke certainly supported, so when Germany invaded Austria on 12 March 1938 and Hitler annexed Austria on the following day, Blaschke approved. He wrote in the preface of one of his books: "Whereas earlier volumes of mine on differential geometry appeared in murky times, this book was completed as a dream of my youth was fulfilled, the union of my more narrowly seen homeland, Austria, with my larger homeland, Germany."

In fact, when the Germany invasion of Austria occurred Blaschke was on a visit to Messina in Italy and the political events must have presented him with an awkward situation. He went to Italy, where he gave a series of lectures, before going on to Greece where again gave several lectures before returning to Germany on 16 April. Blaschke was at this time in the rather difficult position of still being viewed with suspicion in Germany given his fight for internationalism. However, given the German invasion of Austria and other events, as a German who had openly supported the Nazis, he would be treated with suspicion when abroad.

A report to the Hamburg university senate mentioned about Wilhelm Blaschke's political views: "Although he cannot be described as a typical National Socialist, he used political pressure on issues of appointments. The rector indicates Blaschke's old sympathies with fascism." Blaschke described himself as "a Nazi at Heart" and was nicknamed Mussolinetto by his colleagues in Hamburg for his fascist sympathies, so there seems little doubt that he did join the Nazi party because he believed in what they stood for.

Views

One of the leading geometers of his time, Blaschke centered most of his research on differential and integral geometry and kinematics.

Personality

Wilhelm inherited his father’s predilection for the geometry of Jakob Steiner and his love of concrete problems. His father Josef also imparted to the boy a feeling for history and an open-mindedness toward foreign cultures that remained with him throughout his life.

Quotes from others about the person

• Scriba wrote the following about Wilhelm Blaschke: "One of the leading geometers of his time, Blaschke centered most of his research on differential and integral geometry and kinematics. He combined an unusual power of geometrical imagination with consistent and suggestive use of analytical tools; this gave his publications great conciseness and clarity and, with his charming personality, won him many students and collaborators."

Interests

• history, culturology

• Philosophers & Thinkers

  Marius Sophus Lie, Gustav Herglotz

Connections

Wilhelm Blaschke was married to Augusta Meta Röttger and had two children.

Father:

Josef Blaschke

1852-1917, he was a professor of descriptive geometry at the Landes Oberrealschule at Graz.

Wife:

Augusta Meta Röttger

colleague:

Erich Hecke

At Hamburg, Blaschke succeeded within a few years in gaining worldwide recognition for the department of mathematics of the newly founded university, for he was able to attract to Hamburg such well-known mathematicians as Erich Hecke.

colleague:

Emil Artin

colleague:

Helmut Hasse

colleague:

Eduard Study

Eduard Study, more properly Christian Hugo Eduard Study (March 23, 1862 – January 6, 1930), was a German mathematician known for work on the invariant theory of ternary forms (1889) and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.

Friend:

Gustav Herglotz

Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian physicist. He is best known for his works on the theory of relativity and seismology.

References

• Konforme abbildung
  2015
• Dictionary of scientific biography
  1981