Background

Johann Karl August Radon was born in Tetschen, Bohemia, Austria-Hungary (now Děčín, the Czech Republic) on December 16, 1887.

Education

Radon entered the Gymnasium at Leitmeritz (now Litomerice), Bohemia, in 1897 and soon showed a talent for mathematics and physics. In 1905 he enrolled at the University of Vienna to study those subjects and was subsequently influenced by Gustav von Escherich, who introduced him to the theory of real functions and the calculus of variations. His doctoral dissertation (1910), on the latter subject, was also his first published paper.

Career

Radon spent the winter semester of 1911 at the University of Göttingen, served for a year as an assistant professor at the University of Brünn (now Brno), then went to the Technische Hochschule of Vienna in the same capacity. He became Privatdozent at the University of Vienna in 1914 and achieved the same rank a year later at the Technische Hochschule.

In 1919 Radon was appointed associate professor at the University of Hamburg; he became a full professor at Greifswald in 1922, at Erlangen in 1925, and at Breslau in 1928. He left Breslau in 1945 and in 1947 obtained a full professorship at Vienna, where he spent the rest of his life. In the same year, he became a full member of the Austrian Academy of Sciences.

The calculus of variations remained Radon’s favorite field because of its close connections with so many areas of analysis, geometry, and physics. His most important paper in this field (1927) greatly influenced its further development, especially of the difficult Lagrange problem. In 1928, in lectures at Hamburg, Radon presented his results in an expanded form.

He was deeply interested in the applications of the calculus of variations to differential geometry and discovered the so-called Radon curves, which have found applications in number theory. In addition to his work in affine differential geometry (1918–1919), in conformal differential geometry (1926), and in Riemannian geometry, Radon treated mathematical problems of relativity theory.

His important paper on algebra, “Lineare Scharen orthogonaler Matrizen,” was inspired by his work on the calculus of variations and proved to have many applications. Radon’s best-known work, “Theorie und An-wendungen der absolut additiven Mengenfunktionen,” which exerted a great influence, essentially combined the integration theories of Lebesgue and Stieltjes. Led to his research by physical considerations, he studied the most general distributions of masses in space and developed the concept of the integral, now known as the Radon integral. A continuation of this work is the paper “Über lineare Funktionaltransformationen und Funktionalgleichungen.”

An important theorem in the calculus of variations, later generalized by Otton Nikodym, is the Radon-Nikodym theorem. Radon himself applied this theory to the Dirichlet problem of the logarithmic potential. He also developed a technique now known as the Radon transformation (1917), which has many applications. Radon’s interest in the philosophy of mathematics was reflected in his paper “Mathematik und Wirklichkeit.”

Achievements

• 

  Radon's major success was in achieving effective results applying the calculus of variations to differential geometry which led to applications in number theory. It was while he was studying applications of the calculus of variations to differential geometry that he discovered curves which are now named Radon curves.
  
  His best known results involve combining the integration theories of Lebesgue and Stieltjes which first appeared in his habilitation dissertation (which we mentioned above) and then in a second important work Über lineare Funktionaltransformationen und Funktionalgleichungen.
  
  Radon's remarkable contribution to the field of mathematics was greatly recognized and it resulted in a long association with the Austrian Academy of Sciences. His doctoral thesis and his habilitation dissertation were both published by the Academy. He was elected a corresponding member of the Academy in 1939 and a full member in 1947. He was chairman of the Mathematical and Physical Section of the Academy from 1952 to 1956. He also served the Austrian Mathematical Society being president in 1948-50.
  
  After the Austrian Academy of Sciences founded an Institute for Computational and Applied Mathematics in 2003, it was named after Johann Radon in his honor.

Works

More photos

• book

  • Johann Radon: Collected Works 1987
  • Gesammelte Abhandlungen 2 Bände (Contemporary Mathematicians) 1946

Membership

Radon was elected a corresponding member of the Austrian Academy of Sciences in 1939 and a full member in 1947. He was also a member of the Austrian Mathematical Society where he and served as president in 1948-50.

Personality

During his life, Johann Radon did make the impression of a quiet scholar, but he was also sociable and willing to celebrate. He loved music, and he played music with friends at home, being an excellent violinist himself, and a good singer. His love for classical literature lasted through all his life.

Interests

• music, singing, classical literature

Connections

Johann Radon married Maria Rigele, a secondary school teacher, in 1916. They had three sons who died young or very young.

Father:

Anton Radon

Mother:

Anna Schmiedeknecht

Wife:

Maria Rigele

Daughter:

Brigitte Bukovics

She was born in 1924, obtained a Ph.D. in mathematics at the University of Innsbruck and married the Austrian mathematician Erich Bukovics in 1950.

teacher:

Hans Hahn

27 September 1879 – 24 July 1934, an Austrian mathematician who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory.

teacher:

Wilhelm Wirtinger

15 July 1865 – 15 January 1945, an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.

teacher:

Franz Mertens

colleague:

Emanuel Czuber

19 January 1851 – Gnigl, 22 August 1925

References

• Dictionary of Scientific Biography Volume 11
  1975