**Josip Plemelj ** was a Slovenian mathematician who worked in the theory of analytic functions and the application of integral equations to potential theory.

- Slovenia was under Austrian Habsburg rule when Plemelj was born, as it had been for most of the preceding 500 years.
- After four years at high school Plemelj had covered the whole school mathematics syllabus.
- In 1894 Plemelj took his final school examinations and entered the Faculty of Arts of the University of Vienna to study his three favourite school subjects of mathematics, physics and astronomy.
- Plemelj undertook research under von Escherich's supervision and in May 1898 was awarded his doctorate for a thesis on linear homogeneous differential equations with uniform periodical coefficients: über lineare homogene Differentialgleichungen mit eindeutigen periodischen Koeffizienten Ⓣ(On linear homogeneous differential equations with unique periodic coefficients).
- After his doctorate Plemelj travelled to Germany where he studied with Frobenius and Fuchs for the academic year 1899-1900.
- Plemelj was a major contributor to this work and he was among the first to make major advances.
- Chernivtsi is now in south-western Ukraine, but at the time Plemelj was working there it was part of Austria-Hungary.
- Plemelj discovered equations relating to boundary values of holomorphic functions which are now called the "Plemelj formulae" and shortly after this was able to solve Riemann's problem in his paper Riemannian classes of functions with given monodromy group published in Monatshefte für Mathematik und Physik Ⓣ(Mathematics and physics monthly) in 1908.
- the so-called Plemelj formulae are ...
- due to Sokhotsky, who published them in his doctor's thesis in 1873, that is to say 35 years before Plemelj.
- Plemelj's methods for solving the Riemann's problem were further developed by Nikolai Ivanovich Mushelisvili into the theory of singular integral equations.
- During 1912-13 Plemelj was Dean of the Faculty at the University of Chernivtsi.
- Plemelj certainly qualified as an Austrian mathematician but it was ironical that he would be described as such during a period when the various nations which formed the Austrian empire were beginning to look towards independence and Plemelj himself was strongly associated with such aims.
- The Slovene Provincial Government set up a University Commission to oversee the reopening of the University of Ljubljana as a Slovene University and Plemelj was appointed a member of this Commission.
- The University of Ljubljana reopened as a Slovene university in 1919 with Plemelj as its first Rector.
- What with the post-war lack of contact with the scientific world, his professional loneliness, and his illness, Plemelj taught, rather than created much new during his Ljubljana years.
- His final work, Problems in the Sense of Riemann and Klein appeared in 1964 and described those parts of mathematics to which Plemelj had been a major contributor.
- Plemelj received many honours in addition to the Prince Jablonowski Prize and the Richard Lieben Prize which we mentioned above.
- We end this biography with a few comments about Plemelj's style as a lecturer.
- Plemelj retired in 1957 when he was 83 years old and died in Ljubljana in his 94th year.

Born 11 December 1873, Grad on Bled, Austrian Empire (now Slovenia). Died 22 May 1967, Ljubljana, Yugoslavia (now Slovenia).

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Astronomy, Origin Slovenia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive