The habilitation thesis of Heinrich Liebmann, titled Über die Verbiegung der geschlossenen Flächen positiver Krümmung, established a foundational result in differential geometry now recognized as Liebmann’s theorem. His academic career spanned the turn of the twentieth century in the German Reich, marked by significant contributions to both the practice and the historical study of mathematical sciences.
Academic Formation and Early Career
Born in Strasbourg in 1874, Heinrich Liebmann pursued his studies between 1895 and 1897 at universities in Leipzig, Jena, and Göttingen. In 1895, he earned his doctorate under the supervision of Carl Johannes Thomae with the thesis Die einzweideutigen projektiven Punktverwandtschaften der Ebene. Following his doctoral success, he passed the Lehramtsprüfung in 1896 and served as an assistant in Göttingen and Leipzig. His 1898 habilitation work provided critical insights into the bending of closed surfaces with positive curvature, successfully proving that such convex surfaces cannot be deformed.
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Liebmann progressed through the German academic hierarchy, becoming an extraordinary professor in Leipzig in 1905. He moved to the Technischen Hochschule München in 1910 and attained a professorship there by 1915. In 1920, he succeeded Paul Stäckel as a professor at Heidelberg University. During his tenure at Heidelberg, he served as the dean of the faculty of mathematics and natural science during the 1923-1924 and 1928-1929 academic years, and he held the position of university rector in 1926.
Contributions to Geometry
His research focused heavily on differential geometry and non-Euclidean geometry. He developed a method for constructing a triangle from its three angles using only a ruler and compass within the framework of hyperbolic geometry. Furthermore, he facilitated the dissemination of mathematical theory through his German translations of the works of Nikolai Lobachevsky. His intellectual service extended to professional societies, including membership in the Saxon Academy of Sciences, the Bavarian Academy of Sciences and Humanities, and the Heidelberg Academy of Sciences and Humanities.
Political Pressures and Final Years
The stability of Liebmann's academic career ended with the rise of the National Socialists. Due to his Jewish ancestry, he faced political pressure and was subjected to a boycott within his own faculty alongside colleague Arthur Rosenthal. In 1935, these conditions compelled him to request retirement from his post at Heidelberg. He relocated to Munich for his final years and died in Solln in 1939. His personal life included marriages to Natalie Liebmann, daughter of Karl Kraus, and later to Helene Ehlers, with whom he had four children.
Fast facts
- Born: 1874, Strasbourg
- Died: 1939, Solln
- Citizenship: German Reich
- Key area: Differential geometry
- Doctorate awarded: 1895
- Major employer: Heidelberg University
- Languages: German
- Children: 4
Questions readers ask
What is Liebmann's theorem?
It is a theorem in differential geometry, introduced in his 1898 habilitation, stating that a convex closed surface cannot be bent.
Why did Liebmann retire in 1935?
He was forced to request retirement due to political pressure exerted by the national socialists because of his Jewish ancestry.
Achievements
- Held posts at Heidelberg University
- Fields: mathematics
