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Jacob Lüroth

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18 Feb 1844

Mannheim, Germany

14 Sept 1910

Munich, Germany

Jacob Lüroth was interested in astronomy when he was at school and at one stage his heart was set on that subject. He began to make astronomical observations but he soon realised that his poor eyesight was not going to give him a future in that subject so his interest turned to mathematics.

After leaving school he studied at a number of universities as was the usual practice of German students at that time. Between the years 1863 and 1866 he attended three universities, Heidelberg, Berlin and Giessen. He received a doctorate in 1865 for a thesis on the Pascal configuration.

Lüroth was appointed to the teaching staff at Heidelberg and he taught there for two years before being appointed professor of mathematics at the Technische Hochschule in Karlsruhe. He spent 11 years at Karlsruhe, then in 1880 he moved to Munich teaching at the Technische Hochschule there for three years.

In 1883 Lüroth moved again, this time being appointed to the University of Freiburg. He was to spend the rest of his career at Freiburg.

Lüroth was taught by Hesse and Clebsch and continued to develop their work on geometry and invariants. He published results in the areas of analytic geometry, linear geometry and continued the directions of his teachers in his publications on invariant theory . In 1869 Lüroth discovered the "Lüroth quartic". This came out of an investigation he was carrying out into when a ternary quartic form could be represented as the sum of five fourth powers of linear forms.

Some of his work on rational curves, published in Mathematische Annalen in 1876, was extended to surfaces by Castelnuovo in 1895. In 1883 Lüroth published his method on constructing a Riemann surface for a given algebraic curve.

Lüroth also worked on the big problem of the topological invariance of dimension. He made some useful progress but this difficult problem was not completely solved until the work of Brouwer in 1911.

Among his other work, Lüroth undertook editing. He was an editor of the complete works of Hesse and of Grassmann . He also has some fine results on logic, a topic he worked on in collaboration with his friend Ernst Schröder .

Von Staudt 's ideas of geometry interested Lüroth and he further developed von Staudt 's complex geometry. He published Grundriss der Mechanik in 1881. This mechanics book makes heavy use of the vector calculus.

Source:School of Mathematics and Statistics University of St Andrews, Scotland