In the autumn of 1862, Lüroth passed the matriculation examination for the University of Bonn and he began to study astronomy with Friedrich Wilhelm Argelander.
In the autumn of 1862, Lüroth passed the matriculation examination for the University of Bonn and he began to study astronomy with Friedrich Wilhelm Argelander.
Jacob Lüroth was a German mathematician. He worked on rational curves and the invariance of dimension.
Background
Lüroth was born on February 18, 1844, in Mannheim, Germany. His father, also named Jacob Lüroth (1792-1860), was a brewer and a member of the local town council. However, his father died when Jacob was sixteen years old and after that time he was brought up by his mother, Katharina Voisin, who did her utmost to give her son a good education despite financial difficulties.
Education
Lüroth attended the Lyceum in Mannheim where he showed himself to be a gifted linguist. He used his linguistic skills later in life in translating texts from English and Italian into German. However, at high school he also enjoyed mathematics and astronomy, studying these with the help of his mathematics teacher Carl Rapp. In the autumn of 1862, Lüroth passed the matriculation examination for the University of Bonn and he began to study astronomy with Friedrich Wilhelm Argelander. He attended the universities of Heidelberg, Berlin, and Giessen from 1863 until 1866; and had already, in 1865, written his doctoral dissertation on the Pascal configuration.
In 1867 Lüroth became Privatdozent at the University of Heidelberg, and two years later, when he was still only twenty-five years old, he was appointed professor ordinaius at the Technische Hochschule in Karlsruhe. From 1880 until 1883 he taught at the Technische Hochschule of Munich, and from the latter year until his death, at the University of Freiburg.
Lüroth's first mathematical publications were concerned with questions in analytical geometry, linear geometry. and theory of invariants, a development of the work of his teachers Hesse and Clebsch. His name is associated with three specific contributions to science. The first of these, a covariant of a given ternary form of fourth degree, is called the "Lueroth quartic," and Lüroth discovered it when he examined, following Clebsch, the condition under which a ternary quartic form may be represented as a sum of five fourth-powers of linear forms. In 1876 he demonstrated the "Lüroth theorem," whereby each uni-rational curve in rational - Castelnuovo in 1895 proved the analogous but more difficult theorem for surfaces. Finally, the "Clebsch-Lüroth method" may be employed in the construction of a Riemann surface for a given algebraic curve in the complex plane.
In addition, Lüroth worked in other areas of mathematics far removed from algebraic geometry. He obtained partial proof of the topological invariance of dimension (proved in 1911 by L. Brouwer) and, following the work of Staudt, did research in complex geometry. He was also involved in the logical researches of his friend Schroder and published two books in applied mathematics and mechanics.
Achievements
Membership
Royal Bavarian Academy of Sciences
,
Germany
1882
Academy of Sciences Leopoldina
,
Germany
1883
Heidelberg Academy of Sciences
,
Germany
1909
Personality
Lüroth continued to work despite his health deteriorating due to heart problems. He showed remarkable courage and, despite being in severe pain, tried to appear cheerful to all those round him.
Connections
Lüroth married Karoline Antonie Schepp in 1875 and their only child, a daughter Emilie, was born in Karlsruhe in 1876.