Jacob Lüroth – Wikipedia

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Jacob Lüroth (Born February 18, 1844 in Mannheim, † September 14, 1910 in Munich) was a German mathematician who dealt with geometry.

Jacob Lüroth was already interested in astronomy at the school in Mannheim, worked with the head of the Mannheim observatory and also began to study astronomy at the University of Bonn in 1862, but he broke away due to a poor eyesight. From 1863 he studied mathematics at the Ruprecht-Karls University in Heidelberg, where he was received by Otto Hesse (and Gustav Kirchhoff) in 1865 [first] . He then studied at the University of Berlin with Karl Weierstraß and at the University of Gießen with Alfred Clebsch, habilitated in Heidelberg in 1867, where he then acted as a private lecturer. From 1868 he was at the Karlsruhe Technical University, where he became a professor in 1869, and from 1880 as the successor to Felix Klein Professor at the Technical University of Munich. In 1883 he became a professor at the Albert Ludwigs University in Freiburg im Breisgau, where he stayed until his emeritus. In 1889/1890 he was Vice -Rector of the University. In 1905 he became Grand Ducal Badischer Privy Councilor. He died unexpectedly from a heart attack on a vacation in Munich.

Lüroth worked in various areas of geometry. As a student of Hesse and Clebsch, he continued their invariant theoretical work. He discovered the fourth order curve named after him in 1869 [2] As part of the examination of the special conditions that must be met according to Clebsch so that a fourth order curve can be represented as a sum of five fourth potencies (the number of coefficients is the same). The Lürothsche curve can be inscribed in a complete pentagon. The sentence of Lüroth [3] describes the possibility of algebraic reversal of the representation of a curve as a rational function of a parameter by introducing a corresponding new parameter. In “modern language”, he proved that unirational curves are rational. For higher dimensions, this is known as a Lüroth problem. The sentence was extended by Guido Castelnuovo in 1893 to algebraic areas. For three -dimensional varieties, Yuri Manin and Wassili Alexejewitsch Iskowskich in 1971 and Herbert Clemens and Phillip Griffiths in 1972 proved that Lüroth’s sentence generally does not apply there.

Lüroth also dealt with topology and tried to prove the topological invariance of the dimension, but this was only achieved by Brouwer in 1911.

He also published the works of Hesse and Hermann Graßmann and continued the work of Karl Georg Christian von Staudt in projective geometry [4] . Lüroths Fundriß of the mechanics From 1881, according to Max Noether, the first textbook of mechanics is that the vector notation consistently uses (whereby he follows Graßmann).

At the time as a professor at the polytechnic school in Karlsruhe, Jacob Lüroth developed the T distribution, which is usually attributed to William Sealy Gosset; The T distribution comes in a work published in 1876 [5] by Lüroth as A-Posteriori distribution in the treatment of a problem of compensation calculation with Bayesian methods [6] [7] .

Jacob Lüroth was a member of the Bavarian and the Heidelberg Academy of Sciences and since 1883 of the German Academy of Natural Researchers Leopoldina.

  • Helmuth Gericke:  Lüroth, Jacob. In: New German biography (Ndb). Volume 15, Duncker & Humblot, Berlin 1987, ISBN 3-428-00196-6, p. 474 ( Digitized ).
  • Alexander von Brill; Max Noether: Jakob Lüroth. In: Annual report of the German Mathematician Association. Band 20 (1911), S. 279–299. ( Digital edition. Univ. Heidelberg, 2008)
  • Günter Kern: The development of mathematics at the University of Heidelberg 1835-1914. 1992. S. 80–82, 151–152. ( digital , S. 34–35 u. 130)
  1. ↑ On the theory of Pascal’s hexagon.
  2. ↑ Mathematical Annals Vol. 1, p. 37.
  3. ↑ Mathematical Annals Vol. 9, 1876, pp. 163–165.
  4. ↑ Mathematical Annals Vol. 8, 1875, Vol. 11, 1877.
  5. ↑ J. Lüroth: Comparison of two values ​​of the probable error . In: Astron. Nachr . 87th year, No. 14 , 1876, S. 209–220 , doi: 10.1002 / ASNA.18760871402 .
  6. ↑ J. Pfanzagl, O. Sheynin: A forerunner of the t -distribution (Studies in the history of probability and statistics XLIV) . In: Biometric . 83rd year, No. 4 , 1996, S. 891–898 , doi: 10.1093/biomet/83.4.891 .
  7. ↑ P. Gorrochurn: Classic Topics on the History of Modern Mathematical Statistics from Laplace to More Recent Times . Wiley, 2016, doi: 10,1002/9781119127963 .