Jacob Lüroth

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Jacob Lüroth

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

Live and act

Jacob Lüroth was already interested in astronomy at school in Mannheim , worked with the director of the Mannheim observatory and also began to study astronomy at the University of Bonn in 1862 , which he broke off due to poor eyesight. From 1863 he studied mathematics at the Ruprecht-Karls-Universität Heidelberg , where he received his doctorate in 1865 under Otto Hesse (and Gustav Kirchhoff ) . He then studied further at the University of Berlin with Karl Weierstrass and at the University of Gießen with Alfred Clebsch , completed his habilitation in Heidelberg in 1867, where he then worked as a private lecturer . From 1868 he was at the Technical University of Karlsruhe , where he became a professor in 1869, and from 1880 as successor to Felix Klein Professor at the Technical University of Munich . In 1883 he became a professor at the Albert Ludwig University in Freiburg im Breisgau , where he stayed until his retirement . In 1889/1890 he was Vice Rector of the University. In 1905 he became a privy councilor of Baden . He died unexpectedly of a heart attack while on vacation in Munich.

Lüroth worked in various areas of geometry . As a student of Hesse and Clebsch, he continued their work on invariant theory. He discovered the fourth-order curve named after him in 1869 as part of the investigation of the special conditions that must be fulfilled according to Clebsch so that a fourth-order curve can be represented as the sum of five fourth powers (purely formally, the number of coefficients is the same). A complete pentagon can be inscribed on the Lüroth curve. The set of Lüroth describes the possibility of reversal of the algebraic representation of a curve as a rational function of a parameter by introducing a corresponding new parameter. In "modern language" terms, he proved that unirational curves are rational. For higher dimensions this is known as the Lüroth problem. The theorem was extended to algebraic surfaces by Guido Castelnuovo in 1893 . For three-dimensional varieties, Yuri Manin and Wassili Alexejewitsch Iskowskich in 1971 and Herbert Clemens and Phillip Griffiths in 1972 proved that Lüroth's theorem does not generally apply there.

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

He edited the works of Hesse and Hermann Graßmann and continued the work of Karl Georg Christian von Staudt in projective geometry. Lüroth's Grundriß der Mechanik from 1881 is, after Max Noether, the first textbook on mechanics that consistently uses the vector notation (following Graßmann).

During his 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 appears in a work by Lüroth published in 1876 as an a posteriori distribution when dealing with a problem of equalization calculation with Bayesian methods.

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

Fonts

literature

  • Helmuth Gericke:  Lüroth, Jacob. In: New German Biography (NDB). Volume 15, Duncker & Humblot, Berlin 1987, ISBN 3-428-00196-6 , p. 474 ( digitized version ).
  • Alexander von Brill; Max Noether: Jakob Lüroth. In: Annual report of the German Mathematicians Association. Volume 20 (1911), pp. 279-299. ( Digital edition. Univ. Heidelberg, 2008)
  • Günter Kern: The development of the subject of mathematics at the University of Heidelberg 1835-1914. 1992. pp. 80-82, 151-152. ( digital , pp. 34–35 and 130)

Web links

Remarks

  1. ↑ On the theory of Pascal's hexagon.
  2. ^ Mathematische Annalen Vol. 1, p. 37.
  3. ↑ Mathematische Annalen Vol. 9, 1876, pp. 163-165.
  4. ↑ Mathematische Annalen Vol. 8, 1875, Vol. 11, 1877.
  5. ↑ J. Lüroth: Comparison of two values ​​of the probable error . In: Astron. Msg . 87, No. 14, 1876, pp. 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: Biometrika . 83, No. 4, 1996, pp. 891-898. doi : 10.1093 / biomet / 83.4.891 .
  7. ↑ P. Gorroochurn: Classic Topics on the History of Modern Mathematical Statistics from Laplace to More Recent Times . Wiley, 2016, doi : 10.1002 / 9781119127963 .
personal data
SURNAME Lüroth, Jacob
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH February 18, 1844
PLACE OF BIRTH Mannheim
DATE OF DEATH September 14, 1910
Place of death Munich