Hieronymus Georg Zeuthen

Hieronymus Georg Zeuthen

Hieronymus Georg Zeuthen (born February 15, 1839 in Grimstrup in Jutland , † January 6, 1920 in Copenhagen ) was a Danish mathematician who dealt with algebraic geometry and the history of mathematics.

Life

Zeuthen was the son of a pastor. In 1849 the family moved to Sorø , where he went to school until 1857. He then studied mathematics at the University of Copenhagen. In 1862 he made his master's degree and received a scholarship to study abroad. To do this, he went to Michel Chasles in Paris , where he dealt with counting geometry, in which for example the number of curves of a certain type that touch a given curve is asked. Chasles, who was interested in the history of mathematics as well as geometry, became a formative influence for him. In 1865 he received his doctorate in Copenhagen with his dissertation Nyt Bidrag til Læren om Systemer af Keglesnit on the characteristics of systems of conic sections. In 1871 he became associate professor in Copenhagen and editor of the Mathematisk Tidskrift , which he remained until 1889. In 1886 he became a full professor. Zeuthen was twice rector of the university and also taught at the Polytechnic Institute.

Zeuthen was honored with the Dannebrogden in 1880 . For almost forty years he was secretary of the Royal Danish Academy of Sciences . He also belonged to numerous other academies and learned societies.

In addition to his contributions to counting geometry, which for a long time led a shadowy existence because of its less strict methods, but became a more active research area in algebraic geometry again at the end of the 20th century, he is now best known for his contributions to the history of mathematics, especially ancient Greek Mathematics and the mathematics of the Middle Ages. With astute, sometimes speculative considerations, he tried to reconstruct the approach of mathematicians from the point of view and with the methods of the respective time, in contrast to the other great mathematical historian of the 19th century Moritz Cantor , who strictly adhered to the traditional documents . A role model for him was Paul Tannery , with whom he was in correspondence. In Denmark he also worked with his friend, a mathematician historian, Heiberg , for example on the publication of Archimedes' mechanics, which Heiberg found in Constantinople. In his book of 1886 he tries to prove that Apollonius von Perga already used analytical geometry (coordinate systems) in his theory of conic sections (and thus the Greek mathematics of that time in general), but replaced the algebraic calculations with auxiliary geometric constructions. The hypothesis that Greek mathematics knew a geometric form of algebra was already supported by Tannery. In contrast to simple arithmetic, a theory of irrational quantities was also possible in geometry, which Zeuthen traced back to the Pythagoreans in studies. In his investigations on modern mathematics, he dealt in particular with Isaac Barrow , Newton's teacher, whom he considered essential for the conceptual elaboration of the main theorem of analysis that differentiation and integration are mutually inverse operations.

Fonts

• Outline of an elementary geometric conic section theory . Teubner 1882.
• The ancient doctrine of the conic sections . Copenhagen 1886 (published in Danish in Forh.Vid.Selskab one year earlier).
• History of Mathematics in Antiquity and the Middle Ages . Copenhagen 1896 (previously published in Danish in 1893 by the same publisher AFHoest).
• History of Mathematics in the 16th and 17th Centuries . Teubner 1903, and as volume 17 of the essays on the history of mathematical sciences (Ed. Moritz Cantor ). The Danish edition was published in Copenhagen in 1903. ( Review by Moritz Cantor. )
• Text-book of the counting methods of geometry . Teubner 1914.
• Hvorledes Mathematiken i tiden fra Platon til Euclid blev rationel Videnskab . Forh. Dansk Vid. Selskab 1917, pp. 199–369.

literature

• Zeuthen, Hieronymus Georg . In: Carl Frederik Bricka (Ed.): Dansk biografisk Lexikon. Tillige omfattende Norge for Tidsrummet 1537-1814. 1st edition. tape 19 : Vind – Oetken . Gyldendalske Boghandels Forlag, Copenhagen 1905, p. 298-301 (Danish, runeberg.org ).
• Max Steck : The Zeuthen postulate and the principle of interchanging to justify projective geometry , 1932
• Max Noether: Hieronymus Georg Zeuthen . In: Mathematische Annalen , 83, 1921, p. 1.
• HG Zeuthen: Counting methods. Retrieved July 9, 2019 .  In: Encyclopedia of Mathematical Sciences including their applications , Teubner Leipzig, 1903–1915, pp. 257–312

Web links

Wikisource: Hieronymus Georg Zeuthen  - Sources and full texts

• John J. O'Connor, Edmund F. Robertson :  Hieronymus Georg Zeuthen. In: MacTutor History of Mathematics archive .