Ernst Eduard Kummer

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Heartache in the 1870s.

Ernst Eduard Kummer (born January 29, 1810 in Sorau , Niederlausitz , † May 14, 1893 in Berlin ) was a German mathematician and university professor who mainly dealt with number theory , analysis and geometry .

Life

Kummer was the son of a doctor who died when Kummer was three years old. He went to high school in Sorau and initially studied Protestant theology at the Friedrichs University in Halle with the aim of becoming a pastor, but switched to mathematics after attending a lecture by Heinrich Ferdinand Scherk . In 1831 he passed his state examination and received his doctorate. Then Kummer taught physics and mathematics as a high school teacher, first in Sorau and from 1832 to 1842 in Liegnitz . There Leopold Kronecker and Ferdinand Joachimsthal were among his students. He published a paper on the hypergeometric differential equation in Crelle's Journal in 1836 , which led to a correspondence with Carl Gustav Jacobi and Peter Gustav Lejeune Dirichlet . At Dirichlet's suggestion, he was accepted into the Berlin Academy of Sciences in 1839. From 1851 he was a member of the Göttingen Academy of Sciences

In 1842 he became professor at the Silesian Friedrich-Wilhelms-Universität with the support of Jacobi and Dirichlet . During this time he turned to number theory. At the time of the revolution of 1848/1849 he was rector of the University of Wroclaw. He represented politically conservative views and was an opponent of the revolution.

In 1855 he succeeded Dirichlet (who moved to a chair in Göttingen) on his recommendation at the Friedrich-Wilhelms-Universität Berlin . In 1856 he ensured that Karl Weierstraß was also called to Berlin - he had a career similar to Kummer and had been a high school teacher for years - and supported the appointment of his former pupil Kronecker in 1855. In 1857/58 and 1865/66 he was dean and in 1868 / In 69 he was rector of the University of Berlin. Kummer was known for his clear and lively lectures and, together with Weierstrass, held the first seminar for pure mathematics at the University of Berlin in 1861. He was a university professor who was popular with the students and also personally looked after his students.

With Weierstrass and Kronecker he built up the Royal Commercial Institute, which was integrated into the TH Berlin in 1879 . The three friends, Kummer-Weierstrass-Kronecker, made Berlin one of the world's leading centers for mathematics for three decades, but around 1875 there were tensions between Weierstrass and Kronecker, which also affected Kummer, as he stood by his friend Kronecker.

In 1883 he retired as he felt his memory fade.

From 1863 to 1878 he was secretary of the mathematics and physics section of the Berlin Academy of Sciences.

His doctoral students included Paul Bachmann , Heinrich Bruns , Gotthold Eisenstein (who received an honorary doctorate in Breslau at the suggestion of Kummer), Paul Du Bois-Reymond , Georg Cantor , Arthur Moritz Schoenflies , Friedrich Schur , Hermann Amandus Schwarz , and Franz Mertens . He promoted mathematicians such as Alfred Clebsch , who completed his habilitation in Berlin, and Lazarus Fuchs , who was his successor in Berlin.

plant

Kummer initially dealt with analysis and especially the hypergeometric differential equation and hypergeometric series following the investigations of Carl Friedrich Gauß .

He was best known as a number theorist. He dealt with solid circles and in 1847 he introduced ideal numbers when studying the ring of whole numbers , which later became the ideal theory by Richard Dedekind and Kronecker, one of the foundations of the development of abstract algebra. He introduced ideal numbers in order to guarantee the unambiguous prime factorization in circles with these generalized number terms. One motive was the Fermat conjecture , in which various attempts at proof failed in the early 19th century (as Kummer in particular recognized) because they erroneously assumed a clear prime factorization in fields of circular divisions. Kummer was able to prove the Fermat conjecture with his theory for a (presumably infinitely) large number of exponents, those that are divisible by so-called regular prime numbers (of the prime numbers below 100, for example, only three are not regular). His motivation for dealing with number theory, however, was primarily the higher reciprocity laws (generalizations of the quadratical reciprocity law to higher powers), which Gauss and Jacobi (and Eisenstein) began to investigate and which were one of the main motives in the development of algebraic number theory. In 1857 he received the Grand Prize of the Paris Académie des Sciences for his number theory work . The prize was originally awarded for work on solving the Fermat conjecture - Kummer received it for his great progress in this area without having submitted a paper. Soon afterwards he became a correspondent for the Academie des Sciences and, in 1863, a foreign member of the Royal Society . In 1875 he became an Honorary Fellow of the Royal Society of Edinburgh .

Later he dealt with ray systems following William Rowan Hamilton and with algebraic geometry ( Kummer -fläche 1864). He wrote about ballistics and taught the subject at the War Academy.

There are two conjectures named after him:

  • The conjecture of Kummer and Vandiver that p does not divide the class number of the maximum real subfield of the pth field of the circle was confirmed numerically by Kummer for prime numbers up to 200 (and later confirmed by Vandiver up to 600 and then up to much higher numbers, from David Harvey to about ), but is unsolved.
  • Another conjecture made by Kummer about the value distribution of special cubic gausses was refuted in 1979 by Roger Heath-Brown and Samuel Patterson .

Private

Kummer was born in 1840 with Ottilie born in his first marriage . Mendelssohn , the daughter of Nathan Mendelssohn and Henriette geb. Itzig married. Ottilie was the aunt of Rebecca Mendelssohn Bartholdy , the wife of the mathematician Peter Gustav Lejeune Dirichlet. His first wife died in 1848. His second wife, Bertha, the daughter of the reform pedagogue Ludwig Cauer , was the cousin of his first wife. He had a total of 13 children. The daughter Marie married the mathematician Hermann Amandus Schwarz .

literature

  • Kurt-Reinhard Biermann : Sorrow, Ernst Eduard . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 7 : Iamblichus - Karl Landsteiner . Charles Scribner's Sons, New York 1973, p. 521-524 .
  • André Weil (editor): Ernst Eduard Kummer, Collected Works, Springer Verlag, 2 volumes, 1975
  • Heinrich Begehr (ed.): Mathematics in Berlin. History and Documentation, 1st half volume (reports from historical studies). Shaker, Aachen 1998, p. 54, ISBN 3-8265-4225-8 .
  • Moritz Cantor :  Sorrow, Ernst Eduard . In: Allgemeine Deutsche Biographie (ADB). Volume 51, Duncker & Humblot, Leipzig 1906, pp. 438-440.
  • Menso Folkerts , Olaf Neumann (editor): The correspondence between Kummer and Reuschle : a contribution to the history of algebraic number theory, Augsburg, Rauner, 2006
  • Kummer's approach to the Fermat conjecture and his work on number theory are dealt with in detail by Harold Edwards Fermat's last theorem , Springer Verlag 1977
  • Biography of Sorrow in Eric Temple Bell : Men of Mathematics , Dover
  • Harold Edwards: Kummer, Eisenstein, and higher reciprocity laws , in Neal Koblitz (Ed.) Number theory related to Fermat's last theorem , Birkhäuser 1983, pp. 31-43
  • Harold Edwards: The background of Kummer's proof of Fermat's last theorem for regular primes , Arch. History Exact Sci. 1975, 14: 219-236.
  • Kurt Hensel : Commemorative speech on Ernst Eduard Kummer , reprinted in: Hans Reichardt (Ed.) Obituaries to Berlin mathematicians of the 19th century, Teubner Archive for Mathematics, 1988, pp. 72–111 (first in Kurt Hensel (editor) Festschrift for Celebration of Eduard Kummer's 100th birthday , Leipzig, Berlin 1910, pp. 1–37)
  • H. Pieper: CGJ Jacobis judgments about the mathematician EE Kummer , NTM Schr. Geschichte Natur. Tech. Medicine 25 (1988), 23-36.
  • Paulo Ribenboim : Kummer's ideas on Fermat's last theorem , Enseign. Math. 29: 165-177 (1983)
  • Christoph J. Scriba:  Kummer, Ernst Eduard. In: New German Biography (NDB). Volume 13, Duncker & Humblot, Berlin 1982, ISBN 3-428-00194-X , p. 282 f. ( Digitized version ).

Web links

Individual evidence

  1. ^ Biography Ernst Eduard Kummer, Mathematics Genealogy Project ( Memento from June 4, 2016 in the Internet Archive )
  2. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 141.
  3. ^ Mathematics Genealogy Project ( Memento from January 16, 2013 in the Internet Archive ), he was only a second referee for many of those named there, especially for PhD students from Weierstrass.
  4. ↑ Ernst Eduard Kummer and the great Fermatsche sentence. Speech on the occasion of the Kaiser’s birthday by Kurt Hensel , Marburg (January 27) 1910. (E-Book, PDF), accessed on May 24, 2013.
  5. ↑ List of the members, correspondents and foreign partners of the Académie des sciences ( Memento of September 15, 2014 in the Internet Archive ) (PDF; 62 kB), accessed on May 25, 2013.
  6. ^ Entry on grief; Ernst Eduard (1810-1893) in the Archives of the Royal Society , London
  7. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. (PDF file) Royal Society of Edinburgh, accessed December 29, 2019 .
  8. ↑ Kummer published on the effect of air resistance on bodies of various shapes, especially on projectiles , Mathematical Treatises of the Royal Academy of Sciences in Berlin, 1875.
  9. ^ Heath-Brown, Patterson The distribution of Kummer sums at prime arguments , J. Reine Angew. Math. 310, 1979, 111-130.
personal data
SURNAME Grief, Ernst Eduard
BRIEF DESCRIPTION German mathematician and university professor; Rector in Breslau and Berlin
DATE OF BIRTH January 29, 1810
PLACE OF BIRTH Sorau , Lower Lusatia
DATE OF DEATH May 14, 1893
Place of death Berlin