Carl Gustav Jacob Jacobi

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Carl Gustav Jacobi, 1804-1851.

Carl Gustav Jacob Jacobi , actually Jacques Simon Jacobi (born December 10, 1804 in Potsdam , † February 18, 1851 in Berlin ) was a German mathematician .

Life

Carl Gustav Jacob Jacobi came from a wealthy Jewish banking family from Berlin and was three years younger brother of Moritz Hermann von Jacobi . He had a younger brother Eduard, who took over his father's banking business, and a sister Therese. His father Simon (1772–1832) came from Beelitz and was a banker (money changer) and member of the board of the Jewish community in Potsdam, his mother Rachel (1774–1848) was born Lehmann. He was initially called Jacques Simon Jacobi and called himself Carl Gustav Jacob after the conversion to the Christian faith, which he carried out in Berlin in his first semester in 1821.

For the first few years he was tutored by a maternal uncle. His talent for mathematics , but also for languages, was evident early on. Between 1816 and 1821 he attended the high school in Potsdam . During this time he learned mathematics mainly through self-study of literature, for example the Introductio in analysin infinitorum by Leonhard Euler . Due to his outstanding achievements, he was immediately admitted to the top class and obtained his university entrance qualification at the age of 13. However, since the Berlin University did not accept students under the age of 16, Jacobi stayed in the same school class for four years and used the time to study advanced mathematical literature.

In 1821 he began studying at Berlin University . For a long time he vacillated between classical philology, in which he attended the lectures of August Boeckh , and mathematics and also attended the philosophy lectures of Georg Wilhelm Friedrich Hegel and listened to history lectures. He learned mathematics primarily through self-study (e.g. Euler, Lagrange , Laplace ), since the professors of the Berlin University at the time were, according to Jacobi, only mediocre mathematicians. In 1824 he passed the senior teacher exams in Latin, Greek and mathematics. In 1825 he received his doctorate with Enno Dirksen ( Disquisitiones Analyticae de Fractionibus Simplicibus ), with Hegel on the examination board. The habilitation (with an inaugural lecture on differential geometry) took place in the winter semester of 1825/26.

From 1826 to 1843 he worked at the University of Königsberg , where he was transferred at his own request, as he saw better career opportunities there. He reformed university teaching there by founding a mathematical and physical seminar. In addition to Jacobi, the astronomer Friedrich Wilhelm Bessel (with whom he later exchanged letters) and the physicist Franz Ernst Neumann , with whom he became friends, worked in Königsberg and they made the university a magnet for mathematicians and physicists. The establishment of research seminars in mathematics was new at the time (but previously common in classical philology) and had an exemplary effect in Germany. In his lectures, too, he mostly treaded new paths and presented his own research. From 1827 he was associate professor and from 1829 full professor. This was not least thanks to his successful research on elliptical functions, which arose in competition with Niels Henrik Abel's work, who died prematurely in 1829 and also had close ties to the publisher August Crelle , the editor of the Journal for Pure and Applied Mathematics ( Crelles Journal ), in which most of the works by Jacobi (and Abel) appeared. In 1829 he visited Carl Friedrich Gauß in Göttingen (whom he had already contacted by letter in 1827) and Adrien-Marie Legendre , with whom he had already been in correspondence from 1827, mainly on elliptical functions, Joseph Fourier and Siméon Denis Poisson and other mathematicians in Paris. In 1842 he represented Prussia with Bessel at the meeting of the British Association for the Advancement of Science in Manchester and visited Paris again, where he gave a lecture at the Académie des Sciences .

Jacobi married the merchant's daughter Marie Schwinck (1809–1901) in Königsberg in 1831 and had five sons and three daughters with her, including the lawyer and Berlin professor Leonard Jacobi (1832–1900). Marie Schwinck's father was a formerly wealthy councilor of commerce, but at the time of the marriage he had lost his fortune through speculation.

In 1843 he gave up his lectures for health reasons (he suffered from diabetes ) and, through the mediation of his friend Peter Gustav Lejeune Dirichlet and Alexander von Humboldt, received a grant from the Prussian state ( Friedrich Wilhelm IV. ) To cure in Italy. He visited Lucca with his pupil Borchardt and Dirichlet and was in Rome in 1843/44 , where the mathematicians Ludwig Schläfli and Jakob Steiner were at that time .

He then moved to Berlin as a full member of the Prussian Academy of Sciences , received an increase in his salary because of the higher cost of living in the capital and his medical expenses, and gave lectures at the university, albeit not to the same extent as in Königsberg he was eligible as an academician.

In 1849 he got into financial difficulties when he fell out of favor with the Prussian state because of his liberal political attitude in the revolution of 1848 (in which he was involved on the republican side) (a position at the university sought by Jacobi was refused, the increase in his salary 1849 canceled), which, as with Gotthold Eisenstein, was tempered by Alexander von Humboldt . In addition, his father's bank had gone bankrupt a few years earlier. In 1848 he had to send his family to the cheaper Gotha . A call to the University of Vienna in 1850 improved his situation vis-à-vis the Prussian state (feared the loss of prestige due to his departure), but his family initially stayed in Gotha, since the eldest son Leonard Jacobi was about to graduate from high school.

Grave cross by Carl Gustav Jacob Jacobi

Jacobi was also a foreign member of the Royal Society , an honorary member ( Honorary Fellow ) of the Royal Society of Edinburgh and the Academy in St. Petersburg and, since 1830, a corresponding member of the Académie des Sciences in Paris (since 1846 associé étranger ). In 1840 Jacobi was elected a foreign member of the Göttingen Academy of Sciences and in 1850 to the American Academy of Arts and Sciences .

Carl Gustav Jacob Jacobi died in Berlin in 1851 at the age of 46 of complications from a smallpox infection , after having survived the flu shortly before. His grave is on the Trinity Cemetery I in Berlin-Kreuzberg . An iron cross on a base serves as a grave marker. By resolution of the Berlin Senate , the last resting place of Carl Gustav Jacob Jacobi (grave location DV2-SA-1T) has been dedicated as an honorary grave of the State of Berlin since 1980 . The dedication was extended in 2001 by the now usual period of twenty years.

Act

Jacobi is one of the most productive and versatile mathematicians in history. The most original of his creations is probably his theory of elliptical functions , which he published in 1829 in his work Fundamenta nova theoriae functionum ellipticarum . Simultaneously and independently of Abel, he introduced the inverse functions to the elliptic integrals already examined by Euler and others, which he called elliptic functions. They were twofold periodic complex functions. His work on the fourfold periodic functions (so-called hyperelliptic integrals or Abelian integrals ) was also brilliant . He also later gave a formulation of the theory of elliptic functions with theta functions . His investigations into the division of circles and their application to number theory (theory of square, cubic and bicubic remainders including the reciprocity law for cubic remainders) emerged from Carl Friedrich Gauß and his Disquisitiones arithmeticae and his treatise on biquadratic remainders. A planned book on number theory was not completed. In algebra, he systematically dealt with determinants. Jacobi was not only a master at manipulating complicated formulas, but also an excellent mental calculator and published tables of number theory. He also worked with the mental calculator Johann Martin Dase .

Jacobi's investigations into differential geometry (surfaces of the second degree, including geodesics on an ellipsoid ), partial differential equations and the calculus of variations (including his theory of conjugate points) make him a pioneer of mathematical physics , for example in the Hamilton-Jacobi theory of classical mechanics. Following William Rowan Hamilton , whose On a general method in dynamics he read in 1834 or early 1835, Jacobi deals with analytical mechanics, which was at the same time the beginning of his occupation with applied mathematics. Basically, he was a representative of pure mathematics, as he explained in his inaugural address on entering the philosophical faculty in Königsberg in 1832 (and already in one of his theses for the doctoral examination in 1825). For him it was a model for other sciences and did not require any legitimation by philosophy or natural sciences.

He investigated equilibrium figures of rotating fluids, which Colin MacLaurin and others had already investigated, and found new solutions (an ellipsoid with three unequal axes).

Jacobi was also an outstanding personality as a teacher. He was referred to by his students as the " Euler of the 19th century", although he was only active in research for 25 years. His students include Karl Wilhelm Borchardt , Friedrich Julius Richelot , Otto Hesse , Johann Georg Rosenhain , Wilhelm Scheibner (1826–1908), Philipp Ludwig von Seidel , Eduard Heine .

The Jacobi matrix , the Jacobi polynomials , the Jacobi method , the Jacobi method for eigenvalues , the Jacobi identity , the Jacobi symbol , the Jacobi field , and the Jacobi-Perron algorithm as a multi-dimensional generalization of the Euclidean algorithm .

He drew up a plan for the complete edition of Leonhard Euler's works, which was not realized until later. He corresponded about it with Paul-Heinrich Fuß, a descendant of Euler and secretary of the Academy in Saint Petersburg. Other contributions to the history of mathematics included a. a lecture on René Descartes in 1846 in the Sing-Akademie zu Berlin and contributions on ancient Greek mathematicians to Alexander von Humboldt's cosmos. During his stay in Rome he studied the manuscripts of Diophantos of Alexandria in the Vatican library.

Awards

The lunar crater Jacobi and the asteroid (12040) Jacobi are named after him.

Fonts

  • Fundamenta nova theoriae functionum ellipticarum. Königsberg, Bornträger 1829.
  • Collected Works. 7 volumes, (Eds. Karl Wilhelm Borchardt , Alfred Clebsch , Karl Weierstraß ), at the instigation of the Prussian Academy of Sciences. Berlin, Reimer 1881 to 1891, reprint 1969.
    • Volume 1, 1881 (with the memorial speech by Dirichlet and the Fundamenta Nova and other works on elliptical functions, Ed. Borchardt).
    • Volume 2, 1882 (Ed. Weierstraß, also elliptical and Abelian functions).
    • Volume 3, 1884 (Ed. Weierstrass, Algebra, functional determinant).
    • Volume 4, 1886 (Ed. Weierstrass, Partial Differential Equations, Mechanics).
    • Volume 5, 1890 (Ed. Weierstraß, Partial Differential Equations, Mechanics from the estate).
    • Volume 6, 1891 (Ed. Weierstraß, Certain Integrals, Series, Number Theory).
    • Volume 7, 1891 (Ed. Weierstrasse, Geometry, Astronomy, History of Mathematics).
  • Canon arithmeticus sive tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes. Berlin, Akad. Wiss., 1839. New edition ed. by Heinrich Brandt . Berlin, Akademie Verlag 1956 (not in the collected works).
  • Lectures on dynamics by CGJ Jacobi, together with five treatises of the same, edited by A. Clebsch. Berlin, Reimer 1866, 2nd edition 1884 as a supplement to the collected works.
  • Lectures on number theory: Winter semester 1836/37 Königsber. , (Eds. Franz Lemmermeyer , Herbert Pieper, E. Rauner), 2007.
  • Lectures on analytical mechanics: Berlin 1847/48, based on a transcript by Wilhelm Scheibner. ed. by Helmut Pulte. Vieweg 1996.
  • Correspondence Adrien-Marie Legendre - Carl Gustav Jacob Jacobi = Correspondance mathematique entre Legendre et Jacobi: with the essay "CGJ Jacobi in Berlin". (Ed. Herbert Pieper). Teubner 1998.
  • Correspondence between CGJ Jacobi and MH Jacobi. Teubner, Leipzig 1907, archive.org .
  • Correspondence between Alexander von Humboldt and CGJ Jacobi. (Ed. By Herbert Pieper). Akademie Verlag, Berlin 1987.
  • The correspondence between CGJ Jacobi and PH von Fuss about the publication of Leonhard Euler's works. (Ed. By Paul Stäckel and Wilhelm Ahrens ), Teubner, Leipzig 1908.
  • About the functional determinants (De determinantibus functionalibus). (Ed. Paul Stäckel ), Engelmann, Leipzig 1896.
  • About the formation and properties of the determinants. (De formatione et proprietatibus determinantium). (Ed. Paul Stäckel). W. Engelman, Leipzign 1896 (first 1841).
  • Treatises on the calculus of variations, Volume 2 (Lagrange, Legendre, Jacobi). (Ed. Paul Stäckel), Leipzig, Engelmann 1894 (in it by Jacobi: On the theory of the calculus of variations and the differential equations . In: Crelles Journal , Volume 17, 1837, pp. 68-82).
  • About the quadruple periodic functions of two variables on which the theory of Abelian transcendent is based. (Ed. Heinrich Weber ). Engelmann, Leipzig 1895 (translated from Latin).
  • New method for integrating first order partial differential equations between any number of variables. (Ed. G. Kowalewski), Leipzig, Engelmann 1906.
  • Theory of elliptic functions derived from the properties of the theta series. (Ed. Adolf Kneser ). Academic Publishing Company, Leipzig 1927.

See also

literature

Web links

Commons : Carl Gustav Jacob Jacobi  - Album with pictures, videos and audio files
Wikisource: Carl Gustav Jacob Jacobi  - Sources and full texts
Wikiquote: Carl Gustav Jacob Jacobi  - Quotes

Individual evidence

  1. ↑ Although the Jewish emancipation in Prussia took place through the Jewish edict of 1812 , Jews were nevertheless at a disadvantage in their academic careers; from 1822 Jews were excluded from civil service.
  2. ↑ Helmut Pulte (ed.): Jacobi: Lectures on analytical mechanics. Berlin 1847/48, based on a transcript by Wilhelm Scheibner; Vieweg 1996, p. XIX. In his correspondence with his brother, he continued to address Jacques until his death.
  3. ^ A b Stephanie Fröba, Alfred Wassermann: The most important mathematicians. Marix Verlag, Wiesbaden, 2007, p. 112.
  4. ↑ Helmut Pulte (Ed.): Jacobi, Lectures Analyt. Mech. , S. XIX.
  5. ^ Carl Gustav Jacob Jacobi in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  6. ↑ a b c Orden pour le Mérite for Sciences and Arts - The members of the order , Volume 1: 1842–1881 . Gebrüder Mann Verlag, Berlin 1975, ISBN 3-7861-6189-5 , p. 52.
  7. ↑ Gauss's letters to Jacobi are lost, but there was also no regular correspondence as with Legendre.
  8. ^ Scriba: "Jacobi" Dictionary of Scientific Biography.
  9. ^ BBAW: CGJ Jacobi
  10. ^ Entry on Jacobi, Karl Gustav Jacob (1804–1851) in the archive of the Royal Society , London
  11. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. (PDF) Royal Society of Edinburgh, accessed December 23, 2019 .
  12. ↑ Entry on Jacobi, Carl Gustav Jacob at the Russian Academy of Sciences (English)
  13. ^ List of members since 1666: letter J. Académie des sciences, accessed on November 29, 2019 (French).
  14. ↑ 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. 122.
  15. ^ Hans-Jürgen Mende : Lexicon of Berlin burial places . Pharus-Plan, Berlin 2018, ISBN 978-3-86514-206-1 , p. 226.
  16. ↑ Honorary graves of the State of Berlin (as of November 2018) . (PDF, 413 kB) Senate Department for the Environment, Transport and Climate Protection, p. 39; accessed on April 5, 2019. Submission - for information - about the recognition and further preservation of graves of well-known and deserving personalities as honorary graves in Berlin . (PDF, 158 kB). Berlin House of Representatives, printed matter 14/1607 of November 1, 2001, p. 4; accessed on April 5, 2019.
personal data
SURNAME Jacobi, Carl Gustav Jacob
ALTERNATIVE NAMES Jacobi, Jacques Simon (real name)
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH December 10, 1804
PLACE OF BIRTH Potsdam
DATE OF DEATH February 18, 1851
Place of death Berlin