354:, where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc. As a result of the good education he had received from his uncle, as well as his own remarkable abilities, after less than half a year Jacobi was moved to the senior year despite his young age. However, as the University would not accept students younger than 16 years old, he had to remain in the senior class until 1821. He used this time to advance his knowledge, showing interest in all subjects, including Latin, Greek, philology, history and mathematics. During this period he also made his first attempts at research, trying to solve the
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393:. By 1823 he understood that he needed to make a decision between his competing interests and chose to devote all his attention to mathematics. In the same year he became qualified to teach secondary school and was offered a position at the Joachimsthal Gymnasium in Berlin. Jacobi decided instead to continue to work towards a university position. In 1825, he obtained the degree of Doctor of Philosophy with a dissertation on the
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It was in algebraic development that Jacobi's particular power mainly lay, and he made important contributions of this kind in many areas of mathematics, as shown by his long list of papers in Crelle's
Journal and elsewhere from 1826 onwards. He is said to have told his students that when looking for
685:
381:, drawing the professor's attention with his talent. Jacobi did not follow a lot of mathematics classes at the time, finding the level of mathematics taught at Berlin University too elementary. He continued, instead, with his private study of the more advanced works of
350:, would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam
938:, sive tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes, Berlin: Typis Academicis, Berolini, 1839,
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club. This led, after the suppression of the revolution, to his royal grant being cut off – but his fame and reputation were such that it was soon resumed, thanks to the personal intervention of
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for a few months to regain his health. On his return he moved to Berlin, where he lived as a royal pensioner, apart from a very brief interim, until his death. During the
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to arbitrary algebraic curves, may be seen as a higher genus generalization of the relation between elliptic integrals and the Jacobi or
Weierstrass elliptic functions.
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independent variables, which plays an important part in changes of variables in multiple integrals, and in many analytical investigations. In 1841 he reintroduced the
1815:
1810:
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910:, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften, vol. I–VIII (2nd ed.), New York: Chelsea Publishing Co., 1969 ,
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and at the same time converted to
Christianity. Now qualifying for teaching university classes, the 21-year-old Jacobi lectured in 1825/26 on the theory of
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509:. Theta functions are of great importance in mathematical physics because of their role in the inverse problem for periodic and quasi-periodic flows. The
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1027:, Algorismus. Studien zur Geschichte der Mathematik und der Naturwissenschaften , vol. 62, Dr. Erwin Rauner Verlag, Augsburg, 2007 ,
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1541:"Review: Leo Königsberger, Carl Gustav Jacob Jacobi. Festschrift zur Feier der hundertsten Wiederkehr seines Geburtstages"
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He left many manuscripts, portions of which have been published at intervals in Crelle's
Journal. His other works include
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and other particular dynamical problems likewise occupied his attention from time to time. While contributing to
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In his 1835 paper, Jacobi proved the following basic result classifying periodic (including elliptic) functions:
556:), reflecting his belief that inverting known results can open up new fields for research, for example inverting
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134:
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He discovered many of the fundamental properties of theta functions, including the functional equation and the
571:, then such a function cannot have more than two periods, and the ratio of the periods cannot be a real number.
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1534:. Festschrift zur Feier der hundertsten Wiederkehr seines Geburtstages (in German). Leipzig: B.G. Teubner.
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Jacobi was politically involved and unsuccessfully presented his parliamentary candidature on behalf of a
1663:
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1137:, Translation of De investigando ordine systematis æquationibus differentialium vulgarium cujuscunque,
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994:, Dokumente zur Geschichte der Mathematik , vol. 8, Freiburg: Deutsche Mathematiker Vereinigung,
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on 10 December 1804. He was the second of four children of a banker, Simon Jacobi. His elder brother,
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1086:, Translation of De aequationum differentialium systemate non normali ad formam normalem revocando,
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He was also one of the early founders of the theory of determinants. In particular, he invented the
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He was one of the first to introduce and study the symmetric polynomials that are now known as
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315:
919:
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8:
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31:
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1053:, Texts and Readings in Mathematics, vol. 51, New Delhi: Hindustan Book Agency,
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He also made fundamental contributions in the study of differential equations and to
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Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem
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Ollivier, François; Cohn, Sigismund; Borchardt, C. W.; et al., eds. (2009) ,
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1128:"Looking for the order of a system of arbitrary ordinary differential equations"
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677:. This method of inversion, and its subsequent extension by Weierstrass and
1435:(in German), vol. 50, Leipzig: Duncker & Humblot, pp. 598–602
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1500:. Vol. 15 (11th ed.). Cambridge University Press. p. 117.
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a research topic, one should 'Invert, always invert' (German original:
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Ollivier, François; Cohn, Sigismund; Borchardt., C. W., eds. (2009) ,
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Clebsch, A.; Balagangadharan, K.; Banerjee, Biswarup, eds. (2009) ,
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Vorlesungen über
Zahlentheorie---Wintersemester 1836/37, Königsberg
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This article incorporates text from a publication now in the
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Corresponding members of the Saint
Petersburg Academy of Sciences
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Applicable
Algebra in Engineering, Communication and Computing
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Applicable
Algebra in Engineering, Communication and Computing
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Honorary members of the Saint
Petersburg Academy of Sciences
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and focusing on the nature of elliptic and theta functions.
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One of Jacobi's greatest accomplishments was his theory of
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30:"Carl Jacobi" redirects here. For the American author, see
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infection. His grave is preserved at a cemetery in the
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His other work in number theory continued the work of
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537:(planetary motion in a central gravitational field).
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Disquisitiones
Analyticae de Fractionibus Simplicibus
1509:
Remarkable Mathematicians: From Euler to Von Neumann
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Jacobi was the first to apply elliptic functions to
471:(61 Baruther Street). His grave is close to that of
306:; 10 December 1804 – 18 February 1851) was a German
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1205:
List of things named after Carl Gustav Jacob Jacobi
567:If a univariate single-valued function is multiply
377:. In philology, he participated in the seminars of
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606:and later the general Riemann theta function for
1786:Members of the Royal Swedish Academy of Sciences
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887:Fundamenta nova theoriae functionum ellipticarum
502:Fundamenta nova theoriae functionum ellipticarum
1447:Journal für die reine und angewandte Mathematik
955:Journal für die reine und angewandte Mathematik
951:"De formatione et proprietatibus Determinatium"
436:, and held the chair until 1842. He suffered a
1816:Academic staff of the University of Königsberg
1811:Recipients of the Pour le Mérite (civil class)
900:, Reprinted by Cambridge University Press 2012
469:Friedhof I der Dreifaltigkeits-Kirchengemeinde
428:, and in finally 1829, a tenured professor of
1595:Bulletin of the American Mathematical Society
1588:"Current tendencies of mathematical research"
1527:
1442:"Gedächtnißrede auf Carl Gustav Jacob Jacobi"
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1392:Earliest Uses of Various Mathematical Symbols
1306:
1271:Random House Webster's Unabridged Dictionary
1781:Members of the Prussian Academy of Sciences
1710:Carl Gustav Jacob Jacobi - Œuvres complètes
1405:
707:, and similar results for 6 and 8 squares.
499:. This was developed in his great treatise
486:
1801:People from the Margraviate of Brandenburg
1741:Mathematicians from the Kingdom of Prussia
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768:for these, which is a special case of the
579:formula, as well as many other results on
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638:algebraic curve, obtained by quotienting
602:in 1854 required the introduction of the
1806:German people of the Revolutions of 1848
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778:Desnanot–Jacobi formula for determinants
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1651:MacTutor History of Mathematics Archive
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1228:His given name is sometimes written as
440:from overwork in 1843. He then visited
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1388:"Earliest Uses of Symbols of Calculus"
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310:who made fundamental contributions to
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992:Vorlesungen über analytische Mechanik
301:
1776:Humboldt University of Berlin alumni
1761:Foreign members of the Royal Society
401:defended before a commission led by
495:and their relation to the elliptic
405:. He followed immediately with his
24:
1736:19th-century German mathematicians
1200:Last geometric statement of Jacobi
870:(1881–1891) were published by the
662:{\displaystyle {\mathbf {C} }^{g}}
529:, the symmetric Lagrange top in a
25:
1827:
1696:"Jacobi, Karl Gustav Jakob"
1680:"Jacobi, Karl Gustav Jakob"
1664:"Jacobi, Karl Gustav Jakob"
1625:
1440:Dirichlet, P. G. Lejeune (1855),
673:of periods is referred to as the
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757:, which was to become standard.
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365:In 1821 Jacobi went to study at
267:
27:German mathematician (1804–1851)
1608:10.1090/S0002-9904-1916-02863-1
1558:10.1090/S0002-9904-1906-01326-X
1417:. New York: Simon and Schuster.
1386:Aldrich, John (June 23, 2017).
877:
521:in the well-known cases of the
505:(1829), and in later papers in
1686:New International Encyclopedia
1513:. Cambridge University Press.
1505:James, Ioan Mackenzie (2002).
1432:Allgemeine Deutsche Biographie
1222:
890:(in Latin), Königsberg, 1829,
718:, and the introduction of the
705:Lagrange's four-square theorem
395:partial fraction decomposition
13:
1:
1586:Van Vleck, Edward B. (1916).
1268:"Jacobi, Carl Gustav Jacob".
1239:
1051:Jacobi's lectures on dynamics
475:, the astronomer. The crater
417:at the University of Berlin.
1566:Christoph J. Scriba (1974),
1244:
990:Pulte, Helmut, ed. (1996) ,
604:hyperelliptic theta function
333:
7:
1568:"Jacobi, Carl Gustav Jacob"
1528:Koenigsberger, Leo (1904).
1178:
519:Jacobi's elliptic functions
459:Jacobi died in 1851 from a
174:Popularizing the character
171:Jacobi eigenvalue algorithm
131:Jacobi's elliptic functions
10:
1832:
1646:"Carl Gustav Jacob Jacobi"
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835:sidereal coordinate system
29:
1492:Jacobi, Karl Gustav Jacob
1427:Jacobi, Carl Gustav Jacob
1147:10.1007/s00200-009-0087-3
1096:10.1007/s00200-009-0088-2
1000:10.1007/978-3-322-80289-7
776:. He also discovered the
554:"man muss immer umkehren"
420:In 1826, Jacobi became a
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1656:University of St Andrews
1634:Vorlesungen über Dynamik
1573:Neue Deutsche Biographie
1539:Pierpont, James (1906).
1531:Carl Gustav Jacob Jacobi
1215:
1190:Friedrich Wilhelm Bessel
967:10.1515/crll.1841.22.285
843:Vorlesungen über Dynamik
688:Carl Gustav Jacob Jacobi
592:Jacobi inversion problem
487:Scientific contributions
263:Carl Gustav Jacob Jacobi
163:Hamilton–Jacobi equation
41:Carl Gustav Jacob Jacobi
1791:German number theorists
1702:The American Cyclopædia
1497:Encyclopædia Britannica
774:Jacobi–Trudi identities
764:, giving the so-called
741:partial derivatives of
726:, and the invention of
467:section of Berlin, the
1756:Differential geometers
1670:Encyclopedia Americana
770:Weyl character formula
696:, for example proving
689:
663:
632:
618:associated to a genus
594:for the hyperelliptic
573:
546:Hamilton–Jacobi theory
454:Alexander von Humboldt
426:extraodinary professor
424:, in the next year an
320:differential equations
1545:Bull. Amer. Math. Soc
1185:Augustin-Louis Cauchy
961:(22): 285–318. 1841.
801:Hamiltonian mechanics
780:, which underlie the
716:quadratic reciprocity
687:
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585:hypergeometric series
577:Jacobi triple product
565:
434:Königsberg University
203:Königsberg University
1751:Deaths from smallpox
1642:Robertson, Edmund F.
864:Opuscula mathematica
837:. His theory of the
829:, he introduced the
807:often encounter the
735:Jacobian determinant
642:
622:
590:The solution of the
483:is named after him.
116:University of Berlin
98:, Kingdom of Prussia
1796:People from Potsdam
1640:O'Connor, John J.;
1372:, pp. 285–318.
1336:, pp. 193–217.
1321:, pp. 261–262.
827:celestial mechanics
772:, and deriving the
766:bialternant formula
745:given functions of
724:continued fractions
542:classical mechanics
531:gravitational field
511:equations of motion
338:Jacobi was born of
127:Abel–Jacobi theorem
32:Carl Richard Jacobi
1413:Men of Mathematics
1307:Koenigsberger 1904
935:Canon arithmeticus
859:Canon arithmeticus
751:partial derivative
701:two-square theorem
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558:elliptic integrals
493:elliptic functions
446:Revolution of 1848
399:rational fractions
312:elliptic functions
303:[jaˈkoːbi]
147:Jacobi polynomials
74:Kingdom of Prussia
18:Carl Gustav Jacobi
1520:978-0-521-52094-2
1407:Temple Bell, Eric
1348:, pp. 69–74.
1230:Karl Gustav Jakob
1210:Niels Henrik Abel
1034:978-3-936905-25-0
1009:978-3-528-06692-5
897:978-1-108-05200-9
866:(1846–1857). His
805:operator algebras
782:Plücker relations
762:Schur polynomials
631:{\displaystyle g}
367:Berlin University
260:
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239:Doctoral students
183:Scientific career
78:Holy Roman Empire
16:(Redirected from
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1712:Gallica-Math
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1578:; (
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1257:Aldrich 2017
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924:, retrieved
920:the original
906:
886:
878:Publications
867:
863:
862:(1839), and
857:
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845:, edited by
842:
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732:
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589:
574:
566:
562:
553:
550:
539:
517:in terms of
500:
490:
473:Johann Encke
458:
419:
407:Habilitation
403:Enno Dirksen
364:
337:
324:determinants
262:
261:
233:Enno Dirksen
214:
199:Institutions
182:
90:(1851-02-18)
1731:1851 deaths
1726:1804 births
1601:(1): 1–14.
1454:: 193–217,
1370:Jacobi 1841
1141:(1): 7–32,
819:operation.
817:Lie bracket
728:Jacobi sums
600:Weierstrass
430:mathematics
375:mathematics
243:Paul Gordan
193:Mathematics
104:Nationality
1720:Categories
1346:James 2002
1240:References
926:2012-03-20
797:Lie theory
533:, and the
515:integrable
247:Otto Hesse
62:1804-12-10
1632:Jacobi's
1617:0002-9904
1460:0075-4102
1425:(1905), "
1245:Citations
1155:0938-1279
1104:0938-1279
983:123007787
975:0075-4102
527:Euler top
465:Kreuzberg
438:breakdown
371:philology
352:Gymnasium
334:Biography
1409:(1937).
1397:20 April
1179:See also
1171:20652724
856:(1832),
849:(1866).
815:for the
755:Legendre
698:Fermat's
596:Abel map
581:q-series
569:periodic
523:pendulum
461:smallpox
415:surfaces
387:Lagrange
360:radicals
316:dynamics
135:Jacobian
1705:. 1879.
1689:. 1905.
1673:. 1920.
1485::
1468:1104895
1379:Sources
1163:2496659
1112:2496660
1069:2569315
1043:2573816
1018:1414679
944:0081559
916:0260557
679:Riemann
671:lattice
669:by the
479:on the
450:Liberal
391:Laplace
344:Potsdam
299:German:
70:Potsdam
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525:, the
477:Jacobi
411:curves
348:Moritz
326:, and
221:(1825)
219:
210:Thesis
189:Fields
107:German
96:Berlin
1591:(PDF)
1216:Notes
1167:S2CID
1131:(PDF)
1116:S2CID
1080:(PDF)
979:S2CID
712:Gauss
612:genus
442:Italy
383:Euler
379:Böckh
1613:ISSN
1515:ISBN
1456:ISSN
1399:2017
1151:ISSN
1100:ISSN
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1004:ISBN
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959:1841
892:ISBN
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