343:, 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
1465:
382:. 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
38:
540:
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
674:
370:, 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
339:, 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
927:, 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,
1734:
441:
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
1759:
656:
592:
766:
433:
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
1480:
670:
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.
738:
independent variables, which plays an important part in changes of variables in multiple integrals, and in many analytical investigations. In 1841 he reintroduced the
1804:
1799:
1774:
899:, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften, vol. I–VIII (2nd ed.), New York: Chelsea Publishing Co., 1969 ,
625:
204:
398:
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
1769:
498:. Theta functions are of great importance in mathematical physics because of their role in the inverse problem for periodic and quasi-periodic flows. The
1789:
1729:
1193:
811:
1435:
1794:
490:
1259:
1764:
1749:
1016:, Algorismus. Studien zur Geschichte der Mathematik und der Naturwissenschaften , vol. 62, Dr. Erwin Rauner Verlag, Augsburg, 2007 ,
1724:
1485:
689:
1698:
894:
1576:
1639:
754:
515:
1507:
1021:
996:
884:
1530:"Review: Leo Königsberger, Carl Gustav Jacob Jacobi. Festschrift zur Feier der hundertsten Wiederkehr seines Geburtstages"
841:
He left many manuscripts, portions of which have been published at intervals in Crelle's
Journal. His other works include
1415:
1188:
457:
1754:
1047:
693:
403:
1556:
1779:
1744:
823:
814:
and other particular dynamical problems likewise occupied his attention from time to time. While contributing to
723:
552:
In his 1835 paper, Jacobi proved the following basic result classifying periodic (including elliptic) functions:
545:), reflecting his belief that inverting known results can open up new fields for research, for example inverting
399:
123:
1674:
1668:
1420:
564:
He discovered many of the fundamental properties of theta functions, including the functional equation and the
560:, then such a function cannot have more than two periods, and the ratio of the periods cannot be a real number.
507:
383:
119:
1739:
104:
1784:
1684:
860:
805:
762:
534:
151:
1523:. Festschrift zur Feier der hundertsten Wiederkehr seines Geburtstages (in German). Leipzig: B.G. Teubner.
437:
Jacobi was politically involved and unsuccessfully presented his parliamentary candidature on behalf of a
1652:
159:
630:
1126:, Translation of De investigando ordine systematis æquationibus differentialium vulgarium cujuscunque,
1690:
983:, Dokumente zur Geschichte der Mathematik , vol. 8, Freiburg: Deutsche Mathematiker Vereinigung,
335:
on 10 December 1804. He was the second of four children of a banker, Simon Jacobi. His elder brother,
414:
239:
1075:, Translation of De aequationum differentialium systemate non normali ad formam normalem revocando,
722:
He was also one of the early founders of the theory of determinants. In particular, he invented the
1644:
1561:
1178:
1116:
1065:
580:
291:
422:
191:
115:
1634:
367:
1658:
758:
749:
He was one of the first to introduce and study the symmetric polynomials that are now known as
442:
1430:
1173:
789:
743:
704:
573:
565:
308:
1719:
1714:
1456:
1151:
1100:
1057:
1031:
1006:
932:
904:
801:
700:
304:
908:
770:
8:
1630:
815:
600:
584:
530:
519:
499:
495:
340:
20:
922:
874:
1568:
1496:
1400:
1155:
1104:
967:
847:
739:
712:
610:
434:
348:
135:
62:
1667:
1620:
1651:
1601:
1518:
1503:
1444:
1198:
1139:
1088:
1043:
1042:, Texts and Readings in Mathematics, vol. 51, New Delhi: Hindustan Book Agency,
1017:
992:
971:
959:
880:
781:
557:
546:
529:
He also made fundamental contributions in the study of differential equations and to
481:
387:
355:
336:
300:
66:
1596:
1546:
1159:
843:
Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem
1591:
1541:
1529:
1395:
1183:
1131:
1080:
984:
951:
793:
750:
686:
667:
663:
588:
426:
344:
257:
216:
139:
131:
1683:
1108:
1064:
Ollivier, François; Cohn, Sigismund; Borchardt, C. W.; et al., eds. (2009) ,
1452:
1147:
1096:
1053:
1027:
1002:
928:
900:
819:
797:
659:
596:
503:
465:
147:
143:
1117:"Looking for the order of a system of arbitrary ordinary differential equations"
1066:"The reduction to normal form of a non-normal system of differential equations"
835:
523:
485:
1135:
1084:
988:
1708:
1605:
1476:
1471:
1448:
1411:
1143:
1092:
963:
955:
708:
682:
604:
328:
316:
296:
155:
127:
666:. This method of inversion, and its subsequent extension by Weierstrass and
1424:(in German), vol. 50, Leipzig: Duncker & Humblot, pp. 598–602
774:
461:
410:
395:
391:
312:
221:
1565:(in German), vol. 10, Berlin: Duncker & Humblot, pp. 233–234
1376:
785:
418:
363:
231:
181:
1489:. Vol. 15 (11th ed.). Cambridge University Press. p. 117.
716:
541:
a research topic, one should 'Invert, always invert' (German original:
438:
235:
1115:
Ollivier, François; Cohn, Sigismund; Borchardt., C. W., eds. (2009) ,
453:
359:
1038:
Clebsch, A.; Balagangadharan, K.; Banerjee, Biswarup, eds. (2009) ,
939:
358:, where he initially divided his attention between his passions for
1014:
Vorlesungen über
Zahlentheorie---Wintersemester 1836/37, Königsberg
569:
511:
449:
375:
1470:
This article incorporates text from a publication now in the
1735:
Corresponding members of the Saint
Petersburg Academy of Sciences
379:
332:
58:
673:
198:
84:
1318:
1316:
1124:
Applicable
Algebra in Engineering, Communication and Computing
1073:
Applicable
Algebra in Engineering, Communication and Computing
711:; contributions to higher reciprocity laws, investigations of
37:
430:
371:
164:
1760:
Honorary members of the Saint
Petersburg Academy of Sciences
549:
and focusing on the nature of elliptic and theta functions.
1313:
480:
One of Jacobi's greatest accomplishments was his theory of
469:
278:
272:
263:
19:"Carl Jacobi" redirects here. For the American author, see
1301:
260:
1352:
1340:
1289:
452:
infection. His grave is preserved at a cemetery in the
1279:
1277:
1275:
1273:
1271:
1269:
699:
His other work in number theory continued the work of
1328:
633:
613:
526:(planetary motion in a central gravitational field).
269:
205:
Disquisitiones
Analyticae de Fractionibus Simplicibus
1498:
Remarkable Mathematicians: From Euler to Von Neumann
681:
Jacobi was the first to apply elliptic functions to
460:(61 Baruther Street). His grave is close to that of
295:; 10 December 1804 – 18 February 1851) was a German
275:
1554:
1266:
1194:
List of things named after Carl Gustav Jacob Jacobi
556:If a univariate single-valued function is multiply
366:. In philology, he participated in the seminars of
266:
1495:
1399:
1239:
650:
619:
1628:
595:and later the general Riemann theta function for
1775:Members of the Royal Swedish Academy of Sciences
1706:
876:Fundamenta nova theoriae functionum ellipticarum
491:Fundamenta nova theoriae functionum ellipticarum
1436:Journal für die reine und angewandte Mathematik
944:Journal für die reine und angewandte Mathematik
940:"De formatione et proprietatibus Determinatium"
425:, and held the chair until 1842. He suffered a
1805:Academic staff of the University of Königsberg
1800:Recipients of the Pour le Mérite (civil class)
889:, Reprinted by Cambridge University Press 2012
458:Friedhof I der Dreifaltigkeits-Kirchengemeinde
417:, and in finally 1829, a tenured professor of
1584:Bulletin of the American Mathematical Society
1577:"Current tendencies of mathematical research"
1516:
1431:"Gedächtnißrede auf Carl Gustav Jacob Jacobi"
1410:
1381:Earliest Uses of Various Mathematical Symbols
1295:
1260:Random House Webster's Unabridged Dictionary
1770:Members of the Prussian Academy of Sciences
1699:Carl Gustav Jacob Jacobi - Œuvres complètes
1394:
696:, and similar results for 6 and 8 squares.
488:. This was developed in his great treatise
475:
1790:People from the Margraviate of Brandenburg
1730:Mathematicians from the Kingdom of Prussia
1251:
757:for these, which is a special case of the
568:formula, as well as many other results on
36:
1595:
1574:
1545:
1428:
1346:
1322:
627:algebraic curve, obtained by quotienting
591:in 1854 required the introduction of the
1795:German people of the Revolutions of 1848
1527:
1475:
1307:
1283:
767:Desnanot–Jacobi formula for determinants
672:
1640:MacTutor History of Mathematics Archive
1374:
1245:
1217:His given name is sometimes written as
429:from overwork in 1843. He then visited
1707:
1377:"Earliest Uses of Symbols of Calculus"
1358:
1114:
1063:
1037:
1012:
978:
938:
921:
893:
873:
299:who made fundamental contributions to
1493:
1334:
981:Vorlesungen über analytische Mechanik
290:
1765:Humboldt University of Berlin alumni
1750:Foreign members of the Royal Society
390:defended before a commission led by
484:and their relation to the elliptic
394:. He followed immediately with his
13:
1725:19th-century German mathematicians
1189:Last geometric statement of Jacobi
859:(1881–1891) were published by the
651:{\displaystyle {\mathbf {C} }^{g}}
518:, the symmetric Lagrange top in a
14:
1816:
1685:"Jacobi, Karl Gustav Jakob"
1669:"Jacobi, Karl Gustav Jakob"
1653:"Jacobi, Karl Gustav Jakob"
1614:
1429:Dirichlet, P. G. Lejeune (1855),
662:of periods is referred to as the
1463:
746:, which was to become standard.
637:
354:In 1821 Jacobi went to study at
256:
16:German mathematician (1804–1851)
1597:10.1090/S0002-9904-1916-02863-1
1547:10.1090/S0002-9904-1906-01326-X
1406:. New York: Simon and Schuster.
1375:Aldrich, John (June 23, 2017).
866:
510:in the well-known cases of the
494:(1829), and in later papers in
1675:New International Encyclopedia
1502:. Cambridge University Press.
1494:James, Ioan Mackenzie (2002).
1421:Allgemeine Deutsche Biographie
1211:
879:(in Latin), Königsberg, 1829,
707:, and the introduction of the
694:Lagrange's four-square theorem
384:partial fraction decomposition
1:
1575:Van Vleck, Edward B. (1916).
1257:"Jacobi, Carl Gustav Jacob".
1228:
1040:Jacobi's lectures on dynamics
464:, the astronomer. The crater
406:at the University of Berlin.
1555:Christoph J. Scriba (1974),
1233:
979:Pulte, Helmut, ed. (1996) ,
593:hyperelliptic theta function
322:
7:
1557:"Jacobi, Carl Gustav Jacob"
1517:Koenigsberger, Leo (1904).
1167:
508:Jacobi's elliptic functions
448:Jacobi died in 1851 from a
163:Popularizing the character
160:Jacobi eigenvalue algorithm
120:Jacobi's elliptic functions
10:
1821:
1635:"Carl Gustav Jacob Jacobi"
1367:
824:sidereal coordinate system
18:
1481:Jacobi, Karl Gustav Jacob
1416:Jacobi, Carl Gustav Jacob
1136:10.1007/s00200-009-0087-3
1085:10.1007/s00200-009-0088-2
989:10.1007/978-3-322-80289-7
765:. He also discovered the
543:"man muss immer umkehren"
409:In 1826, Jacobi became a
245:
240:Friedrich Julius Richelot
227:
215:
197:
187:
177:
170:
111:
100:
92:
73:
44:
35:
28:
1755:19th-century German Jews
1645:University of St Andrews
1623:Vorlesungen über Dynamik
1562:Neue Deutsche Biographie
1528:Pierpont, James (1906).
1520:Carl Gustav Jacob Jacobi
1204:
1179:Friedrich Wilhelm Bessel
956:10.1515/crll.1841.22.285
832:Vorlesungen über Dynamik
677:Carl Gustav Jacob Jacobi
581:Jacobi inversion problem
476:Scientific contributions
252:Carl Gustav Jacob Jacobi
152:Hamilton–Jacobi equation
30:Carl Gustav Jacob Jacobi
1780:German number theorists
1691:The American Cyclopædia
1486:Encyclopædia Britannica
763:Jacobi–Trudi identities
753:, giving the so-called
730:partial derivatives of
715:, and the invention of
456:section of Berlin, the
1745:Differential geometers
1659:Encyclopedia Americana
759:Weyl character formula
685:, for example proving
678:
652:
621:
607:associated to a genus
583:for the hyperelliptic
562:
535:Hamilton–Jacobi theory
443:Alexander von Humboldt
415:extraodinary professor
413:, in the next year an
309:differential equations
1534:Bull. Amer. Math. Soc
1174:Augustin-Louis Cauchy
950:(22): 285–318. 1841.
790:Hamiltonian mechanics
769:, which underlie the
705:quadratic reciprocity
676:
653:
622:
574:hypergeometric series
566:Jacobi triple product
554:
423:Königsberg University
192:Königsberg University
1740:Deaths from smallpox
1631:Robertson, Edmund F.
853:Opuscula mathematica
826:. His theory of the
818:, he introduced the
796:often encounter the
724:Jacobian determinant
631:
611:
579:The solution of the
472:is named after him.
105:University of Berlin
87:, Kingdom of Prussia
1785:People from Potsdam
1629:O'Connor, John J.;
1361:, pp. 285–318.
1325:, pp. 193–217.
1310:, pp. 261–262.
816:celestial mechanics
761:, and deriving the
755:bialternant formula
734:given functions of
713:continued fractions
531:classical mechanics
520:gravitational field
500:equations of motion
327:Jacobi was born of
116:Abel–Jacobi theorem
21:Carl Richard Jacobi
1402:Men of Mathematics
1296:Koenigsberger 1904
924:Canon arithmeticus
848:Canon arithmeticus
740:partial derivative
690:two-square theorem
679:
648:
617:
547:elliptic integrals
482:elliptic functions
435:Revolution of 1848
388:rational fractions
301:elliptic functions
292:[jaˈkoːbi]
136:Jacobi polynomials
63:Kingdom of Prussia
1509:978-0-521-52094-2
1396:Temple Bell, Eric
1337:, pp. 69–74.
1219:Karl Gustav Jakob
1199:Niels Henrik Abel
1023:978-3-936905-25-0
998:978-3-528-06692-5
886:978-1-108-05200-9
855:(1846–1857). His
794:operator algebras
771:Plücker relations
751:Schur polynomials
620:{\displaystyle g}
356:Berlin University
249:
248:
228:Doctoral students
172:Scientific career
67:Holy Roman Empire
1812:
1695:
1687:
1679:
1671:
1663:
1655:
1647:
1609:
1599:
1581:
1569:full text online
1566:
1551:
1549:
1524:
1513:
1501:
1490:
1469:
1467:
1466:
1459:
1425:
1407:
1405:
1391:
1389:
1387:
1362:
1356:
1350:
1349:, pp. 1–13.
1344:
1338:
1332:
1326:
1320:
1311:
1305:
1299:
1293:
1287:
1281:
1264:
1255:
1249:
1243:
1222:
1215:
1184:Jacobi logarithm
1162:
1121:
1111:
1070:
1060:
1034:
1009:
975:
935:
918:
917:
916:
907:, archived from
896:Gesammelte Werke
890:
857:Gesammelte Werke
812:Planetary theory
800:, the analog of
726:formed from the
703:: new proofs of
664:Jacobian variety
657:
655:
654:
649:
647:
646:
641:
640:
626:
624:
623:
618:
597:algebraic curves
496:Crelle's Journal
411:private lecturer
345:quintic equation
329:Ashkenazi Jewish
294:
289:
285:
284:
281:
280:
277:
274:
271:
268:
265:
262:
217:Doctoral advisor
211:
140:Jacobi transform
132:Jacobi ellipsoid
80:
77:18 February 1851
55:10 December 1804
54:
52:
40:
26:
25:
1820:
1819:
1815:
1814:
1813:
1811:
1810:
1809:
1705:
1704:
1682:
1666:
1650:
1617:
1612:
1579:
1510:
1479:, ed. (1911). "
1464:
1462:
1385:
1383:
1370:
1365:
1357:
1353:
1345:
1341:
1333:
1329:
1321:
1314:
1306:
1302:
1294:
1290:
1282:
1267:
1256:
1252:
1244:
1240:
1236:
1231:
1226:
1225:
1216:
1212:
1207:
1170:
1165:
1119:
1068:
1050:
1024:
999:
914:
912:
887:
869:
828:last multiplier
820:Jacobi integral
798:Jacobi identity
642:
636:
635:
634:
632:
629:
628:
612:
609:
608:
478:
325:
287:
259:
255:
238:
234:
209:
162:
158:
154:
150:
148:Jacobi operator
146:
144:Jacobi identity
142:
138:
134:
130:
126:
122:
118:
101:Alma mater
88:
82:
78:
69:
56:
50:
48:
31:
24:
17:
12:
11:
5:
1818:
1808:
1807:
1802:
1797:
1792:
1787:
1782:
1777:
1772:
1767:
1762:
1757:
1752:
1747:
1742:
1737:
1732:
1727:
1722:
1717:
1703:
1702:
1696:
1680:
1664:
1648:
1626:
1616:
1615:External links
1613:
1611:
1610:
1572:
1552:
1540:(5): 261–262.
1525:
1514:
1508:
1491:
1477:Chisholm, Hugh
1460:
1426:
1408:
1392:
1371:
1369:
1366:
1364:
1363:
1351:
1347:Van Vleck 1916
1339:
1327:
1323:Dirichlet 1855
1312:
1300:
1288:
1265:
1250:
1237:
1235:
1232:
1230:
1227:
1224:
1223:
1209:
1208:
1206:
1203:
1202:
1201:
1196:
1191:
1186:
1181:
1176:
1169:
1166:
1164:
1163:
1112:
1061:
1048:
1035:
1022:
1010:
997:
976:
936:
919:
891:
885:
870:
868:
865:
861:Berlin Academy
836:Alfred Clebsch
830:is treated in
742:∂ notation of
645:
639:
616:
533:, notably the
524:Kepler problem
486:theta function
477:
474:
324:
321:
247:
246:
243:
242:
229:
225:
224:
219:
213:
212:
201:
195:
194:
189:
185:
184:
179:
175:
174:
168:
167:
113:
112:Known for
109:
108:
102:
98:
97:
94:
90:
89:
83:
81:(aged 46)
75:
71:
70:
57:
46:
42:
41:
33:
32:
29:
15:
9:
6:
4:
3:
2:
1817:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1786:
1783:
1781:
1778:
1776:
1773:
1771:
1768:
1766:
1763:
1761:
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1712:
1710:
1700:
1697:
1693:
1692:
1686:
1681:
1677:
1676:
1670:
1665:
1661:
1660:
1654:
1649:
1646:
1642:
1641:
1636:
1632:
1627:
1625:
1624:
1619:
1618:
1607:
1603:
1598:
1593:
1589:
1585:
1578:
1573:
1570:
1564:
1563:
1558:
1553:
1548:
1543:
1539:
1535:
1531:
1526:
1522:
1521:
1515:
1511:
1505:
1500:
1499:
1492:
1488:
1487:
1482:
1478:
1473:
1472:public domain
1461:
1458:
1454:
1450:
1446:
1442:
1438:
1437:
1432:
1427:
1423:
1422:
1417:
1413:
1412:Moritz Cantor
1409:
1404:
1403:
1397:
1393:
1382:
1378:
1373:
1372:
1360:
1355:
1348:
1343:
1336:
1331:
1324:
1319:
1317:
1309:
1308:Pierpont 1906
1304:
1297:
1292:
1285:
1284:Chisholm 1911
1280:
1278:
1276:
1274:
1272:
1270:
1262:
1261:
1254:
1247:
1242:
1238:
1220:
1214:
1210:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1182:
1180:
1177:
1175:
1172:
1171:
1161:
1157:
1153:
1149:
1145:
1141:
1137:
1133:
1129:
1125:
1118:
1113:
1110:
1106:
1102:
1098:
1094:
1090:
1086:
1082:
1078:
1074:
1067:
1062:
1059:
1055:
1051:
1049:9788185931913
1045:
1041:
1036:
1033:
1029:
1025:
1019:
1015:
1011:
1008:
1004:
1000:
994:
990:
986:
982:
977:
973:
969:
965:
961:
957:
953:
949:
945:
941:
937:
934:
930:
926:
925:
920:
911:on 2013-05-13
910:
906:
902:
898:
897:
892:
888:
882:
878:
877:
872:
871:
864:
862:
858:
854:
850:
849:
844:
839:
837:
833:
829:
825:
822:(1836) for a
821:
817:
813:
809:
807:
803:
802:associativity
799:
795:
791:
787:
783:
782:vector fields
778:
776:
775:Grassmannians
772:
768:
764:
760:
756:
752:
747:
745:
741:
737:
733:
729:
725:
720:
718:
714:
710:
709:Jacobi symbol
706:
702:
697:
695:
691:
688:
684:
683:number theory
675:
671:
669:
665:
661:
643:
614:
606:
605:complex torus
602:
599:of arbitrary
598:
594:
590:
586:
582:
577:
575:
571:
567:
561:
559:
553:
550:
548:
544:
538:
536:
532:
527:
525:
521:
517:
513:
509:
505:
501:
497:
493:
492:
487:
483:
473:
471:
467:
463:
459:
455:
451:
446:
444:
440:
436:
432:
428:
424:
420:
416:
412:
407:
405:
401:
397:
393:
389:
385:
381:
377:
373:
369:
365:
361:
357:
352:
350:
346:
342:
338:
334:
331:parentage in
330:
320:
318:
317:number theory
314:
310:
306:
302:
298:
297:mathematician
293:
283:
253:
244:
241:
237:
233:
230:
226:
223:
220:
218:
214:
207:
206:
202:
200:
196:
193:
190:
186:
183:
180:
176:
173:
169:
166:
161:
157:
156:Jacobi method
153:
149:
145:
141:
137:
133:
129:
128:Jacobi symbol
125:
121:
117:
114:
110:
107:(Ph.D., 1825)
106:
103:
99:
95:
91:
86:
76:
72:
68:
64:
60:
47:
43:
39:
34:
27:
22:
1701:Gallica-Math
1689:
1673:
1657:
1638:
1622:
1587:
1583:
1567:; (
1560:
1537:
1533:
1519:
1497:
1484:
1440:
1434:
1419:
1401:
1384:. Retrieved
1380:
1354:
1342:
1330:
1303:
1291:
1258:
1253:
1246:Aldrich 2017
1241:
1218:
1213:
1127:
1123:
1079:(1): 33–64,
1076:
1072:
1039:
1013:
980:
947:
943:
923:
913:, retrieved
909:the original
895:
875:
867:Publications
856:
852:
851:(1839), and
846:
842:
840:
834:, edited by
831:
827:
810:
780:Students of
779:
748:
735:
731:
727:
721:
698:
680:
578:
563:
555:
551:
542:
539:
528:
506:in terms of
489:
479:
462:Johann Encke
447:
408:
396:Habilitation
392:Enno Dirksen
353:
326:
313:determinants
251:
250:
222:Enno Dirksen
203:
188:Institutions
171:
79:(1851-02-18)
1720:1851 deaths
1715:1804 births
1590:(1): 1–14.
1443:: 193–217,
1359:Jacobi 1841
1130:(1): 7–32,
808:operation.
806:Lie bracket
717:Jacobi sums
589:Weierstrass
419:mathematics
364:mathematics
232:Paul Gordan
182:Mathematics
93:Nationality
1709:Categories
1335:James 2002
1229:References
915:2012-03-20
786:Lie theory
522:, and the
504:integrable
236:Otto Hesse
51:1804-12-10
1621:Jacobi's
1606:0002-9904
1449:0075-4102
1414:(1905), "
1234:Citations
1144:0938-1279
1093:0938-1279
972:123007787
964:0075-4102
516:Euler top
454:Kreuzberg
427:breakdown
360:philology
341:Gymnasium
323:Biography
1398:(1937).
1386:20 April
1168:See also
1160:20652724
845:(1832),
838:(1866).
804:for the
744:Legendre
687:Fermat's
585:Abel map
570:q-series
558:periodic
512:pendulum
450:smallpox
404:surfaces
376:Lagrange
349:radicals
305:dynamics
124:Jacobian
1694:. 1879.
1678:. 1905.
1662:. 1920.
1474::
1457:1104895
1368:Sources
1152:2496659
1101:2496660
1058:2569315
1032:2573816
1007:1414679
933:0081559
905:0260557
668:Riemann
660:lattice
658:by the
468:on the
439:Liberal
380:Laplace
333:Potsdam
288:German:
59:Potsdam
1604:
1506:
1468:
1455:
1447:
1158:
1150:
1142:
1109:219629
1107:
1099:
1091:
1056:
1046:
1030:
1020:
1005:
995:
970:
962:
931:
903:
883:
603:. The
514:, the
466:Jacobi
400:curves
337:Moritz
315:, and
210:(1825)
208:
199:Thesis
178:Fields
96:German
85:Berlin
1580:(PDF)
1205:Notes
1156:S2CID
1120:(PDF)
1105:S2CID
1069:(PDF)
968:S2CID
701:Gauss
601:genus
431:Italy
372:Euler
368:Böckh
1602:ISSN
1504:ISBN
1445:ISSN
1388:2017
1140:ISSN
1089:ISSN
1044:ISBN
1018:ISBN
993:ISBN
960:ISSN
948:1841
881:ISBN
792:and
773:for
692:and
572:and
502:are
470:Moon
402:and
378:and
362:and
74:Died
45:Born
1592:doi
1542:doi
1483:".
1418:",
1132:doi
1081:doi
985:doi
952:doi
587:by
421:at
386:of
347:by
1711::
1688:.
1672:.
1656:.
1643:,
1637:,
1633:,
1600:.
1588:23
1586:.
1582:.
1559:,
1538:12
1536:.
1532:.
1453:MR
1451:,
1441:52
1439:,
1433:,
1379:.
1315:^
1268:^
1154:,
1148:MR
1146:,
1138:,
1128:20
1122:,
1103:,
1097:MR
1095:,
1087:,
1077:20
1071:,
1054:MR
1052:,
1028:MR
1026:,
1003:MR
1001:,
991:,
966:.
958:.
946:.
942:.
929:MR
901:MR
863:.
788:,
784:,
777:.
719:.
576:.
537:.
445:.
374:,
351:.
319:.
311:,
307:,
303:,
286:;
273:oʊ
261:dʒ
65:,
61:,
1608:.
1594::
1571:)
1550:.
1544::
1512:.
1390:.
1298:.
1286:.
1263:.
1248:.
1221:.
1134::
1083::
987::
974:.
954::
736:n
732:n
728:n
644:g
638:C
615:g
282:/
279:i
276:b
270:k
267:ˈ
264:ə
258:/
254:(
165:∂
53:)
49:(
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
