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890:(1872), profoundly influenced the evolution of mathematics. This program was initiated by Klein's inaugural lecture as professor at Erlangen, although it was not the actual speech he gave on the occasion. The program proposed a unified system of geometry that has become the accepted modern method. Klein showed how the essential properties of a given geometry could be represented by the group of
578:. Klein's years at Leipzig, 1880 to 1886, fundamentally changed his life. In 1882, his health collapsed and he battled with depression for the next two years. Nevertheless, his research continued; his seminal work on hyperelliptic sigma functions, published between 1886 and 1888, dates from around this period.
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appointed Klein professor in 1872, when he was only 23 years old. For this, he was endorsed by
Clebsch, who regarded him as likely to become the best mathematician of his time. Klein did not wish to remain in Erlangen, where there were very few students, and was pleased to be offered a professorship
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Currently, the significance of Klein's contributions to geometry is evident. They have become so much part of mathematical thinking that it is difficult to appreciate their novelty when first presented, and understand the fact that they were not immediately accepted by all his contemporaries.
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covered most areas of mathematics then known as well as their applications. Klein also devoted considerable time to mathematical instruction, and promoted mathematics education reform at all grade levels in
Germany and abroad. He became the first president of the
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had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, PlĂĽcker's interest was mainly geometry. Klein received his doctorate, supervised by PlĂĽcker, from the
University of Bonn in 1868.
798:, but it may be immersed as a cylinder looped back through itself to join with its other end from the "inside". It may be embedded in the Euclidean space of dimensions 4 and higher. The concept of a Klein Bottle was devised as a 3-Dimensional
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in 1886. From then on, until his 1913 retirement, he sought to re-establish Göttingen as the world's prime center for mathematics research. However, he never managed to transfer from
Leipzig to Göttingen his own leading role as developer of
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The research facility Klein established at Göttingen served as model for the best such facilities throughout the world. He introduced weekly discussion meetings, and created a mathematical reading room and library. In 1895, Klein recruited
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Vorlesungen ĂĽber die
Theorie der automorphen Functionen. Zweiter Band: Die funktionentheoretischen AusfĂĽhrungen und die Anwendungen. 1. Lieferung: Engere Theorie der automorphen Funktionen
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Klein considered equations of degree > 4, and was especially interested in using transcendental methods to solve the general equation of the fifth degree. Building on methods of
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that would establish the new theory more completely. Klein succeeded in formulating such a theorem and in describing a strategy for proving it. He came up with his proof during an
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had published an outline of his theory of automorphic functions in 1881, which resulted in a friendly rivalry between the two men. Both sought to state and prove a grand
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concept be taught in secondary schools. This recommendation was gradually implemented in many countries around the world. In 1908, Klein was elected president of the
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668:. Due partly to Klein's efforts, Göttingen began admitting women in 1893. He supervised the first Ph.D. thesis in mathematics written at Göttingen by a woman, by
419:, Klein was able to turn it into a center for mathematical and scientific research through the establishment of new lectures, professorships, and institutes. His
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Around 1900, Klein began to become interested in mathematical instruction in schools. In 1905, he was instrumental in formulating a plan recommending that
2352:"Felix Klein, David Hilbert, and the Göttingen Mathematical Tradition", in Science in Germany: The Intersection of Institutional and Intellectual Issues,
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became one of the best mathematical journals in the world. Founded by
Clebsch, it grew under Klein's management, to rival, and eventually surpass
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783:. It was Lie who introduced Klein to the concept of group, which was to have a major role in his later work. Klein also learned about groups from
622:. This appointment proved of great importance; Hilbert continued to enhance Göttingen's primacy in mathematics until his own retirement in 1932.
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1921. "Felix Klein gesammelte mathematische
Abhandlungen" R. Fricke and A. Ostrowski (eds.) Berlin, Springer. 3 volumes. (online copy at
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641:. Klein established a small team of editors who met regularly, making decisions in a democratic spirit. The journal first specialized in
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703:. Under his guidance, the German part of the Commission published many volumes on the teaching of mathematics at all levels in Germany.
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in 1912. He retired the following year due to ill health, but continued to teach mathematics at his home for several further years.
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that preserve those properties. Thus the program's definition of geometry encompassed both
Euclidean and non-Euclidean geometry.
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was, giving the same status to geometries
Euclidean and non-Euclidean, and ending all controversy about non-Euclidean geometry.
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602:. He taught a variety of courses at Göttingen, mainly concerning the interface between mathematics and physics, in particular,
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F. Klein, "On the transformation of the general second-degree equation in line coordinates into canonical coordinates"
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821:. During 1894, he initiated the idea of an encyclopedia of mathematics including its applications, which became the
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parents. His father, Caspar Klein (1809–1889), was a
Prussian government official's secretary stationed in the
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In 1893, Klein was a major speaker at the International Mathematical Congress held in Chicago as part of the
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Vorlesungen ĂĽber die Theorie der automorphen Functionen. Erster Band; Die gruppentheoretischen Grundlagen
827:. This enterprise, which endured until 1935, provided an important standard reference of enduring value.
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In 1871, while at Göttingen, Klein made major discoveries in geometry. He published two papers
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Klein's first important mathematical discoveries were made in 1870. In collaboration with
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After spending five years at the Technische Hochschule, Klein was appointed to a chair of
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729:, a document penned in support of the German invasion of Belgium in the early stages of
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incomplete. Klein was the obvious person to complete the second part of PlĂĽcker's
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Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5ten Grade
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Lectures on the Ikosahedron; and the Solution of Equations of the Fifth Degree
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Routes of Learning: Highways, Pathways, Byways in the History of Mathematics
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Non-Euclidean geometry models proposed by Klein (left) and Poincaré (right)
802:, with one method of construction being the attachment of the edges of two
30:
This article is about the German mathematician. For the French priest, see
880:
as the study of the properties of a space that is invariant under a given
771:, he discovered the fundamental properties of the asymptotic lines on the
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and was an influential synthesis of much of the mathematics of the time.
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showing that Euclidean and non-Euclidean geometries could be considered
428:
in 1908 at the Fourth International Congress of Mathematicians in Rome.
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1932:
1900:
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1027:
Ueber Riemann's Theorie der algebraischen Funktionen und ihre Integrale
776:
449:
1109:Ăśber Riemann's Theorie der Algebraischen Functionen und ihre Integrale
676:'s, whom Klein admired. In 1897, Klein became a foreign member of the
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F. Klein, "On the theory of line complexes of first and second order"
1377:
From Kant to Hilbert: A Source Book in the Foundations of Mathematics
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1916:
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as his major contribution to mathematics, specifically his work on:
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In 1875, Klein married Anne Hegel, granddaughter of the philosopher
2108:
von Robert Fricke & Felix Klein, Erste Band & Zweiter Band"
2251:
Vorlesungen ĂĽber die Entwicklung der Mathematik im 19. Jahrhundert
1345:
Vorlesungen ĂĽber die Entwicklung der Mathematik im 19. Jahrhundert
1339:
Vorlesungen ĂĽber die Entwicklung der Mathematik im 19. Jahrhundert
840:
743:
580:
435:
1512:
Felix Klein in Leipzig: mit F. Kleins Antrittsrede, Leipzig 1880
1361:, Grundlehren der mathematischen Wissenschaften, Springer Verlag
1354:, Grundlehren der mathematischen Wissenschaften, Springer Verlag
2925:
2476:
476:
PlĂĽcker died in 1868, leaving his book concerning the basis of
1029:(1882) treats complex analysis in a geometric way, connecting
873:
never accepted Klein's argument, believing it to be circular.
520:
taught advanced courses to many excellent students, including
3450:
Members of the Royal Netherlands Academy of Arts and Sciences
1953:
Vorlesungen ĂĽber die Theorie der elliptischen Modulfunktionen
1183:
Vorlesungen ĂĽber die Theorie der elliptischen Modulfunktionen
468:, 1865–1866, intending to become a physicist. At that time,
1743:. Springer Science & Business Media. pp. 499–500.
1659:
Come to the Fair: The Chicago Mathematical Congress of 1893
1174:. Zweiter Aufsatz, pp. 357–387, Math. Annalen, Bd. 32,
464:
in DĂĽsseldorf, then studied mathematics and physics at the
1859:. 2008. Retrieved 4 December 2014 from Encyclopedia.com:
1341:(2 Bände), Julius Springer Verlag, Berlin & 1927. S.
2106:
Vorlesungen ĂĽber die Theorie der automorphen Functionen
2053:
Vorträge über ausgewählte Fragen der Elementargeometrie
1222:
Vorträge über ausgewählte Fragen der Elementargeometrie
1206:(1893) reported and published by Ziwet (New York, 1894)
1056:. This work enabled him to write a series of papers on
3440:
Foreign associates of the National Academy of Sciences
3425:
Academic staff of the University of Erlangen-Nuremberg
1770:. Springer Science & Business Media. p. 503.
1713:
The Routledge International Encyclopedia of Education
748:
Construction of a Klein Bottle from two Möbius strips
3430:
Academic staff of the Technical University of Munich
3385:
German military personnel of the Franco-Prussian War
697:
International Commission on Mathematical Instruction
426:
International Commission on Mathematical Instruction
1861:
http://www.encyclopedia.com/doc/1G2-2830902326.html
1198:Ăśber lineare Differentialgleichungen der 2. Ordnung
348:
231:
215:
193:
185:
157:
124:
114:
84:
55:
39:
1582:Landmark Writings in Western Mathematics 1640–1940
1515:(in German). Ed. am Gutenbergplatz. p. 195.
948:, especially equations he invented, satisfied by
725:Klein was one of ninety-three signatories of the
492:and Paris. In July 1870, at the beginning of the
2463:F. Klein, "On line geometry and metric geometry"
2094:
2092:
2003:The Evanston Colloquium: Lectures on Mathematics
1767:Handbook on the History of Mathematics Education
1740:Handbook on the History of Mathematics Education
1691:. Royal Netherlands Academy of Arts and Sciences
1615:, August 2007, Volume 54, Number 8, pp. 960–970.
760:, classified second degree line complexes using
456:. His mother was Sophie Elise Klein (1819–1890,
1359:Vorlesungen ĂĽber die hypergeometrische Funktion
1332:Elementarmathematik vom höheren Standpunkte aus
980:, and obtained an explicit representation of a
3455:Recipients of the Pour le MĂ©rite (civil class)
972:the plane. In 1879, he examined the action of
824:Encyklopädie der mathematischen Wissenschaften
678:Royal Netherlands Academy of Arts and Sciences
3420:Academic staff of the University of Göttingen
2937:
2488:
2260:Bulletin of the American Mathematical Society
2203:, 1796—1814. Mit Anmerkungen von Felix Klein"
2115:Bulletin of the American Mathematical Society
1764:Alexander Karp; Gert Schubring, eds. (2014).
1737:Alexander Karp; Gert Schubring, eds. (2014).
1667:. American Mathematical Society. p. 64.
1226:1897: English translation by W. W. Beman and
687:, the rudiments of differential and integral
8:
1612:Notices of the American Mathematical Society
1147:English translation by G. G. Morrice (1888)
988:. He showed that it was a complex curve in
653:. It also provided an important outlet for
1856:Complete Dictionary of Scientific Biography
1661:by David E. Rowe and Karen Hunger Parshall"
1352:Vorlesungen ĂĽber nichteuklidische Geometrie
376:; 25 April 1849 – 22 June 1925) was a
2944:
2930:
2922:
2495:
2481:
2473:
1710:Gary McCulloch; David Crook, eds. (2013).
1295:1796—1814. Mit Anmerkungen von Felix Klein
47:
36:
2333:Indra's Pearls: The Vision of Felix Klein
2309:
2221:
2171:
2073:
2023:
1973:
1631:. New York: Springer-Verlag. p. 19.
1493:
444:Felix Klein was born on 25 April 1849 in
1094:in a four volume treatise, written with
714:in 1893. He was elected a member of the
701:International Congress of Mathematicians
2410:MacTutor History of Mathematics Archive
2294:"Three books on non-euclidean geometry"
1802:MacTutor History of Mathematics Archive
1464:
851:On the So-called Non-Euclidean Geometry
809:During the 1890s, Klein began studying
504:(lecturer) at Göttingen in early 1871.
3470:Scientists from North Rhine-Westphalia
3395:Members of the Prussian House of Lords
1454:List of things named after Felix Klein
1309:(in German), Leipzig: B. G. Teubner.,
1232:Famous Problems of Elementary Geometry
1013: = 0, and that its group of
861:. This insight had the corollary that
593:Klein accepted a professorship at the
2453:Felix Klein (Encyclopædia Britannica)
1829:from the original on 11 December 2021
1303:Fricke, Robert; Klein, Felix (1912),
1258:(in German), Leipzig: B. G. Teubner,
1252:Fricke, Robert; Klein, Felix (1897),
1216:, New York, London: Macmillan and Co.
1172:Ăśber hyperelliptische Sigmafunktionen
1161:Ăśber hyperelliptische Sigmafunktionen
408:classified geometries by their basic
371:
143:Encyclopedia of Mathematical Sciences
7:
3445:Foreign members of the Royal Society
3435:Academic staff of Leipzig University
3415:Humboldt University of Berlin alumni
2330:, Caroline Series, and David Wright
2281:from the original on 9 October 2022.
2233:from the original on 9 October 2022.
2183:from the original on 9 October 2022.
2136:from the original on 9 October 2022.
2085:from the original on 9 October 2022.
2035:from the original on 9 October 2022.
1985:from the original on 9 October 2022.
1605:Chislenko, Eugene; Tschinkel, Yuri.
1379:, 2 vols. Oxford Uni. Press: 965–71.
1293:Gauss' wissenschaftliches Tagebuch,
1163:. Erster Aufsatz, pp. 323–356,
1071:, associating algebra and geometry.
964:moves the fundamental region of the
779:, curves invariant under a group of
1191:Ăśber die hypergeometrische Funktion
3370:20th-century German mathematicians
3365:19th-century German mathematicians
2201:Gauss' wissenschaftlichen Tagebuch
1665:A Century of Mathematical Meetings
1539:(1894). "Biography: Felix Klein".
1373:"The arithmetizing of mathematics"
914:The link between certain ideas of
764:'s theory of elementary divisors.
484:, and thus became acquainted with
210:Georg-August-Universität Göttingen
25:
2356:, ed., Osiris, 5 (1989), 186–213.
1905:The American Mathematical Monthly
1542:The American Mathematical Monthly
1375:in Ewald, William B., ed., 1996.
1248:(later volumes: 1898, 1903, 1910)
1098:over a period of about 20 years.
1037:. This work drew on notions from
813:more intensively, writing on the
1067:, Klein established a theory of
976:, considered as an image of the
440:Klein during his Leipzig period.
172:Ackermann–Teubner Memorial Award
27:German mathematician (1849–1925)
2346:. Teubner Verlag, Leipzig 1981.
2311:10.1090/S0002-9904-1929-04726-8
2272:10.1090/S0002-9904-1928-04589-5
2223:10.1090/s0002-9904-1902-00959-2
2173:10.1090/s0002-9904-1899-00643-8
2147:Thompson, Henry Dallas (1899).
2127:10.1090/S0002-9904-1903-01020-9
2075:10.1090/s0002-9904-1896-00328-1
2025:10.1090/s0002-9904-1894-00190-6
1975:10.1090/S0002-9904-1892-00049-3
1495:10.1090/S0002-9904-1922-03510-0
1083:at 2:30 A.M. on 23 March 1882.
396:, and the associations between
3405:Recipients of the Copley Medal
3400:People from the Rhine Province
2364:L'oeuvre mathematique de Klein
2336:. Cambridge Univ. Press. 2002.
2292:Allen, Edward Switzer (1929).
2151:Mathematical Theory of the Top
1880:Johns Hopkins University Press
1283:Mathematical Theory of the Top
944:in more than 3 dimensions and
865:was consistent if and only if
736:He died in Göttingen in 1925.
1:
2701:Edward Albert Sharpey-Schafer
2448:Felix Klein, Klein Protokolle
2425:Mathematics Genealogy Project
2390:Works by or about Felix Klein
1286:(Princeton address, New York)
1086:Klein summarized his work on
727:Manifesto of the Ninety-Three
718:in 1885, and was awarded its
553:Georg Wilhelm Friedrich Hegel
514:Technische Hochschule MĂĽnchen
202:Technische Hochschule MĂĽnchen
2253:von Felix Klein. Erste Band"
1955:von Felix Klein, Erste Band"
1901:"The Uniformization Theorem"
1819:Numberphile (22 June 2015),
1689:"Felix C. Klein (1849–1925)"
1419:Grünbaum–Rigby configuration
666:World's Columbian Exposition
2789:Charles Thomson Rees Wilson
1822:Klein Bottles – Numberphile
1607:"The Felix Klein Protocols"
1391:Nicht-Euklidische Geometrie
1137:also available from Cornell
708:London Mathematical Society
349:Other notable students
3486:
3360:Scientists from DĂĽsseldorf
2435:"Klein, Felix (1849–1925)"
1853:"Klein, Christian Felix."
1716:. Routledge. p. 373.
1092:elliptic modular functions
1058:elliptic modular functions
950:elliptic modular functions
834:
781:projective transformations
775:. They later investigated
625:Under Klein's editorship,
585:Klein (1912). Painting of
566:. His colleagues included
29:
3410:University of Bonn alumni
2959:
2725:Charles Scott Sherrington
2717:Frederick Gowland Hopkins
2511:
1899:Abikoff, William (1981).
1585:. Elsevier. p. 546.
1477:"Klein's Collected Works"
752:Klein's dissertation, on
482:Neue Geometrie des Raumes
460:Kayser). He attended the
415:During his tenure at the
358:
178:
46:
2733:Charles Algernon Parsons
2431:Weisstein, Eric Wolfgang
2415:University of St Andrews
1807:University of St Andrews
1625:Reid, Constance (1996).
1063:In his 1884 book on the
992:, that its equation was
882:group of transformations
756:and its applications to
672:, an English student of
620:University of Königsberg
546:Gregorio Ricci-Curbastro
384:, known for his work in
3465:Prussian Army personnel
1509:RĂĽdiger Thiele (2011).
1213:Lectures on Mathematics
595:University of Göttingen
500:before being appointed
417:University of Göttingen
297:Ferdinand von Lindemann
3375:Differential geometers
2973:James Joseph Sylvester
2861:Geoffrey Ingram Taylor
2645:Pierre Paul Émile Roux
2047:Scott, Charlotte Angas
1482:Bull. Amer. Math. Soc.
1444:Uniformization theorem
1077:uniformization theorem
960:Klein showed that the
946:differential equations
906:Klein saw his work on
863:non-Euclidean geometry
846:
749:
590:
516:in 1875. There he and
509:University of Erlangen
441:
394:non-Euclidean geometry
3133:George Neville Watson
2669:Horace Tabberer Brown
2573:Alfred Russel Wallace
2298:Bull. Amer. Math. Soc
2210:Bull. Amer. Math. Soc
2160:Bull. Amer. Math. Soc
2062:Bull. Amer. Math. Soc
2012:Bull. Amer. Math. Soc
1962:Bull. Amer. Math. Soc
1872:Ivor Grattan-Guinness
1577:Ivor Grattan-Guinness
1537:Halsted, George Bruce
1449:Felix Klein Protocols
1210:Klein, Felix (1894),
1185:(2 volumes) and 1892)
1165:Mathematische Annalen
1069:automorphic functions
954:automorphic functions
876:Klein's synthesis of
844:
747:
628:Mathematische Annalen
584:
439:
365:Felix Christian Klein
18:Christian Felix Klein
3460:De Morgan Medallists
3380:Hyperbolic geometers
3309:John Griggs Thompson
3301:Keith William Morton
3085:Godfrey Harold Hardy
2953:De Morgan Medallists
2877:Edgar Douglas Adrian
2517:Josiah Willard Gibbs
2401:Robertson, Edmund F.
2381:Works by Felix Klein
1851:de:Bruno Schoeneberg
1793:Robertson, Edmund F.
1246:Theorie des Kreisels
1235:via Internet Archive
811:mathematical physics
670:Grace Chisholm Young
639:University of Berlin
382:mathematics educator
378:German mathematician
341:Grace Chisholm Young
198:Universität Erlangen
137:Beltrami–Klein model
2749:William Henry Bragg
2581:George William Hill
2565:Albert A. Michelson
2399:O'Connor, John J.;
2342:(with Fritz König)
2245:Smith, David Eugene
1791:O'Connor, John J.;
1404:Dianalytic manifold
1277:Zweiter Band. 1901.
1204:Evanston Colloquium
859:Cayley–Klein metric
790:Klein devised the "
518:Alexander von Brill
494:Franco-Prussian War
313:Friedrich Schilling
301:Alexander Ostrowski
277:Philipp Furtwängler
261:Friedrich Dingeldey
206:Universität Leipzig
100:Province of Hanover
2821:Thomas Hunt Morgan
2805:Henry Hallett Dale
2781:John Scott Haldane
2765:George Ellery Hale
1878:, pp 44, 45, 90,
1035:conformal mappings
867:Euclidean geometry
847:
750:
710:awarded Klein its
647:algebraic geometry
591:
564:Leipzig University
466:University of Bonn
442:
119:University of Bonn
3335:
3334:
3253:Albrecht Fröhlich
3213:C. Ambrose Rogers
3141:A. S. Besicovitch
3029:J. W. L. Glaisher
2919:
2918:
2685:Ernest Rutherford
2504:Copley Medallists
2385:Project Gutenberg
2360:Federigo Enriques
2100:Hutchinson, J. I.
1777:978-1-4614-9155-2
1750:978-1-4614-9155-2
1723:978-1-317-85358-9
1653:Case, Bettye Anne
1592:978-0-08-045744-4
1522:978-3-937219-47-9
1316:978-1-4297-0552-3
1265:978-1-4297-0551-6
1242:Arnold Sommerfeld
1132:Project Gutenberg
1054:icosahedral group
1050:Leopold Kronecker
819:Arnold Sommerfeld
685:analytic geometry
362:
361:
337:Alexander Witting
333:Henry Seely White
257:Frank Nelson Cole
241:Ludwig Bieberbach
232:Doctoral students
217:Doctoral advisors
180:Scientific career
16:(Redirected from
3477:
3328:
3320:
3312:
3304:
3296:
3293:Bryan John Birch
3288:
3280:
3272:
3264:
3256:
3248:
3240:
3237:J. W. S. Cassels
3232:
3224:
3216:
3208:
3200:
3192:
3184:
3176:
3168:
3160:
3152:
3149:E. C. Titchmarsh
3144:
3136:
3128:
3120:
3112:
3109:J. E. Littlewood
3104:
3096:
3093:Bertrand Russell
3088:
3080:
3072:
3064:
3056:
3048:
3040:
3032:
3024:
3016:
3008:
3005:William Burnside
3000:
2992:
2984:
2976:
2968:
2946:
2939:
2932:
2923:
2912:
2904:
2901:George de Hevesy
2896:
2888:
2880:
2872:
2864:
2856:
2848:
2840:
2832:
2824:
2816:
2808:
2800:
2792:
2784:
2776:
2768:
2760:
2752:
2744:
2736:
2728:
2720:
2712:
2704:
2696:
2688:
2680:
2672:
2664:
2656:
2648:
2640:
2632:
2624:
2616:
2608:
2600:
2592:
2584:
2576:
2568:
2560:
2557:Élie Metchnikoff
2552:
2549:Dmitri Mendeleev
2544:
2536:
2528:
2520:
2497:
2490:
2483:
2474:
2444:
2417:
2394:Internet Archive
2316:
2315:
2313:
2289:
2283:
2282:
2280:
2257:
2241:
2235:
2234:
2232:
2225:
2207:
2191:
2185:
2184:
2182:
2175:
2157:
2144:
2138:
2137:
2135:
2112:
2096:
2087:
2086:
2084:
2077:
2059:
2055:von Felix Klein"
2043:
2037:
2036:
2034:
2027:
2009:
1993:
1987:
1986:
1984:
1977:
1959:
1943:
1937:
1936:
1896:
1890:
1869:
1863:
1844:
1838:
1837:
1836:
1834:
1816:
1810:
1809:
1788:
1782:
1781:
1761:
1755:
1754:
1734:
1728:
1727:
1707:
1701:
1700:
1698:
1696:
1685:
1679:
1678:
1649:
1643:
1642:
1622:
1616:
1603:
1597:
1596:
1573:
1567:
1566:
1533:
1527:
1526:
1506:
1500:
1499:
1497:
1469:
1327:
1299:
1276:
1217:
1153:Internet Archive
1134:
1031:potential theory
990:projective space
930:abstract algebra
920:invariant theory
908:complex analysis
902:Complex analysis
887:Erlangen program
857:determined by a
837:Erlangen program
831:Erlangen program
651:invariant theory
643:complex analysis
634:Crelle's Journal
608:potential theory
568:Walther von Dyck
526:Walther von Dyck
406:Erlangen program
390:complex analysis
375:
370:
325:Walther von Dyck
321:Edward Van Vleck
305:Julio Rey Pastor
269:Erwin Freundlich
226:Rudolf Lipschitz
152:Klein four-group
129:Erlangen program
91:
65:
63:
51:
37:
21:
3485:
3484:
3480:
3479:
3478:
3476:
3475:
3474:
3390:Group theorists
3340:
3339:
3336:
3331:
3323:
3315:
3307:
3299:
3291:
3283:
3275:
3267:
3259:
3251:
3243:
3235:
3227:
3219:
3211:
3203:
3195:
3189:Mary Cartwright
3187:
3179:
3171:
3163:
3155:
3147:
3139:
3131:
3123:
3115:
3107:
3101:E. T. Whittaker
3099:
3091:
3083:
3075:
3067:
3059:
3051:
3043:
3035:
3027:
3019:
3013:A. G. Greenhill
3011:
3003:
2995:
2987:
2979:
2971:
2963:
2955:
2950:
2920:
2915:
2907:
2899:
2891:
2883:
2875:
2867:
2859:
2853:Joseph Barcroft
2851:
2845:Robert Robinson
2843:
2835:
2827:
2819:
2811:
2803:
2795:
2787:
2779:
2771:
2763:
2757:Arthur Schuster
2755:
2747:
2739:
2731:
2723:
2715:
2709:Albert Einstein
2707:
2699:
2691:
2683:
2675:
2667:
2661:William Bayliss
2659:
2653:Hendrik Lorentz
2651:
2643:
2635:
2627:
2619:
2611:
2603:
2595:
2587:
2579:
2571:
2563:
2555:
2547:
2541:William Crookes
2539:
2531:
2523:
2515:
2507:
2501:
2429:
2398:
2377:
2324:
2322:Further reading
2319:
2291:
2290:
2286:
2278:
2255:
2243:
2242:
2238:
2230:
2205:
2193:
2192:
2188:
2180:
2166:(10): 486–487.
2155:
2153:by Felix Klein"
2146:
2145:
2141:
2133:
2110:
2098:
2097:
2090:
2082:
2057:
2045:
2044:
2040:
2032:
2007:
2005:by Felix Klein"
1997:White, Henry S.
1995:
1994:
1990:
1982:
1957:
1945:
1944:
1940:
1917:10.2307/2320507
1898:
1897:
1893:
1870:
1866:
1847:de:Werner Burau
1845:
1841:
1832:
1830:
1818:
1817:
1813:
1790:
1789:
1785:
1778:
1763:
1762:
1758:
1751:
1736:
1735:
1731:
1724:
1709:
1708:
1704:
1694:
1692:
1687:
1686:
1682:
1675:
1651:
1650:
1646:
1639:
1624:
1623:
1619:
1604:
1600:
1593:
1575:
1574:
1570:
1555:10.2307/2969034
1549:(12): 416–420.
1535:
1534:
1530:
1523:
1508:
1507:
1503:
1471:
1470:
1466:
1462:
1429:Ping-pong lemma
1400:
1368:
1317:
1302:
1290:
1266:
1251:
1209:
1124:
1104:
1046:Charles Hermite
984:now termed the
982:Riemann surface
904:
892:transformations
884:, known as the
839:
833:
796:Euclidean space
742:
712:De Morgan Medal
637:, based at the
576:Friedrich Engel
434:
410:symmetry groups
373:[klaÉŞn]
368:
344:
343:
339:
335:
331:
327:
323:
319:
315:
311:
307:
303:
299:
295:
291:
287:
283:
279:
275:
271:
267:
263:
259:
255:
251:
247:
243:
238:
208:
204:
200:
170:
165:
162:De Morgan Medal
150:
146:
139:
135:
131:
115:Alma mater
110:
93:
89:
80:
67:
61:
59:
42:
35:
28:
23:
22:
15:
12:
11:
5:
3483:
3481:
3473:
3472:
3467:
3462:
3457:
3452:
3447:
3442:
3437:
3432:
3427:
3422:
3417:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3377:
3372:
3367:
3362:
3357:
3352:
3342:
3341:
3333:
3332:
3330:
3329:
3321:
3317:Timothy Gowers
3313:
3305:
3297:
3289:
3281:
3273:
3265:
3257:
3249:
3241:
3233:
3225:
3221:Michael Atiyah
3217:
3209:
3201:
3193:
3185:
3177:
3169:
3165:W. V. D. Hodge
3161:
3153:
3145:
3137:
3129:
3125:Sydney Chapman
3121:
3113:
3105:
3097:
3089:
3081:
3073:
3069:P. A. MacMahon
3065:
3057:
3049:
3041:
3033:
3025:
3017:
3009:
3001:
2993:
2985:
2977:
2969:
2960:
2957:
2956:
2951:
2949:
2948:
2941:
2934:
2926:
2917:
2916:
2914:
2913:
2909:James Chadwick
2905:
2897:
2893:Archibald Hill
2889:
2881:
2873:
2865:
2857:
2849:
2841:
2833:
2825:
2817:
2809:
2801:
2793:
2785:
2777:
2773:Theobald Smith
2769:
2761:
2753:
2745:
2737:
2729:
2721:
2713:
2705:
2697:
2689:
2681:
2673:
2665:
2657:
2649:
2641:
2633:
2625:
2617:
2609:
2601:
2593:
2589:Francis Galton
2585:
2577:
2569:
2561:
2553:
2545:
2537:
2529:
2521:
2512:
2509:
2508:
2502:
2500:
2499:
2492:
2485:
2477:
2471:
2470:
2465:
2460:
2455:
2450:
2445:
2427:
2418:
2396:
2387:
2376:
2375:External links
2373:
2372:
2371:
2357:
2354:Kathryn Olesko
2347:
2340:Tobies, Renate
2337:
2323:
2320:
2318:
2317:
2284:
2266:(4): 521–522.
2236:
2216:(2): 125–126.
2195:BĂ´cher, Maxime
2186:
2139:
2121:(9): 470–492.
2088:
2068:(6): 157–164.
2038:
2018:(5): 119–122.
1988:
1968:(5): 105–120.
1938:
1911:(8): 574–592.
1891:
1864:
1839:
1811:
1783:
1776:
1756:
1749:
1729:
1722:
1702:
1680:
1673:
1655:, ed. (1996).
1644:
1637:
1617:
1598:
1591:
1579:, ed. (2005).
1568:
1528:
1521:
1501:
1488:(3): 125–129.
1473:Snyder, Virgil
1463:
1461:
1458:
1457:
1456:
1451:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1406:
1399:
1396:
1395:
1394:
1387:
1380:
1367:
1364:
1363:
1362:
1355:
1348:
1335:
1328:
1315:
1300:
1287:
1278:
1264:
1249:
1238:
1237:
1236:
1218:
1207:
1200:
1194:
1186:
1175:
1168:
1157:
1156:
1155:
1139:
1122:
1121:
1120:
1103:
1102:Selected works
1100:
1039:fluid dynamics
958:
957:
939:
933:
923:
903:
900:
835:Main article:
832:
829:
785:Camille Jordan
773:Kummer surface
741:
738:
587:Max Liebermann
486:Alfred Clebsch
470:Julius PlĂĽcker
454:Rhine Province
433:
430:
360:
359:
356:
355:
350:
346:
345:
285:Mellen Haskell
239:
236:
235:
233:
229:
228:
222:Julius PlĂĽcker
219:
213:
212:
195:
191:
190:
187:
183:
182:
176:
175:
159:
155:
154:
148:Kleinian group
126:
125:Known for
122:
121:
116:
112:
111:
94:
92:(aged 76)
86:
82:
81:
74:Rhine Province
68:
57:
53:
52:
44:
43:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3482:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3351:
3348:
3347:
3345:
3338:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3298:
3294:
3290:
3286:
3285:Roger Penrose
3282:
3278:
3274:
3270:
3266:
3262:
3258:
3254:
3250:
3246:
3245:D. G. Kendall
3242:
3238:
3234:
3230:
3226:
3222:
3218:
3214:
3210:
3206:
3205:Graham Higman
3202:
3198:
3194:
3190:
3186:
3182:
3178:
3174:
3170:
3166:
3162:
3158:
3154:
3150:
3146:
3142:
3138:
3134:
3130:
3126:
3122:
3118:
3117:Louis Mordell
3114:
3110:
3106:
3102:
3098:
3094:
3090:
3086:
3082:
3078:
3077:A. E. H. Love
3074:
3070:
3066:
3062:
3058:
3054:
3050:
3046:
3042:
3038:
3034:
3030:
3026:
3022:
3018:
3014:
3010:
3006:
3002:
2998:
2994:
2990:
2986:
2982:
2981:Lord Rayleigh
2978:
2974:
2970:
2966:
2965:Arthur Cayley
2962:
2961:
2958:
2954:
2947:
2942:
2940:
2935:
2933:
2928:
2927:
2924:
2910:
2906:
2902:
2898:
2894:
2890:
2886:
2882:
2878:
2874:
2870:
2866:
2862:
2858:
2854:
2850:
2846:
2842:
2838:
2834:
2830:
2829:Paul Langevin
2826:
2822:
2818:
2814:
2810:
2806:
2802:
2798:
2794:
2790:
2786:
2782:
2778:
2774:
2770:
2766:
2762:
2758:
2754:
2750:
2746:
2742:
2738:
2734:
2730:
2726:
2722:
2718:
2714:
2710:
2706:
2702:
2698:
2694:
2690:
2686:
2682:
2678:
2677:Joseph Larmor
2674:
2670:
2666:
2662:
2658:
2654:
2650:
2646:
2642:
2638:
2634:
2630:
2626:
2622:
2621:J. J. Thomson
2618:
2614:
2613:Ray Lankester
2610:
2606:
2602:
2598:
2597:George Darwin
2594:
2590:
2586:
2582:
2578:
2574:
2570:
2566:
2562:
2558:
2554:
2550:
2546:
2542:
2538:
2534:
2530:
2526:
2525:Joseph Lister
2522:
2518:
2514:
2513:
2510:
2505:
2498:
2493:
2491:
2486:
2484:
2479:
2478:
2475:
2469:
2466:
2464:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2442:
2441:
2436:
2432:
2428:
2426:
2422:
2419:
2416:
2412:
2411:
2406:
2405:"Felix Klein"
2402:
2397:
2395:
2391:
2388:
2386:
2382:
2379:
2378:
2374:
2369:
2365:
2361:
2358:
2355:
2351:
2348:
2345:
2341:
2338:
2335:
2334:
2329:
2328:David Mumford
2326:
2325:
2321:
2312:
2307:
2303:
2299:
2295:
2288:
2285:
2277:
2273:
2269:
2265:
2261:
2254:
2252:
2246:
2240:
2237:
2229:
2224:
2219:
2215:
2211:
2204:
2202:
2196:
2190:
2187:
2179:
2174:
2169:
2165:
2161:
2154:
2152:
2143:
2140:
2132:
2128:
2124:
2120:
2116:
2109:
2107:
2101:
2095:
2093:
2089:
2081:
2076:
2071:
2067:
2063:
2056:
2054:
2048:
2042:
2039:
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2026:
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986:Klein quartic
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978:modular group
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966:complex plane
963:
962:modular group
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871:Arthur Cayley
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855:metric spaces
852:
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655:real analysis
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616:David Hilbert
611:
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519:
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293:Edward Kasner
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286:
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66:25 April 1849
58:
54:
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45:
38:
33:
19:
3337:
3325:Andrew Wiles
3269:R. A. Rankin
3261:W. K. Hayman
3157:G. I. Taylor
3061:E. W. Hobson
2988:
2869:Oswald Avery
2837:Thomas Lewis
2797:Arthur Evans
2604:
2533:Eduard Suess
2440:ScienceWorld
2438:
2408:
2367:
2343:
2331:
2301:
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2150:
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2002:
1991:
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1961:
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1908:
1904:
1894:
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1831:, retrieved
1821:
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1683:
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1485:
1480:
1467:
1424:Homomorphism
1414:Line complex
1376:
1366:Bibliography
1358:
1351:
1344:
1343:Felix Klein
1338:
1331:
1305:
1296:
1292:
1282:
1254:
1245:
1240:1897: (with
1230:
1221:
1212:
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1177:1890: (with
1171:
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1108:
1085:
1062:
1043:
1026:
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1007:
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993:
959:
936:Group theory
905:
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885:
875:
850:
848:
823:
808:
800:Möbius strip
792:Klein bottle
789:
766:
751:
735:
724:
720:Copley Medal
705:
699:at the Rome
682:
663:
659:group theory
657:and the new
632:
626:
624:
612:
592:
572:Eduard Study
557:
550:
506:
502:Privatdozent
501:
481:
475:
443:
414:
402:group theory
386:group theory
364:
363:
329:Adolf Weiler
281:Axel Harnack
253:Max BrĂĽckner
194:Institutions
179:
167:Copley Medal
142:
133:Klein bottle
90:(1925-06-22)
88:22 June 1925
3355:1925 deaths
3350:1849 births
3277:J. A. Green
3197:Kurt Mahler
3181:Philip Hall
3053:W. H. Young
3037:Horace Lamb
3021:H. F. Baker
2989:Felix Klein
2885:G. H. Hardy
2693:Horace Lamb
2637:James Dewar
2629:Ivan Pavlov
2605:Felix Klein
2506:(1901–1950)
2421:Felix Klein
2350:Rowe, David
2344:Felix Klein
2304:: 271–276.
1947:Cole, F. N.
1409:j-invariant
1228:D. E. Smith
1088:automorphic
1065:icosahedron
762:Weierstrass
731:World War I
404:. His 1872
249:Oskar Bolza
189:Mathematics
41:Felix Klein
32:FĂ©lix Klein
3344:Categories
3229:K. F. Roth
3173:Max Newman
2997:S. Roberts
2813:Niels Bohr
2741:Max Planck
1460:References
1434:Prime form
1325:32.0430.01
1274:28.0334.01
1116:14.0358.01
1015:symmetries
970:tessellate
769:Sophus Lie
691:, and the
538:Max Planck
534:Carl Runge
446:DĂĽsseldorf
70:DĂĽsseldorf
62:1849-04-25
3045:J. Larmor
2249:"Review:
2199:"Review:
2149:"Review:
2104:"Review:
2051:"Review:
2001:"Review:
1925:0002-9890
1334:(Leipzig)
1025:168. His
968:so as to
815:gyroscope
758:mechanics
618:from the
604:mechanics
530:Karl Rohn
462:Gymnasium
96:Göttingen
2368:Scientia
2276:Archived
2247:(1928).
2228:Archived
2197:(1902).
2178:Archived
2131:Archived
2102:(1903).
2080:Archived
2049:(1896).
2030:Archived
1999:(1894).
1980:Archived
1949:(1892).
1833:26 April
1827:archived
1475:(1922).
1398:See also
1073:Poincaré
1019:PSL(2,7)
974:PSL(2,7)
942:Geometry
878:geometry
777:W-curves
693:function
689:calculus
600:geometry
570:, Rohn,
560:geometry
450:Prussian
421:seminars
398:geometry
141:Klein's
2433:(ed.).
2423:at the
2392:at the
2362:(1921)
1933:2320507
1874:(2009)
1695:22 July
1628:Hilbert
1563:2969034
1439:W-curve
1389:1890. "
1167:Bd. 27,
916:Riemann
512:at the
369:German:
108:Germany
104:Prussia
78:Prussia
3327:(2019)
3319:(2016)
3311:(2013)
3303:(2010)
3295:(2007)
3287:(2004)
3279:(2001)
3271:(1998)
3263:(1995)
3255:(1992)
3247:(1989)
3239:(1986)
3231:(1983)
3223:(1980)
3215:(1977)
3207:(1974)
3199:(1971)
3191:(1968)
3183:(1965)
3175:(1962)
3167:(1959)
3159:(1956)
3151:(1953)
3143:(1950)
3135:(1947)
3127:(1944)
3119:(1941)
3111:(1938)
3103:(1935)
3095:(1932)
3087:(1929)
3079:(1926)
3071:(1923)
3063:(1920)
3055:(1917)
3047:(1914)
3039:(1911)
3031:(1908)
3023:(1905)
3015:(1902)
3007:(1899)
2999:(1896)
2991:(1893)
2983:(1890)
2975:(1887)
2967:(1884)
2911:(1950)
2903:(1949)
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2887:(1947)
2879:(1946)
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2767:(1932)
2759:(1931)
2751:(1930)
2743:(1929)
2735:(1928)
2727:(1927)
2719:(1926)
2711:(1925)
2703:(1924)
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2687:(1922)
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158:Awards
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