Editing Felix Klein (section)

==Life==
[[File:Felix Klein, Leipzig years.png|thumb|upright|Klein during his Leipzig period.]]
Felix Klein was born on 25 April 1849 in [[Düsseldorf]],<ref>{{cite journal|author=Snyder, Virgil|author-link=Virgil Snyder|title=Klein's Collected Works|journal=[[Bulletin of the American Mathematical Society|Bull. Amer. Math. Soc.]]|year=1922|volume=28|issue=3|pages=125–129|url=http://projecteuclid.org/euclid.bams/1183425933|doi=10.1090/S0002-9904-1922-03510-0|doi-access=free}}</ref> to [[Prussia]]n parents. His father, Caspar Klein (1809–1889), was a Prussian government official's secretary stationed in the [[Rhine Province]]. His mother was Sophie Elise Klein (1819–1890, [[Name at birth|née]] Kayser).<ref>{{cite book|author=Rüdiger Thiele|title=Felix Klein in Leipzig: mit F. Kleins Antrittsrede, Leipzig 1880|url=https://books.google.com/books?id=KznSxd-HcckC&pg=PA195|year=2011|isbn=978-3-937219-47-9|pages=195|publisher=Ed. am Gutenbergplatz |language=de}}</ref> He attended the [[Gymnasium (school)|Gymnasium]] in Düsseldorf, then studied mathematics and physics at the [[University of Bonn]],<ref>{{cite journal|author=Halsted, George Bruce|author-link=G. B. Halsted|title=Biography: Felix Klein|journal=[[The American Mathematical Monthly]]|year=1894|volume=1|issue=12|pages=416–420|jstor=2969034|doi=10.2307/2969034}}</ref> 1865–1866, intending to become a physicist. At that time, [[Julius Plücker]] had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest was mainly geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868.

Plücker died in 1868, leaving his book concerning the basis of [[line geometry]] incomplete. Klein was the obvious person to complete the second part of Plücker's ''Neue Geometrie des Raumes'', and thus became acquainted with [[Alfred Clebsch]], who had relocated to Göttingen in 1868. Klein visited Clebsch the next year, along with visits to [[Berlin]] and Paris. In July 1870, at the beginning of the [[Franco-Prussian War]], he was in Paris and had to leave the country. For a brief time he served as a medical orderly in the [[Prussian army]] before being appointed ''Privatdozent'' (lecturer) at Göttingen in early 1871.

The [[University of Erlangen–Nuremberg|University of Erlangen]] appointed Klein professor in 1872, when he was only 23 years old.<ref>{{cite book|editor=Ivor Grattan-Guinness|editor-link=Ivor Grattan-Guinness|title=Landmark Writings in Western Mathematics 1640–1940|url=https://books.google.com/books?id=UdGBy8iLpocC&pg=PA546|year=2005|publisher=Elsevier|isbn=978-0-08-045744-4|page=546}}</ref> 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 at the [[Technical University of Munich|Technische Hochschule München]] in 1875. There he and [[Alexander von Brill]] taught advanced courses to many excellent students, including [[Adolf Hurwitz]], [[Walther von Dyck]], [[Karl Rohn]], [[Carl Runge]], [[Max Planck]], [[Luigi Bianchi]], and [[Gregorio Ricci-Curbastro]].

In 1875, Klein married Anne Hegel, granddaughter of the philosopher [[Georg Wilhelm Friedrich Hegel]].<ref>Chislenko, Eugene; Tschinkel, Yuri. [https://www.ams.org/notices/200708/tx070800960p.pdf "The Felix Klein Protocols"], ''[[Notices of the American Mathematical Society]]'', August 2007, Volume 54, Number 8, pp. 960–970.</ref>

After spending five years at the Technische Hochschule, Klein was appointed to a chair of [[geometry]] at [[Leipzig University]]. His colleagues included [[Walther von Dyck]], Rohn, [[Eduard Study]] and [[Friedrich Engel (mathematician)|Friedrich Engel]]. 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.<ref>{{Cite book|url=https://books.google.com/books?id=-pTwBwAAQBAJ&q=mental|title=Hilbert|last=Reid|first=Constance|publisher=Springer-Verlag|year=1996|isbn=9781461207399|location=New York|pages=19|language=en}}</ref> Nevertheless, his research continued; his seminal work on hyperelliptic sigma functions, published between 1886 and 1888, dates from around this period.

[[File:Max Liebermann Felix Klein 1912.png|thumb|upright|Klein (1912). Painting of [[Max Liebermann]].]]
Klein accepted a professorship at the [[University of Göttingen]] 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 [[geometry]]. He taught a variety of courses at Göttingen, mainly concerning the interface between mathematics and physics, in particular, [[mechanics]] and [[potential theory]].

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 [[David Hilbert]] from the [[University of Königsberg]]. This appointment proved of great importance; Hilbert continued to enhance Göttingen's primacy in mathematics until his own retirement in 1932.

Under Klein's editorship, ''[[Mathematische Annalen]]'' became one of the best mathematical journals in the world. Founded by Clebsch, it grew under Klein's management, to rival,  and eventually surpass ''[[Crelle's Journal]]'', based at the [[University of Berlin]]. Klein established a small team of editors who met regularly, making decisions in a democratic spirit. The journal first specialized in [[complex analysis]], [[algebraic geometry]], and [[invariant theory]]. It also provided an 
important outlet for [[real analysis]] and the new [[group theory]].

In 1893,  Klein was a major speaker at the International Mathematical Congress held in Chicago as part of the [[World's Columbian Exposition]].<ref>{{cite book|editor=Case, Bettye Anne|editor-link=Bettye Anne Case|title=A Century of Mathematical Meetings|chapter=''Come to the Fair: The Chicago Mathematical Congress of 1893'' by David E. Rowe and Karen Hunger Parshall|year=1996|publisher=American Mathematical Society|page=64|isbn=9780821804650|chapter-url=https://books.google.com/books?id=UnkYqxyWGz8C&pg=PA64}}</ref> 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 [[Grace Chisholm Young]], an English student of [[Arthur Cayley]]'s, whom Klein admired. In 1897, Klein became a foreign member of the [[Royal Netherlands Academy of Arts and Sciences]].<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00001270 |title=Felix C. Klein (1849–1925) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=22 July 2015}}</ref>

Around 1900, Klein began to become interested in mathematical instruction in schools. In 1905, he was instrumental in formulating a plan recommending that [[analytic geometry]], the rudiments of differential and integral [[calculus]], and the [[Function (mathematics)|function]] concept be taught in secondary schools.<ref>{{cite book|editor1=Gary McCulloch|editor2=David Crook|title=The Routledge International Encyclopedia of Education|url=https://books.google.com/books?id=dCMuAgAAQBAJ&pg=PA373|year=2013|publisher=Routledge|isbn=978-1-317-85358-9|page=373}}</ref><ref>{{cite book|editor1=Alexander Karp|editor2=Gert Schubring|title=Handbook on the History of Mathematics Education|url=https://books.google.com/books?id=MYy9BAAAQBAJ&pg=PA499|year=2014|publisher=Springer Science & Business Media|isbn=978-1-4614-9155-2|pages=499–500}}</ref> This recommendation was gradually implemented in many countries around the world. In 1908, Klein was elected president of the [[International Commission on Mathematical Instruction]] at the Rome [[International Congress of Mathematicians]].<ref>{{cite book|editor1=Alexander Karp|editor2=Gert Schubring|title=Handbook on the History of Mathematics Education|url=https://books.google.com/books?id=MYy9BAAAQBAJ&q=%22Felix%20Klein%20as%20its%20first%20president%22&pg=PA503|year=2014|publisher=Springer Science & Business Media|isbn=978-1-4614-9155-2|page=503}}</ref> Under his guidance, the German part of the Commission published many volumes on the teaching of mathematics at all levels in Germany.

The [[London Mathematical Society]] awarded Klein its [[De Morgan Medal]] in 1893. He was elected a member of the [[Royal Society]] in 1885, and was awarded its [[Copley Medal]] in 1912. He retired the following year due to ill health, but continued to teach mathematics at his home for several further years.

Klein was one of ninety-three signatories of the [[Manifesto of the Ninety-Three]], a document penned in support of the German invasion of Belgium in the early stages of [[World War I]].

He died in Göttingen in 1925.