What organization or association or team did Sophus Lie join in May 1886?
Sophus Lie Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899 ) was a Norwegian mathematician . He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations . Biography . His first mathematical work , Repräsentation der Imaginären der Plangeometrie , was published in 1869 by the Academy of Sciences in Christiania and also by Crelles Journal . That same year he received a scholarship and traveled to Berlin , where he stayed from September to February 1870 . There , he met Felix Klein and they became close friends . When he left Berlin , Lie traveled to Paris , where he was joined by Klein two months later . There , they met Camille Jordan and Gaston Darboux . But on 19 July 1870 the Franco-Prussian War began and Klein ( who was Prussian ) had to leave France very quickly . Lie left for Fontainebleau where after a while he was arrested under suspicion of being a German spy , an event that made him famous in Norway . He was released from prison after a month , thanks to the intervention of Darboux . Lie obtained his PhD at the University of Christiania ( present day Oslo ) in 1871 with a thesis entitled Over en Classe geometriske Transformationer ( On a Class of Geometric Transformations ) . It would be described by Darboux as one of the most handsome discoveries of modern Geometry . The next year , the Norwegian Parliament established an extraordinary professorship for him . That same year , Lie visited Klein , who was then at Erlangen and working on the Erlangen program . In 1872 Lie spent eight years together with Peter Ludwig Mejdell Sylow , editing and publishing the mathematical works of their countryman , Niels Henrik Abel . At the end of 1872 , Sophus Lie proposed to Anna Birch , then eighteen years old , and they were married in 1874 . The couple had three children : Marie ( b . 1877 ) , Dagny ( b . 1880 ) and Herman ( b . 1884 ) . In 1884 , Friedrich Engel arrived at Christiania to help him , with the support of Klein and Adolph Mayer ( who were both professors at Leipzig , by then ) . Engel would help Lie to write his most important treatise , Theorie der Transformationsgruppen , published in Leipzig in three volumes from 1888 to 1893 . Decades later , Engel would also be one of the two editors of Lies collected works . In 1886 Lie became professor at Leipzig , replacing Klein , who had moved to Göttingen . In November 1889 , Lie suffered a mental breakdown and had to be hospitalized until June 1890 . After that , he returned to his post , but over the years his anaemia progressed to the point where he decided to return to his homeland . Consequently , in 1898 he tendered his resignation in May , and left for home ( for good ) in September the same year . He died the following year , 1899 . He was made Honorary Member of the London Mathematical Society in 1878 , Member of the French Academy of Sciences in 1892 , Foreign Member of the Royal Society of London in 1895 and foreign associate of the National Academy of Sciences of the United States of America in 1895 . Sophus Lie died at the age of 56 , due to pernicious anemia , a disease caused by impaired absorption of vitamin B . Legacy . Lies principal tool , and one of his greatest achievements , was the discovery that continuous transformation groups ( now called , after him , Lie groups ) could be better understood by linearizing them , and studying the corresponding generating vector fields ( the so-called infinitesimal generators ) . The generators are subject to a linearized version of the group law , now called the commutator bracket , and have the structure of what is today called a Lie algebra . Hermann Weyl used Lies work on group theory in his papers from 1922 and 1923 , and Lie groups today play a role in quantum mechanics . However , the subject of Lie groups as it is studied today is vastly different from what the research by Sophus Lie was about and among the 19th century masters , Lies work is in detail certainly the least known today . Sophus Lie was an eager proponent in the establishment of the Abel Prize . Inspired by the Nansen fund named after Fridtjof Nansen , and the lack of a prize for mathematics in the Nobel Prize . He gathered support for the establishment of an award for outstanding work in pure mathematics . Lie advised many doctoral students who went on to become successful mathematicians . Élie Cartan became widely regarded as one of the greatest mathematicians of the twentieth century . Kazimierz Żorawskis work was proved to be of importance to a variety of fields . Hans Frederick Blichfeldt made great contributions to various fields of mathematics . Books . - . Written with the help of Friedrich Engel . English translation available : Edited and translated from the German and with a foreword by Joël Merker , see and - . Written with the help of Friedrich Engel . - . Written with the help of Georg Scheffers . - . Written with the help of Georg Scheffers . - . Written with the help of Friedrich Engel . - . Written with the help of Georg Scheffers .