Sophus Lie | |
|---|---|
 Lie in 1896 | |
| Born | Marius Sophus Lie (1842-12-17)17 December 1842 Nordfjordeid, Norway |
| Died | 18 February 1899(1899-02-18) (aged 56) Kristiania, Norway |
| Nationality | Norwegian |
| Alma mater | University of Christiania |
| Known for | One-parameter group Differential invariant Contact transformation Infinitesimal transformation W-curve Carathéodory–Jacobi–Lie theorem Lie algebra Lie bracket Lie group Lie product formula Lie sphere geometry Lie theory Lie transform Lie's theorem Lie's third theorem Lie–Kolchin theorem See full list |
| Awards | Lobachevsky Medal (1897) ForMemRS (1895) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Christiania University of Leipzig |
| Doctoral advisor | Carl Anton Bjerknes Cato Maximilian Guldberg |
| Doctoral students | Hans Blichfeldt Lucjan Emil Böttcher Gerhard Kowalewski Kazimierz Żorawski Élie Cartan Elling Holst Edgar Odell Lovett |
Marius Sophus Lie (/liː/LEE;Norwegian:[liː]; 17 December 1842 – 18 February 1899) was aNorwegianmathematician. He largely created the theory ofcontinuous symmetry and applied it to the study ofgeometry anddifferential equations. He also made substantial contributions to the development of algebra.
Marius Sophus Lie was born on 17 December 1842 in the small town ofNordfjordeid. He was the youngest of six children born to Lutheran pastor Johann Herman Lie and his wife, who came from a well-knownTrondheim family.[1]
He had his primary education in the south-eastern coast of Moss, before attending high school inOslo (known then as Christiania). After graduating from high school, his ambition towards a military career was dashed when the army rejected him due to poor eyesight. He then enrolled at theUniversity of Christiania.
Sophus Lie's first mathematical work,Repräsentation der Imaginären der Plangeometrie, was published in 1869 by the Academy of Sciences inChristiania and also byCrelle's Journal. That same year he received a scholarship and travelled toBerlin, where he stayed from September to February 1870. There, he metFelix Klein and they became close friends. When he left Berlin, Lie travelled toParis, where he was joined by Klein two months later. There, they metCamille Jordan andGaston Darboux. But on 19 July 1870 theFranco-Prussian War began and Klein (who wasPrussian) had to leave France very quickly. Lie left forFontainebleau where he was arrested, suspected of being a German spy, garnering him fame in Norway. He was released from prison after a month, thanks to the intervention of Darboux.[2]
Lie obtained his PhD at the University of Christiania (in present-dayOslo) in 1871 with a thesis entitledOver en Classe geometriske Transformationer (On a Class of Geometric Transformations).[3] 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 atErlangen and working on theErlangen program.
In 1872, Lie spent eight months together withPeter 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).
From 1876, he co-edited the journalArchiv for Mathematik og Naturvidenskab, together with the physician Jacob Worm-Müller, and the biologistGeorg Ossian Sars.
In 1884,Friedrich Engel arrived at Christiania to help him, with the support ofKlein andAdolph Mayer (who were both professors atLeipzig 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 Lie's collected works.
In 1886, Lie became a professor at Leipzig, replacing Klein, who had moved toGöttingen. In November 1889, Lie suffered a mental breakdown and had to be hospitalized until June 1890. Subsequently he returned to his post, but over the years his anaemia progressed to the point where he returned to his homeland. In 1898 he tendered his resignation in May, and left for home in September the same year. He died the following year in 1899 at the age of 56, due topernicious anemia, a disease caused by impaired absorption ofvitamin B12.
He was made Honorary Member of theLondon Mathematical Society in 1878, Corresponding Member of theFrench Academy of Sciences in 1892, Foreign Member of theRoyal Society of London in 1895 and foreign associate of theNational Academy of Sciences of the United States of America in 1895.
Lie's principal tool, and one of his greatest achievements, was the discovery that continuoustransformation groups (now called, after him,Lie groups) could be better understood by "linearizing" them, and studying the corresponding generatingvector fields (the so-calledinfinitesimal generators). The generators are subject to a linearized version of thegroup law, now called thecommutator bracket, and have the structure of what is today called aLie algebra.[4][5]
Hermann Weyl used Lie's work on group theory in his papers from 1922 and 1923, and Lie groups today play a role inquantum mechanics.[5] 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, Lie's work isin detail certainly the least known today".[6]
Sophus Lie was an eager proponent in the establishment of theAbel Prize. Inspired by the Nansen fund named afterFridtjof Nansen, and the lack of a prize for mathematics in theNobel Prize. He gathered support for the establishment of an award for outstanding work in pure mathematics.[7]
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 20th century.Kazimierz Żorawski's work was proved to be of importance to a variety of fields.Hans Frederick Blichfeldt made contributions to various fields of mathematics.
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