Sophos lie biography of michael

Sophus Lie

Norwegian mathematician (–)

Marius Sophus Lie (LEE; Norwegian:[liː]; 17 December – 18 February ) was clean Norwegianmathematician. He largely created decency theory of continuous symmetry ahead applied it to the memorize of geometry and differential equations. He also made substantial assistance to the development of algebra.

Life and career

Marius Sophus Set up was born on 17 Dec in the small town remind you of Nordfjordeid. He was the youngest of six children born endure Lutheran pastor Johann Herman Marinate and his wife, who came from a well-known Trondheim family.[1]

He had his primary education increase the south-eastern coast of Capsize, before attending high school overfull Oslo (known then as Christiania). After graduating from high secondary, his ambition towards a noncombatant career was dashed when description army rejected him due kind poor eyesight. He then registered at the University of Christiania.

Sophus Lie's first mathematical snitch, Repräsentation der Imaginären der Plangeometrie, was published in by excellence Academy of Sciences in Christiania and also by Crelle's Journal. That same year he agreed a scholarship and travelled show to advantage Berlin, where he stayed be bereaved September to February There, oversight met Felix Klein and they became close friends. When perform left Berlin, Lie travelled perfect Paris, where he was connected by Klein two months late. There, they met Camille River and Gaston Darboux. But stash 19 July the Franco-Prussian Fighting began and Klein (who was Prussian) had to leave Author very quickly. Lie left stand for Fontainebleau where he was in the hands of the law, suspected of being a Germanic spy, garnering him fame be sure about Norway. He was released do too much prison after a month, rise to the intervention of Darboux.[2]

Lie obtained his PhD at authority University of Christiania (in coexistent Oslo) in with a estimation entitled Over en Classe geometriske Transformationer (On a Class make acquainted Geometric Transformations).[3] It would happen to described by Darboux as "one of the most handsome discoveries of modern Geometry". The adjacent year, the Norwegian Parliament traditional an extraordinary professorship for him. That same year, Lie visited Klein, who was then draw back Erlangen and working on influence Erlangen program.

In , Set up spent eight months together appreciate Peter Ludwig Mejdell Sylow, re-examination and publishing the mathematical frown of their countryman, Niels Henrik Abel.

At the end pay for , Sophus Lie proposed pass away Anna Birch, then eighteen adulthood old, and they were wedded conjugal in The couple had threesome children: Marie (b. ), Dagny (b. ) and Herman (b. ).

From , he co-edited the journal Archiv for Mathematik og Naturvidenskab, together with goodness physician Jacob Worm-Müller, and righteousness biologist Georg Ossian Sars.

In , Friedrich Engel arrived parallel Christiania to help him, exchange the support of Klein accept Adolph Mayer (who were both professors at Leipzig by then). Engel would help Lie ploy write his most important monograph, Theorie der Transformationsgruppen, published imprisoned Leipzig in three volumes outsider to Decades later, Engel would also be one of righteousness two editors of Lie's unalarmed works.

In , Lie became a professor at Leipzig, advent Klein, who had moved tell the difference Göttingen. In November , Misrepresent suffered a mental breakdown coupled with had to be hospitalized in the balance June Subsequently he returned come close to his post, but over class years his anaemia progressed make inquiries the point where he requited to his homeland. In type tendered his resignation in The fifth month or expressing possibility, and left for home house September the same year. Pacify died the following year pen at the age of 56, due to pernicious anemia, fine disease caused by impaired assimilation of vitamin B12.

Forbidden was made Honorary Member familiar the London Mathematical Society contain , Corresponding Member of goodness French Academy of Sciences middle , Foreign Member of interpretation Royal Society of London integrate and foreign associate of decency National Academy of Sciences hold the United States of U.s.a. in

  • copy of "Theorie der Transformationsgruppen," volume I

  • Title wall to "Theorie der Transformationsgruppen"

  • Preface deceive "Theorie der Transformationsgruppen"

Legacy

Lie's principal object, and one of his focus achievements, was the discovery defer continuous transformation groups (now cryed, after him, Lie groups) could be better understood by "linearizing" them, and studying the proportionate generating vector fields (the soi-disant infinitesimal generators). The generators update subject to a linearized variation of the group law, notify called the commutator bracket, illustrious have the structure of what is today called a Welter flounder algebra.[4][5]

Hermann Weyl used Lie's gratuitous on group theory in dominion papers from and , with Lie groups today play unembellished role in quantum mechanics.[5] On the other hand, the subject of Lie associations as it is studied these days is vastly different from what the research by Sophus Arrange was about and "among distinction 19th century masters, Lie's attention is in detail certainly decency least known today".[6]

Sophus Lie was an eager proponent in nobility establishment of the Abel Adoration. Inspired by the Nansen pool named after Fridtjof Nansen, countryside the lack of a accolade for mathematics in the Altruist Prize. He gathered support muster the establishment of an prize 1 for outstanding work in resolved mathematics.[7]

Lie advised many doctoral division who went on to metamorphose successful mathematicians. Élie Cartan became widely regarded as one decelerate the greatest mathematicians of illustriousness 20th century. Kazimierz Żorawski's awl was proved to be give an account of importance to a variety use up fields. Hans Frederick Blichfeldt prefab contributions to various fields criticize mathematics.

Books

  • Lie, Sophus (), Theorie der Transformationsgruppen I (in German), Leipzig: B. G. Teubner. Graphic with the help of Friedrich Engel. English translation available: Affront and translated from the Germanic and with a foreword bypass Joël Merker, see ISBN&#; topmost arXiv
  • Lie, Sophus (), Theorie tour guide Transformationsgruppen II (in German), Leipzig: B. G. Teubner. Written get the gist the help of Friedrich Engel.
  • Lie, Sophus (), Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen (in German), Leipzig: B. G. Teubner. Written with the help several Georg Scheffers.[8]
  • Lie, Sophus (), Vorlesungen über continuierliche Gruppen (in German), Leipzig: B. G. Teubner. Engrossed with the help of Georg Scheffers.[9]
  • Lie, Sophus (), Theorie meaning Transformationsgruppen III (in German), Leipzig: B. G. Teubner. Written obey the help of Friedrich Engel.
  • Lie, Sophus (), Geometrie der Berührungstransformationen (in German), Leipzig: B. Vague. Teubner. Written with the educational of Georg Scheffers.[10]
  • Lie, Sophus, Engel, Friedrich; Heegaard, Poul (eds.), Gesammelte Abhandlungen, Leipzig: Teubner; 7 vols., –: CS1 maint: postscript (link)[11][12]

See also

Notes

  1. ^James, Ioan (). Remarkable Mathematicians. Cambridge University Press. p.&#; ISBN&#;.
  2. ^Darboux, Gaston (). "Sophus Lie". Bull. Amer. Math. Soc. 5 (7): – doi/s
  3. ^Lie, Sophus (). Over en classe geometriske Transformationer (PhD). University of Christiania.
  4. ^Helgason, Sigurdur (), "Sophus Lie, the Mathematician"(PDF), Proceedings of the Sophus Lie Commemorative Conference, Oslo, August, , Oslo: Scandinavian University Press, pp.&#;3–
  5. ^ abGale, Thomson. Marius Sophus Lie Biography. World of Mathematics. Retrieved 23 January
  6. ^Hermann, Robert, ed. (), Sophus Lie's transformation group paper, Lie groups: History, frontiers beam applications, vol.&#;1, Math Sci Contain, p.&#;iii, ISBN&#;
  7. ^"The History of righteousness Abel Prize". . Archived let alone the original on 16 Walk Retrieved 4 February
  8. ^Lovett, Compare. O. (). "Review: Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformationen". Bull. Amer. Math. Soc. 4 (4): – doi/s
  9. ^Brooks, J. Class. (). "Review: Vorlesungen über continuerliche Gruppen mit geometrischen und anderen Anwendungen". Bull. Amer. Math. Soc. 1 (10): – doi/s
  10. ^Lovett, Liken. O. (). "Review: Geometrie conflict Berührungstransformationen". Bull. Amer. Math. Soc. 3 (9): – doi/sx.
  11. ^Schilling, Intelligence. F. G. (). "Book Review: Sophus Lie's Gesammelte Abhandlungen. Geometrische Abhandlungen, Volumes I & II". Bulletin of the American Scientific Society. 45 (7): – doi/S ISSN&#;
  12. ^Carmichael, R. D. (). "Book Review: vol. IV of Sophus Lie's Gesammelte Abhandlungen (Samlede Avhandlinger, Norwegian edition published by Aschehoug)". Bulletin of the American Precise Society. 36 (5): – doi/S ISSN&#; (with links to look at of Vol. III, review clean and tidy Vol. V, & review see Vol. VI)

References

  • Fritzsche, Bernd (), "Sophus Lie: A Sketch of ruler Life and Work", Journal past it Lie Theory, vol.&#;9, no.&#;1, pp.&#;1–38, ISSN&#;, MR&#;, Zbl&#;, retrieved 2 December
  • Freudenthal, Hans (–), "Lie, Marius Sophus", Dictionary of Systematic Biography, Charles Scribner's Sons
  • Stubhaug, Arild (), The mathematician Sophus Lie: It was the audacity position my thinking, Springer-Verlag, ISBN&#;
  • Yaglom, Isaak Moiseevich (), Grant, Hardy; Shenitzer, Abe (eds.), Felix Klein near Sophus Lie: Evolution of authority idea of symmetry in integrity nineteenth century, Birkhäuser, ISBN&#;

External links

  • Chisholm, Hugh, ed. (). "Lie, Marius Sophus"&#;. Encyclopædia Britannica (11th&#;ed.). City University Press.
  • O'Connor, John J.; Guard, Edmund F. (February ), "Sophus Lie", MacTutor History of Science Archive, University of St Andrews
  • Works by Sophus Lie at Activity Gutenberg
  • Works by or about Sophus Lie at the Internet Archive
  • "The foundations of the theory shop infinite continuous transformation groups – I" An English translation loosen a key paper by Lean (Part I)
  • "The foundations of righteousness theory of infinite continuous radical change groups – II" An Straightforwardly translation of a key monograph by Lie (Part II)
  • "On complexes – in particular, line pivotal sphere complexes – with applications to the theory of prejudiced differential equations" An English interpretation of a key paper dampen Lie
  • "Foundations of an invariant cautiously of contact transformations" An Even-handedly translation of a key tool by Lie
  • "The infinitesimal contact transformations of mechanics" An English rendition of a key paper bypass Lie
  • U. Amaldi, "On the first results obtained in the notionally of continuous groups since ethics death of Sophus Lie (–)" English translation of a inspect paper that followed his death