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The Mathematician Sophus Lie: It was the Audacity of My Thinking
 
 

The Mathematician Sophus Lie: It was the Audacity of My Thinking [Kindle Edition]

Arild Stubhaug , R. Daly
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Editorial Reviews

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"... Es ist besonders erfreulich, dass sich der Autor zum Ziel gesetzt hat, nach Abel auch Lie einem über die Mathematiker weit hinausgehenden Leserkreis nahe zu bringen. In seinem lesenswerten Buch stellt er den interessanten Lebenslauf eines nicht immer bequemen Genies voll irrtümlicher Lebenskraft, abe auch mit Schattenseiten dar. ... Ein spannendes Buch, das auch Einblick in die deutsche Universitätsgeschichte des späten 19. Jahrhunderts gibt, aber auch ein tröstliches und ermutignedes Buch für junge Mathematiker. ... Zusammenfassend, ein Buch, das man gerne im eigenen Bücherregal stehen hat." (P. Gruber, Internationale Mathematische Nachrichten 2003, Heft 57, Ausgabe 192)

"... Ich muss allerdings eingestehen, dass sich mir, als ich das sorgfältig und mit Liebe aufgemachte Buch zum ersten Mal in Händen hielt, die Frage aufdrängte, wen denn dieses Buch interessieren könnte. Beim ersten Lesen ertappte ich mich oft dabei, dass ich Passagen, die nicht unmittelbar mit seiner Tätigkeit als Mathematiker zu tun hatten, diagonal las oder zu überspringen suchte, in der Hoffnung eingeweiht zu werden in eine Gedankenwelt, der die bahnbrechenden neuen, partielle Differentialgleichungen und Geometrie vereinenden Ideen entsprangen, die zur Theorie der Transformationsgruppen führten. Das fand ich zwar nicht: wie in der Biographie über N.H. Abel vom gleichen Autor(siehe die Besprechung von E. Behrends) ist auch dieses Buch von Stubhaug ohne eine einzige Formel oder präzise mathematische Definition. Was aber Stubhaug uns durch seine umfangreichen Nachforschungen, hauptsächlich in Briefen Lies an seine Frau, an seine Freunde in Norwegen und Briefe an und von seinen Kollegen, mitteilen kann, lässt in vielen Einzelheiten, Stück für Stück, ein breiteres Bild von Lie, der wissenschaftlichen und politischen Situation Norwegens zu Lies Zeit, und des wissenschaftlichen und gesellschaftlichen Lebens an Lies Wirkungsstätten entstehen. Die Darstellung, in der zum Teil die Inhalte einer Reihe von Briefen nacheinander auch mit Hilfe kurzer Zitate referiert werden, birgt die Gefahr der Ermüdung. Dem entgeht Stubhaug einmal durch seinen angenehmen Erzählstil, zum anderen durch gelegentliche Unterbrechungen, in denen der zeitliche und geschichtliche Hintergrund angesprochen wird. Jedenfalls fiel mir auf, dass ich mit wachsender Neugierde die zu Beginn überflogenen Stellen eine nach der anderen wieder aufsuchte und mit Interesse las. ..........

Das Buch bringt allen großen Gewinn, die sich für Sophus Lie und seine Zeit interessieren. Insbesondere erfährt man viel über den wissenschaftlichen Kontakt zwischen Lie und anderen mathematischen Größen der damaligen Zeit wie Klein, Kummer, Study, Darboux, Poincar und anderen. Wen die mathematischen Ideen Lies interessieren, der kommt nicht umhin, sich mit dessen Arbeiten auseinanderzusetzen, um dann in Verbindung mit Stubhaugs Buch vielleicht doch etwas von der "audacity of my (Lie's) thinking" zu

Product Description

Sophus Lie (1842-1899) is one of Norways greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms "Lie groups" and "Lie algebra" are part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug introduces us to both the person Sophus Lie and his time. We follow him through: childhood at the vicarage in Nordfjordeid; his youthful years in Moss; education in Christiania; travels in Europe; and learn about his contacts with the leading mathematicians of his time.

Product Details

  • Format: Kindle Edition
  • File Size: 8261 KB
  • Print Length: 566 pages
  • Publisher: Springer; 1 edition (January 10, 2002)
  • Sold by: Amazon Digital Services
  • Language: English
  • ASIN: B001BZPKRG
  • Text-to-Speech: Enabled
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #630,823 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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5.0 out of 5 stars Where Lie groups came from, December 7, 2011
I received this book in Norwegian as a gift several years ago and have only read it in part, but I can strongly recommend it. The book is thick, it covers Lie's personal life as well as his mathematical contributions.

Lie was born in Nordfjoreid, a small village in Norway just south of the Sunnmøre Alps. He studied and taught at the University of Oslo (UiO), where he was reputed to have jumped out a window after the students locked him in a classroom as prank. He was apparently extreme as Norwegians go. Every Norwegian, more or less, hikes and skis in the mountains from an early age, but Lie is reported to have walked 80 km/day consistently during his years at UiO. He became a friend of Felix Klein early-on. Both were geometers. Lie was arrested and held as German spy while hiking south from Paris toward the Alps during the Franco-Prussian War. He was carrying letters from Klein in German which the French police feared were coded information. When Klein left Leipzig he got Lie the position there. The many volumes with Engel and Scheffers were written there. If you ask a Leipziger today who were Klein and Lie, you will likely be treated with a blank stare. Lie eventually left Leipzig and returned to Oslo.

Lie set for himself and answered the question: when is a continuous group of transformations integrable. He thereby constructed Lie algebras as on the road to the answer. Lie algebras arise from following Lie's path: study a tranformation near the identity. Lie's work is directly applicable to classical mechanics. My book 'Classical Mechanics' has a chapter on Lie groups and uses Lie's ideas throughout. The extension of the theory of Lie algebras by Cartan has been used heavily in nuclear physics and quantum field theory. The discovery of root diagrams for a Lie algebra provided the system for classifying particles in the SU(3) theory. Modern physics, and our deeper understanding of integrable systems in classical mechanics, would be unthinkable without Lie groups and Lie algebras.
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5.0 out of 5 stars Mathematical Reviews' reference, September 26, 2007
Stubhaug/Daly contribution is welcome indeed. Here is information for finding the other book that Mathematical Reviews review of Stubhaug/Daly calls a "definitive history of the mathematical theory" and like Stubhaug/Daly "(a blessing to) the study of the history of Lie groups":

Thomas Hawkins, "Emergence of The Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926", ISBN 0-387-98963-3, Springer, 2000.

Hawkins' history has sections on the contributions of Sophus Lie, Wilhelm Killing, Elie Cartan, and Hermann Weyl.
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