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

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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.

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.