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Lie, Marius Sophus

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[lee] (1842–99) Norwegian mathematician: discovered the theory of continuous transformation groups.

Lie was inspired to study mathematics by reading and J Plücker (1801–68) on geometry, and spent his life fruitfully developing the latter’s idea of creating geometries from shapes as elements of space rather than points. Research in Berlin and in Paris was somewhat marred by being arrested as a German spy (1870), but this false charge was soon dropped and he left Paris just before the Germans besieged it. A year in a mental hospital interrupted later work at Leipzig, and he then returned to a post created for him at Christiania in Norway (now Oslo University).

Lie, along with his close friend Klein, introduced group theory into geometry, using it to classify geometries. Lie discovered the contact transformation which maps curves into surfaces (1870). Work on transformation groups followed (1873) and he invented Lie groups, which use continuous or infinitesimal transformations. Lie used these groups to classify partial differential equations, making the traditional methods of solution all reduce to a single principle. The Lie group also gave the basis for the growth of modern topology.

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