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Portrait of the Norwegian mathematician Marius Sophus Lie, 1842-1899. Lie worked in Paris and Berlin, and later in Leipzig and Oslo. His research was interrupted by his unjust arrest as a spy in 1870, and a spell in a mental hospital. Lie introduced group theory into geometry, using it to classify geometries. He discovered the contact transformation which maps curves into surfaces. He invented Lie groups which he used 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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