Sophus Lie

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Marius Sophus Lie (Norwegian pronunciation: [liː] "Lee") (17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry, and applied it to the study of geometry and differential equations.



His first mathematical work, Repräsentation der Imaginären der Plangeometrie, was published, in 1869, by the Academy of Sciences in Christiana and also by Crelle's Journal. That same year he received a scholarship and traveled to Berlin, where he stood from September to February 1870. There, he met Felix Klein and they became close friends. When he left Berlin, Lie traveled to Paris, where he was joined by Klein two months later. There, they met Camille Jordan and Gaston Darboux. But on the 19th July 1870 the Franco-Prussian War began and Klein (who was Prussian) had to leave France very quickly. Lie decided then to visit Luigi Cremona in Milan but he was arrested at Fontainebleau under suspicion of being a German spy, an event which made him famous in Norway. He was released from prison after a month, thanks to the intervention of Darboux.

Lie obtained his Ph.D., at the University of Christiania (present day Oslo), in 1871, with a thesis entitled On a class of geometric transformations. It would be described by Darboux as “one of the most handsome discoveries of modern Geometry”. The next year, the Norwegian Parliament established an extraordinary professorship for him. That same year, Lie visited Klein, who was then at Erlangen and working on the Erlangen program.

At the end of 1872, Sophus Lie proposed to Anna Birch, then eighteen-year-old, and they were married in 1874. The couple had three children: Marie (b. 1877), Dagny (b. 1880) and Herman (b. 1884).

In 1884, Friedrich Engel arrived at Christiania to help him, with the support of Klein and Adolph Mayer (who were both professors at Leipzig, by then). Engel would help Lie to write his most important treatise, Theorie der Transformationsgruppen, published in Leipzig in three volumes from 1888 to 1893. Decades later, Engel would also be one of the two editors of Lie's collected works.

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