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Ludwig Sylow was born on December 12, 1832, in Christiania (now Oslo), Norway. While a student at Christiania University, Sylow won a gold medal for competitive problem solving. In 1855, he became a high school teacher, and despite the long hours required by this teaching duties, Sylow found time to study the papers of Abel. During the school year 1862-1863, Sylow received a temporary appointment at Christiana University and gave lectures on Galois's theory and permutation groups. Among his students that year was the great mathematician Sophus Lie, after who's Lie algebras and Lie groups are named. From 1873 to 1881, Sylow, with some help from Lie, prepared a new edition of Abel's work. In 1902, Sylow and Ellington Hoslt published Abel's correspondence.
Sylow's great discovery, Sylow's Theorem, came in 1872. Upon learning of Sylow's result, C. Jorden called it "one of the essential points in the theory of permutations." The result took on greater importance when the theory of abstract groups flowered on the late 19th century and early 20th century.
In 1869, Sylow's was offered a professorship at Christiania University, but turned it down. Upon Sylow's retirement at the age 6t from high school teaching, Lie mounted a successful campaign to establish a chair for Sylow's at Christiania University. Sylow held this position until his death on September 7, 1918.
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