The son of a Lutheran minister, Lie was born in Nordfjordeid, Norway, and was the youngest of six children. He was first educated at Nissen’s Private Latin School in Christiania (later known as Oslo) and was keen to join the army, but was prevented by poor eyesight. He decided instead to study science at the University of Christiania, graduating in 1865.
The following few years were spent teaching private students, while he studied astronomy, mechanics and mathematics (especially geometry) - Lie was unsure what he wanted to do! In 1869 he published his first paper on geometry, on the basis of which he was awarded a scholarship to travel to Prussia to meet two of the foremost mathematicians - Reye and Clebsch - at the University of Berlin. It was in Berlin that Lie met Felix Klein, who was to become a life-long friend as well as a collaborator in Lie’s future research.
1870 saw both Lie and Klein in Paris, at the time of the outbreak of the Franco-Prussian war. It was not long before Lie realised that the Prussians were to start a blockade of Paris, and decided to leave. Before he was able to leave France, he was arrested as a Prussian spy and his mathematical papers - considered as coded messages - ended him up in prison for a short time.
Returning to Norway, Lie became an assistant tutor at the University of Christiania, as well as a teacher at his old school. He received his doctorate in 1872 for A class of geometric transformations based on his earlier published paper. It was received so well that the University appointed him to a senior position, though not all mathematicians gave him the credit he felt he deserved! Lie’s work did lead to one of the most important aspects of modern mathematics - Lie groups and Lie algebras.
Because of some of the problems Lie had in getting his work properly recognised, his friend Klein introduced him to Friedrich Engel, and the two were to spent nine years collaborating on their major published work, Theory of Transformation Groups (1888-1893). Lie was later appointed a chair at the University of Leipzig (1886) having succeeded Klein, while still maintaining his position at Christiania. Lie returned to Norway in 1898 but died of pernicious anaemia the following year.