Legacy
Lie's principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called, after him, Lie groups) could be better understood by "linearizing" them, and studying the corresponding generating vector fields (the so-called infinitesimal generators). The generators are subject to a linearized version of the group law, now called the commutator bracket, and have the structure of what is today called a Lie algebra.
Hermann Weyl used Lie's work on group theory in his papers from 1922 and 1923, and Lie groups today play a role in quantum mechanics. However, the subject of Lie groups as it is studied today is vastly different from what the research by Sophus Lie was about and “among the 19th century masters, Lie's work is in detail certainly the least known today”.
Read more about this topic: Sophus Lie
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“What is popularly called fame is nothing but an empty name and a legacy from paganism.”
—Desiderius Erasmus (c. 1466–1536)