# 1911 Encyclopædia Britannica/Lie, Marius Sophus

**LIE, MARIUS SOPHUS** (1842–1899), Norwegian mathematician,
was born at Nordfjordeif, near Bergen, on the 17th of
December 1842, and was educated at the university of Christiania,
where he took his doctor’s degree in 1868 and became
extraordinary professor of mathematics (a chair created specially
for him) four years later. In 1886 he was chosen to succeed
Felix Klein in the chair of geometry at Leipzig, but as his fame
grew a special post was arranged for him in Christiania. But
his health was broken down by too assiduous study, and he died
at Christiania on the 18th of February 1899, six months after
his return. Lie’s work exercised a great influence on the progress
of mathematical science during the later decades of the 19th
century. His primary aim has been declared to be the advancement
and elaboration of the theory of differential equations,
and it was with this end in view that he developed his theory
of transformation groups, set forth in his *Theorie der Transformationsgruppen*
(3 vols., Leipzig, 1888–1893), a work of
wide range and great originality, by which probably his name
is best known. A special application of his theory of continuous
groups was to the general problem of non-Euclidean geometry.
The latter part of the book above mentioned was devoted
to a study of the foundations of geometry, considered from
the standpoint of B. Riemann and H. von Helmholtz; and
he intended to publish a systematic exposition of his geometrical
investigations, in conjunction with Dr G. Scheffers, but only
one volume made its appearance (*Geometrie der Berührungstransformationen*,
Leipzig, 1896). Lie was a foreign member
of the Royal Society, as well as an honorary member of the
Cambridge Philosophical Society and the London Mathematical
Society, and his geometrical inquiries gained him the much-coveted
honour of the Lobatchewsky prize.

An analysis of Lie’s works is given in the *Bibliotheca Mathematica* (Leipzig, 1900).