Marius Sophus Lie was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra.
Lie in 1896
1888 copy of "Theorie der Transformationsgruppen," volume I
Title page to "Theorie der Transformationsgruppen"
Preface to "Theorie der Transformationsgruppen"
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
A European and an Arab practicing geometry in the 15th century
Woman teaching geometry. Illustration at the beginning of a medieval translation of Euclid's Elements, (c. 1310).
Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Zhoubi Suanjing 500–200 BC. The Pythagorean theorem is a consequence of the Euclidean metric.
Quintic Calabi–Yau threefold
