German mathematician, author of the Erlangen Program (1849-1925)
Klein's 1872 Erlangen program did for geometry what Darwin did for biology: it found the organizing principle. By showing that every geometry is defined by its symmetry group, he turned a jumble of competing systems into a unified field.
Felix Christian Klein was born 25 April 1849 in Germany and trained in an era when geometries were proliferating — Euclidean, hyperbolic, projective — with no clear framework to relate them. In 1872 he published the Erlangen program, which classified geometries by their underlying symmetry groups and synthesized much of contemporary mathematics in one stroke. His work spanned group theory, complex analysis, and the deep ties between algebra and shape. At Göttingen he built an institution: new chairs, new institutes, seminars that covered nearly every branch of mathematics and its applications.…
Sourced, dated quotes from Felix Klein
In ordinary geometry a surface is conceived as a locus of points; in Lie's geometry it appears as the totality of all the spheres having contact with the surface.
It has been the final aim of Lie from the beginning to make progress in the theory of differential equations ...
As regards quartic surfaces, Rohn has investigated an enormous number of special cases; but a complete enumeration he has not reached.
Next to the elementary transcental functions the elliptic functions are usually regarded as the most important.
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