klein

Klein is a surname of German origin, derived from the word klein meaning small or little. It is common in German- and Dutch-speaking regions and has spread to other language communities through migration. While primarily a family name, Klein also appears in various scientific terms named after individuals who bore the name.

Notable individuals bearing the name include Felix Klein (1849–1925), a German mathematician known for his work in geometry, group theory, and the development of the Erlangen program, which classified geometries by their transformation groups. Another prominent figure is Oskar Klein (1894–1977), a Swedish theoretical physicist recognized for contributions to early ideas about extra dimensions and relativistic quantum mechanics, including work related to the Kaluza–Klein framework.

In mathematics and physics, several concepts carry the Klein name. The Klein bottle is a non-orientable surface that cannot be embedded in ordinary three-dimensional space without self-intersection; it is associated with Felix Klein. The Klein four-group, a small finite abelian group of four elements, is another term linked to Felix Klein. The Klein paradox is a phenomenon in relativistic quantum mechanics described by Oskar Klein. The Kaluza–Klein theory, an early approach to unifying gravity with electromagnetism via extra dimensions, is named for Theodor Kaluza and Oskar Klein. These usages reflect Klein’s influence across multiple fields and illustrate how a surname can become embedded in mathematical and physical terminology.