Work
Klein's dissertation, on line geometry and its applications to mechanics, classified second degree line complexes using Weierstrass's theory of elementary divisors.
Klein's first important mathematical discoveries were made in 1870. In collaboration with Sophus Lie, he discovered the fundamental properties of the asymptotic lines on the Kummer surface. They went on to investigate W-curves, curves invariant under a group of projective transformations. It was Lie who introduced Klein to the concept of group, which was to play a major role in his later work. Klein also learned about groups from Camille Jordan.
Klein devised the bottle named after him, a one-sided closed surface which cannot be embedded in three-dimensional Euclidean space, but it may be immersed as a cylinder looped back through itself to join with its other end from the "inside". It may be embedded in Euclidean space of dimensions 4 and higher.
In the 1890s, Klein turned to mathematical physics, a subject from which he had never strayed far, writing on the gyroscope with Arnold Sommerfeld. In 1894 he launched the idea of an encyclopedia of mathematics including its applications, which became the Encyklopädie der mathematischen Wissenschaften. This enterprise, which ran until 1935, provided an important standard reference of enduring value.
Read more about this topic: Felix Klein
Famous quotes containing the word work:
“How did you get in the Navy? How did you get on our side? Ah, you ignorant, arrogant, ambitious—keeping sixty two men in prison cause you got a palm tree for the work they did. I don’t know which I hate worse, you or that malignant growth that stands outside your door. How did you ever get command of a ship? I realize in wartime they have to scrape the bottom of the barrel. But where’d they ever scrape you up?”
—Frank S. Nugent (1908–1965)
“Most childhood problems don’t result from “bad” parenting, but are the inevitable result of the growing that parents and children do together. The point isn’t to head off these problems or find ways around them, but rather to work through them together and in doing so to develop a relationship of mutual trust to rely on when the next problem comes along.”
—Fred Rogers (20th century)
“when I work I am pure as an angel
tiger and clear is my eye and hot
my brain and silent all the whining
grunting piglets of the appetites.”
—Marge Piercy (b. 1936)