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.
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“In some withdrawn, unpublic mead
Let me sigh upon a reed,
Or in the woods, with leafy din,
Whisper the still evening in:
Some still work give me to do,—
Only—be it near to you!
For I’d rather be thy child
And pupil, in the forest wild,
Than be the king of men elsewhere,
And most sovereign slave of care:
To have one moment of thy dawn,
Than share the city’s year forlorn.”
—Henry David Thoreau (1817–1862)
“The work of Henry James has always seemed divisible by a simple dynastic arrangement into three reigns: James I, James II, and the Old Pretender.”
—Philip Guedalla (1889–1944)
“Idleness makes people feeble and peevish. Work makes them stalwart and prone to anger.”
—Mason Cooley (b. 1927)