History
The emergence of differential geometry as a distinct discipline is generally credited to Carl Friedrich Gauss and Bernhard Riemann. Riemann first described manifolds in his famous habilitation lecture before the faculty at Göttingen. He motivated the idea of a manifold by an intuitive process of varying a given object in a new direction, and presciently described the role of coordinate systems and charts in subsequent formal developments:
- Having constructed the notion of a manifoldness of n dimensions, and found that its true character consists in the property that the determination of position in it may be reduced to n determinations of magnitude, ...– B. Riemann
The works of physicists such as James Clerk Maxwell, and mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita led to the development of tensor analysis and the notion of covariance, which identifies an intrinsic geometric property as one that is invariant with respect to coordinate transformations. These ideas found a key application in Einstein's theory of general relativity and its underlying equivalence principle. A modern definition of a 2-dimensional manifold was given by Hermann Weyl in his 1913 book on Riemann surfaces. The widely accepted general definition of a manifold in terms of an atlas is due to Hassler Whitney.
Read more about this topic: Differentiable Manifold
Famous quotes containing the word history:
“The history of this country was made largely by people who wanted to be left alone. Those who could not thrive when left to themselves never felt at ease in America.”
—Eric Hoffer (1902–1983)
“The history of the world is the record of the weakness, frailty and death of public opinion.”
—Samuel Butler (1835–1902)
“Both place and time were changed, and I dwelt nearer to those parts of the universe and to those eras in history which had most attracted me.”
—Henry David Thoreau (1817–1862)