
[A theorem on locally euclidean groups, Annals of Mathematics, 1947, 650–658, 10.2307/1969132]
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[A theorem on locally euclidean groups, Annals of Mathematics, 1947, 650–658, 10.2307/1969132]
[The Eternally Existing, Self-reproducing, Frequently Puzzling Inflationary Universe, Preposterous Universe blog, 21 October 2011, http://www.preposterousuniverse.com/blog/2011/10/21/the-eternally-existing-self-reproducing-frequently-puzzling-inflationary-universe/]
“Remember though thatTHERE IS NO GENERAL RULE FOR CONVERTING A LIST INTO A SCALAR.”
In the perl man page.
Documentation
Interview in The Hindu (2013)
Context: The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple — particularly symmetric — theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.
"Einstein and the Search for Unification", p. 11 https://books.google.com/books?id=rEaUIxukvy4C&pg=PA11, in The legacy of Albert Einstein: a collection of essays in celebration of the year of physics (2007)
"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 170. Reported in Moritz (1914)
Journals
[Mirror symmetry and elliptic curves by Robert Dijkgraaf, The moduli space of curves, 149–163, Progress in Mathematics, vol. 129, Birkhäuser Boston, 1995, 10.1007/978-1-4612-4264-2_5]
The Structure of the Universe: An Introduction to Cosmology (1949)
Context: The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity.
It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.<!--p.82