Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Geometry and Physics / Endlessly Intertwined
Geometry and Physics / Endlessly Intertwined
Pages 49-52
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From page 49... ...
Nearly four of profound centuries later, we can only marvel at his prescience, because what he wrote then is even more true today. The secrets of the universe are still written in geometric terms, discoveries although the figures Galileo wrote about have now been replaced by more exotic and followed from abstract ones: manifolds, fiber bundles, and Calabi-Yau spaces.
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From page 50... ...
In the later 1930s and 1940s, physicists and mathematicians started losing touch with one another. Physicists started thinking about fields that permeate all of space, which they called "gauge fields." (Examples include the electromagnetic field and the weak and strong nuclear forces.)
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From page 51... ...
The twist given to the fibers makes the Mobius band topologically different from an ordinary cylindrical band. / 24 / A cross-section of a quintic hypersurface.
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From page 52... ...
Except that "ball" is not really the correct word. They actually form a manifold -- a type of space discovered by mathematical scientists.
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