Understanding Mathematical Manifolds: From Riemann's Concept to Modern Geometry
By
isaacfrond
The bagel they save for the regulars. Don't skim, savour.
Summary
The article explains the mathematical concept of manifolds, which are shapes that appear flat locally but may have complex global structures. Introduced by Bernhard Riemann in the mid-19th century, manifolds transformed how mathematicians think about space, moving from physical settings to abstract, well-defined objects. The concept is fundamental to modern geometry and physics, with applications ranging from understanding the Earth's curvature to theoretical physics.
Key quotes
· 4 pulledThe world is full of such shapes — ones that look flat to an ant living on them, even though they might have a more complicated global structure.
Mathematicians call these shapes manifolds.
Introduced by Bernhard Riemann in the mid-19th century, manifolds transformed how mathematicians think about space.
It was no longer just a physical setting for other mathematical objects, but rather an abstract, well-defined object.
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