SMRTR Science & EngineeringNov 3, 2025Quanta Magazine

What Is a Manifold?

SMRTR summary

Manifolds are mathematical shapes that appear flat when viewed locally but have complex global structures, like Earth appearing flat to us despite being spherical. Introduced by Bernhard Riemann in the mid-19th century, manifolds revolutionized mathematics by providing tools to study curved spaces and higher dimensions, becoming essential for Einstein's relativity theory and modern physics applications.

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