WHAT IS A MANIFOLD?

Summary from the TLDR Dev newsletter

Manifolds are mathematical spaces that appear Euclidean when viewed locally, similar to how the Earth seems flat on a small scale. This concept revolutionized mathematics by treating space as an abstract object, enabling the rigorous study of higher dimensions and the development of modern topology. Mathematicians use "charts" and "atlases" to translate regions of manifolds into familiar Euclidean space, allowing the use of calculus and other techniques to analyze their properties.