How to See the 4th Dimension with Topology

Mathematician Maggie Miller explores the strange and fascinating world of 4D topology — the study of shapes, or manifolds, that resemble flat Euclidean space when viewed up close. Four-dimensional manifolds behave in unexpectedly complex ways, pushing mathematicians to develop advanced techniques to understand them.

Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin. She was also a former Visiting Clay Fellow and Stanford Science Fellow.

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CHAPTERS

00:00 4D topology is weird
00:45 What is topology?
01:00 Manifolds
01:33 Examples of 1D manifolds
01:48 Examples of 2D manifolds
02:26 We live in a 3D manifold
03:05 4D manifolds explained
04:09 Why 4D topologists study 4D manifolds
05:11 4-torus manifold explained by analogy
10:28 Problems unique to 4D topology
10:44 Smooth vs continuous equivalency
12:04 Big open questions

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