Space · region

Geometry and topology

Shape, packing and space. Some of the oldest problems in mathematics live here, and some of the newest were settled by computer-checked proof.

Mathematics Subject Classification: 51, 54, 57.

Problems

Poincaré conjecture (solved)
Smooth 4-dimensional Poincaré conjecture (open)
Kepler conjecture (solved)
Sphere packing in dimensions 8 and 24 (solved)
Kakeya conjecture in three dimensions (solved)
Kakeya set conjecture, all dimensions (open)
Einstein problem (aperiodic monotile) (solved)
Moving sofa problem (partial)
Squaring the circle (refuted)

Part of Mathematics.

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