# Geometry and topology

- kind: region

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](/wiki/Problem:poincare-conjecture.md) (solved)
- [Smooth 4-dimensional Poincaré conjecture](/wiki/Problem:smooth-poincare-4.md) (open)
- [Kepler conjecture](/wiki/Problem:kepler-conjecture.md) (solved)
- [Sphere packing in dimensions 8 and 24](/wiki/Problem:sphere-packing-8-24.md) (solved)
- [Kakeya conjecture in three dimensions](/wiki/Problem:kakeya-3d.md) (solved)
- [Kakeya set conjecture, all dimensions](/wiki/Problem:kakeya-general.md) (open)
- [Einstein problem (aperiodic monotile)](/wiki/Problem:einstein-tile.md) (solved)
- [Moving sofa problem](/wiki/Problem:moving-sofa.md) (partial)
- [Squaring the circle](/wiki/Problem:squaring-the-circle.md) (refuted)

Part of [Mathematics](/wiki/Continent:mathematics.md).

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