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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.