The Problems

Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.

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Tagged sphere-packings — 2 entries. Clear

The Tammes Problem open

How evenly can N points spread on a sphere? The botanist's problem behind spherical codes — exact optima known only for scattered N, including the kissing twelve.

Posed by Pieter Tammes · 1930 · discrete geometry · difficulty 4/5

sphere-packings

The Kepler Conjecture historic

Grocers stack oranges in hexagonal layers for good reason: Kepler said no arrangement beats face-centred cubic packing at 74.05%. Proof took 387 years and a computer.

Posed by Johannes Kepler · 1611 · discrete geometry · resolved 1998 · difficulty 4/5

sphere-packings