A planar set of dimension > 1 determines a positive-measure set of distances. Conjectured threshold d/2; plane record 5/4 — Kakeya's distance cousin.
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.
Tagged harmonic-analysis — 2 entries. Clear
How small can a set be that contains a unit line segment pointing in every direction? Dimension three fell in 2025 in a proof hailed as a once-in-a-century achievement; dimension four and beyond remain open.