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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Borel's Conjecture open

Every strong measure zero set of reals is countable. Independent of ZFC like the continuum hypothesis: consistent (Laver 1976), refuted under CH (Sierpiński 1928).

· set theory · difficulty 4/5

descriptive-set-theory