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 independence — 2 entries. Clear
Does the countable chain condition characterise ℝ? Independent of ZFC: Suslin lines exist under V = L, consistently none exist (Solovay–Tennenbaum 1971).
Is there a cardinality strictly between the integers and the reals? The first Hilbert problem dissolved into independence: yes in Gödel\'s universe, no in Cohen\'s — and both are legitimate.
