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 arithmetic-geometry — 3 entries. Clear
Szpiro's discriminant–conductor inequality for elliptic curves: equivalent to abc, claimed via inter-universal Teichmüller theory, but the proof is disputed and the problem stays open.
Which integers are areas of rational right triangles? Tunnell's criterion decides it assuming BSD; unconditionally, no general method is known.
An elliptic curve has infinitely many rational points precisely when its L-function vanishes at s = 1. Deep arithmetic meets deep analysis.
