Small doubling forces approximate linear structure with polynomial — not exponential — losses. Conjectured for decades; proved by Gowers–Green–Manners–Tao in November 2023.
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 additive-combinatorics — 2 entries. Clear
The Cap Set Problem
open
How large can a subset of \(F_3^n\) be containing no three-term arithmetic progression? Bounds have collapsed twice — once by the polynomial method, once to DeepMind's FunSearch.