Given a group presentation and a word, decide if the word equals the identity. Dehn asked for algorithms; logic answered that none can exist — for some groups.
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 decidability — 2 entries. Clear
Hilbert's Tenth Problem
historic
Give an algorithm deciding whether a polynomial has integer roots. Impossible — and proving impossibility wove Diophantine equations, Fibonacci numbers and computability into one of the 20th century\'s great joint theorems.