We haven't determined whether it's possible to build a truly complete and consistent mathematical system that can prove every true statement without any contradictions.
open
Global / Unspecified, Global
WS01285
Gödel's theorems already limit what's possible here for sufficiently powerful systems, but the full landscape of alternative systems and their limitations remains an active and unresolved area of mathematical logic. This continues to shape our understanding of the foundations of mathematics itself.