∞ Gödel's Incompleteness Visualizer

What Is This?

Gödel's Incompleteness Theorems (1931) proved that any consistent mathematical system complex enough to include arithmetic contains true statements that cannot be proven within that system. It shattered the dream of a complete, self-verifying mathematics.

Think of a legal system that tries to write a law about all laws — it inevitably encounters rules that cannot be judged by its own courts.

Imagine a dictionary that must define every word using only words already in the dictionary — some meanings will always escape capture.