Gödel's
incompleteness
theorems — true
statements a system
can't prove from
within itself. Why it shook math.

Walk Me Through Gödel's Incompleteness Theorems

A true statement, unprovable from within its own system. Math's floor has a hole in it.

Prompt

Explain what Gödel's incompleteness theorems actually prove — that any sufficiently powerful mathematical system contains true statements it can't prove — and why this shook the foundations of mathematics.