1931Reputable sourceWell documented
Gödel's Incompleteness Theorems
On the timeline · around 1931 · The Modern Age
What happened
As mathematicians sought to place all of mathematics on a complete and certain logical foundation, the young Austrian logician Kurt Gödel proved, in 1931, that this was impossible: in any consistent formal system rich enough for arithmetic, there are true statements that can never be proved within it.
Why it matters
Gödel's incompleteness theorems are among the most profound results in the history of logic. They revealed permanent limits to what mathematics can prove about itself, reshaping philosophy, logic, and our understanding of certainty.