Definition
Plain language
A single case that shows a general claim is false.
As stated in the literature
An instance that violates a universally-quantified statement, disproving it; used in formal review to demonstrate a missing hypothesis in a theorem as stated.
Also called: counterexamples
Why it matters: One well-chosen counterexample can collapse a sweeping claim, which is why it's a sharp tool for catching flawed reasoning or missing assumptions.
For example, the claim 'all swans are white' is undone the moment someone points to a single black swan.
Heard on the show
“The published proof has a hole, and the system handed back a counterexample you can check by hand.”Episode 188 — A Coding Agent Found a Hole in a Peer-Reviewed STOC Proof for Five Dollars