Paradox

The word comes from the ancient Greek paradoxon — para ("contrary to") combined with doxa ("opinion" or "expectation"). Philosophical paradoxes date to antiquity: Zeno of Elea formulated his paradoxes of motion around 450 BCE, and Eubulides of Miletus introduced the Liar Paradox ("This sentence is false") around the 4th century BCE. The concept took on urgent mathematical importance in 1901, when Bertrand Russell's paradox of set theory — the set of all sets that do not contain themselves — exposed a fatal contradiction at the foundations of mathematics.