Russell's Paradox
Consider the set of all sets that do not contain themselves. Does that set contain itself? Either answer is wrong.
1901 (discovered), 1902 (letter to Frege), 1903 (published)19 min read
German logic and philosophy of mathematics
Gottlob Frege
1848 – 1925
Inventor of modern quantificational logic and the founder of logicism, the programme of deriving arithmetic from logic alone. His Grundgesetze der Arithmetik rested on Basic Law V, which Russell's 1902 letter showed to be inconsistent. Frege appended a candid acknowledgement to the second volume and eventually abandoned the logicist project.