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 mathematics, axiomatic set theory
Ernst Zermelo
1871 – 1953
German mathematician who discovered the paradox of the set of all sets not members of themselves independently of Russell, around 1899-1902, and discussed it with Hilbert's circle in Göttingen without publishing it. His 1908 axiomatisation of set theory replaced unrestricted comprehension with the axiom schema of separation, the move that still keeps mathematics consistent today.