Russell’s Paradox (1901)

---

In 1901, Bertrand Russell uncovered a paradox in set theory that shook the very foundations of mathematics. This paradox arises when we consider the set of all sets that do not include themselves as members. If such a set does include itself, it contradicts its own definition. Conversely, if it does not include itself, then it should be a member of itself, which again leads to a contradiction.

Russell’s discovery revealed deep inconsistencies in the naive set theory of the time. This revelation prompted the development of more robust frameworks, such as axiomatic set theory and type theory, to address these issues. The implications of Russell’s Paradox extended far beyond mathematics, influencing logic and the philosophy of language as well.

---