Russell's Paradox
Russell's Paradox is a famous problem in set theory, discovered by the philosopher Bertrand Russell in 1901. It highlights a contradiction that arises when we consider the set of all sets that do not contain themselves. If such a set exists, we can ask whether it contains itself. If it does, then by definition, it should not. But if it does not contain itself, then it must contain itself. This creates a logical inconsistency.
The paradox challenges the foundations of mathematics and led to significant changes in how sets are understood. To resolve this issue, mathematicians developed new theories, such as Zermelo-Fraenkel set theory, which impose stricter rules on how sets can be formed.