Russell’s paradox

Russell’s paradox, discovered by Bertrand Russell in 1901, was a paradox with set theory as it existed at the time. It struck at the heart of set theory and to some extent mathematics itself. This led to significant changes in set theory and the general formalisation of mathematics.

As an introduction, we will look at a simple paradox developed by Russell himself to help explain Russell’s paradox. We will then look at main problem and the most widely accepted resolution.

The barber’s paradox