The History of Mathematics

Into Modern Mathematics

What was Bertrand Russell’s “great paradox”?

In the early 1900s, Bertrand Russell discovered what is known as the “great paradox” as it applies to the set of all sets: The set either contains itself or it does not, but if it does, then it does not, and vice versa. The reason that this paradox became so important was its affect on mathematics. It created problems for those people who tried to base mathematics on logic, and it also indicated that something was wrong with Georg Cantor’s intuitive set theory, which at that time was one of the backbones of set theory. (For more about Russell and set theory, see “Foundations of Mathematics.”)


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