Incomplete proof

This page lists notable examples of incomplete published mathematical proofs. Most of these were accepted as correct for several years but later discovered to contain gaps. There are both examples where a complete proof was later found and where the alleged result turned out to be false.

This section lists examples of proofs that were published and accepted as complete before a gap or error was found in them. It does not include any of the many incomplete attempted solutions by amateurs of famous problems such as Fermat's last theorem or the squaring of the circle. It also does not include unpublished preprints that were withdrawn because an error was found before publication.

The examples are arranged roughly in order of the publication date of the incomplete proof. Several of the examples on the list were taken from answers to questions on the MathOverflow site, listed in the external links below. The examples use the following symbols:

Lecat (1935) is a list over a hundred pages long of (mostly rather trivial) published errors made by mathematicians.

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