TITLE: Did Gauss ever make a mistake?
QUESTION [21 upvotes]: I have read a bit about Gauss, who was well known for being careful in only publishing work he had perfected (or in his own words "few, but ripe"). What is interesting to me about Gauss though is that all accounts of his students and contemporaries essentially make him appear flawless. Dedekind's recollections of how whenever Gauss wrote out an argument he used exactly the amount of space he had available, etc. In Disquistiones Arithmeticae, Gauss for example points out the flaws and shortcomings of other famous mathematicians such as Euler, who some might rank close to Gauss.
So I am curious if there is a single recorded instance of Gauss ever having made a mathematical error. 
Thanks,
Matt

REPLY [2 votes]: There is at least one record that I'm aware of in which Gauss effectively concedes to having made a mathematical error, although it appears in casual correspondence rather than in publication.  This correspondence involved some recreational mathematics involving the eight-queens problem that was posed when Gauss was in his 70s.  In that correspondence, Gauss asks that his value of 76 confirmed solutions be reduced to 72 (although he correctly asserts that there may be others, as the full answer is 92).  Details of this episode can be found in the article "Gauss and the eight queens problem: A study in miniature of the propagation of historical error" by
Paul J. Campbell (1977).