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Fermat's Last Theorem was open for more than 350 years until Andrew Wiles proved it in 1995. Are there possible (historical or other) reasons why David Hilbert did not include this famous open problem in his problem list in 1900?

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    $\begingroup$ Perhaps Hilbert did not consider the problem conceptually important. Gauss had no interest in it. Until the 1980s it was not at all clear the possibility of a counterexample would have any relation to important themes in mathematics even though Hilbert considered FLT important as motivation for the creation of some very useful ideas by Kummer (whether or not that is historically accurate): are you aware that Hilbert does mention FLT in the introduction of his speech, preceding the list of problems? $\endgroup$
    – KCd
    May 12 at 7:14

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Hilbert included in his list a much more general Problem 21:

Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

Probably he did not think that Fermat's equation by itself is sufficiently important to deserve a separate entry in his list.

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