Hilbert's eleventh problem

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Hilbert's eleventh problem, a furthering of the theory of quadratic forms, was stated thus in his landmark speech:

Our present knowledge of the theory of quadratic number fields puts us in a position to attack successfully the theory of quadratic forms with any number of variables and with any algebraic numerical coefficients. This leads in particular to the interesting problem: to solve a given quadratic equation with algebraic numerical coefficients in any number of variables by integral or fractional numbers belonging to the algebraic realm of rationality determined by the coefficients.

It is considered to have been addressed by Helmut Hasse's local-global principle in 1923 and 1924; see Hasse principle, Hasse-Minkowski theorem.