Hilbert's eleventh problem
Hilbert's eleventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. A furthering of the theory of quadratic forms, he stated the problem as follows:
- 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.[1]
It is considered to have been addressed by Helmut Hasse's local-global principle in 1923 and 1924; see Hasse principle, Hasse-Minkowski theorem.
See also
References
- ^ David Hilbert, "Mathematical Problems". http://www.ams.org/journals/bull/1902-08-10/home.html. , Bulletin of the American Mathematical Society, vol. 8, no. 10 (1902), pp. 437-479. Earlier publications (in the original German) appeared in Göttinger Nachrichten, 1900, pp. 253-297, and Archiv der Mathematik und Physik, 3dser., vol. 1 (1901), pp. 44-63, 213-237.