Hilbert's eleventh problem
Encyclopedia
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:
It is considered to have been addressed by Helmut Hasse
's local-global principle in 1923 and 1924; see Hasse principle
, Hasse-Minkowski theorem.
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
'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.
It is considered to have been addressed by Helmut Hasse
Helmut Hasse
Helmut Hasse was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry , and to local zeta functions.-Life:He was born in Kassel, and died in...
's local-global principle in 1923 and 1924; see Hasse principle
Hasse principle
In mathematics, Helmut Hasse's local-global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number...
, Hasse-Minkowski theorem.