Hilbert's Number Theory

Author: Carlos Gómez Bermúdez, a professor at the University of A Coruña, has published commented works by G. Cantor and B. Riemann, and has been part of the French group “réseau Cantor,” responsible for the French translation of Cantor's work.

David Hilbert was one of the most important mathematicians of the 20th century and one of the last to make significant contributions to very diverse branches of mathematics: invariant theory, number theory, foundations of geometry, analysis, logic and foundations of mathematics, physics, etc.

Presented here is his famous report on the state of number theory (Zahlbericht), along with other works of his on number theory. As P. Roquette points out, "the report has been and continues to be useful as a study manual for many generations of mathematicians. But... Hilbert's truly new results only come later; they grow in the terrain that the report prepared, and continue (as Hasse says) "from there to unexpected heights".