Page "David Hilbert" Paragraph 60

Hilbert unified the field of algebraic number theory with his 1897 treatise Zahlbericht ( literally " report on numbers ").

He also resolved a significant number-theory problem formulated by Waring in 1770.

As with the finiteness theorem, he used an existence proof that shows there must be solutions for the problem rather than providing a mechanism to produce the answers.

He then had little more to publish on the subject ; but the emergence of Hilbert modular forms in the dissertation of a student means his name is further attached to a major area.