Constance Reid, in Chapter VII of her book Hilbert, tells the story of
the writing of the Zahlbericht, as his report entitled Die Theorie der
algebra is- chen Zahlkorper has always been known. At its annual meeting
in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical
Society) invited Hilbert and Minkowski to prepare a report on the
current state of affairs in the theory of numbers, to be completed in
two years. The two mathematicians agreed that Minkowski should write
about rational number theory and Hilbert about algebraic number theory.
Although Hilbert had almost completed his share of the report by the
beginning of 1896 Minkowski had made much less progress and it was
agreed that he should withdraw from his part of the project. Shortly
afterwards Hilbert finished writing his report on algebraic number
fields and the manuscript, carefully copied by his wife, was sent to the
printers. The proofs were read by Minkowski, aided in part by Hurwitz,
slowly and carefully, with close attention to the mathematical
exposition as well as to the type-setting; at Minkowski's insistence
Hilbert included a note of thanks to his wife. As Constance Reid writes,
"The report on algebraic number fields exceeded in every way the
expectation of the members of the Mathemati- cal Society. They had asked
for a summary of the current state of affairs in the theory. They
received a masterpiece, which simply and clearly fitted all the
difficult developments of recent times into an elegantly integrated
theory.
