The theory of algebraic number fields

Viac o knihe

Constance Reid, in Chapter VII, recounts the creation of the Zahlbericht, known as Die Theorie der algebraischen Zahlkörper. In 1893, the Deutsche Mathematiker-Vereinigung invited Hilbert and Minkowski to report on the state of number theory, with a two-year deadline. They agreed that Minkowski would cover rational number theory while Hilbert focused on algebraic number theory. By early 1896, Hilbert had nearly completed his section, but Minkowski had made little progress and decided to withdraw. Hilbert then finished his report on algebraic number fields, which his wife carefully transcribed before sending it to the printers. The proofs were meticulously reviewed by Minkowski, with assistance from Hurwitz, ensuring both mathematical clarity and proper typesetting. At Minkowski's suggestion, Hilbert included a note of gratitude to his wife. Reid notes that the report exceeded the expectations of the Mathematical Society; instead of a simple summary, they received a masterpiece that elegantly integrated recent complex developments into a cohesive theory.