An open door to number theory

摘要

In 1993, my daughter showed me the New York Times article that announced Andrew Wiles's 100-plus-page proof (to be successfully corrected two years later) of Fermat's last theorem (FLT) [1]. Wiles's "20th-century" proof comprised excursions into algebraic geometry and other territory that did not at all resemble the seemingly clean and pure realm of number theory "proper." The book captures the best spirit of contemporary mathematics at large, and achieves cohesion among the natural numbers N = {1, 2, 3,...}; the whole numbers W = {0, 1, 2,...}; the integers Z; the rational numbers Q; the algebraic numbers A; the real numbers R; and the complex numbers C.