Editing Algebraic number theory (section)

===Gauss===
One of the founding works of algebraic number theory, the '''''Disquisitiones Arithmeticae''''' ([[Latin]]: ''Arithmetical Investigations'') is a textbook of number theory written in Latin<ref>{{citation |first1=Carl Friedrich |last1=Gauss |first2=William C. |last2=Waterhouse |title=Disquisitiones Arithmeticae |url=https://books.google.com/books?id=DyFLDwAAQBAJ |date=2018 |orig-year=1966 |publisher=Springer |isbn=978-1-4939-7560-0}}</ref> by [[Carl Friedrich Gauss]] in 1798 when Gauss was 21 and first published in 1801 when he was 24. In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, [[Euler]], [[Joseph Louis Lagrange|Lagrange]] and [[Adrien-Marie Legendre|Legendre]] and adds important new results of his own. Before the ''Disquisitiones'' was published, number theory consisted of a collection of isolated theorems and conjectures. Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways.

The ''Disquisitiones'' was the starting point for the work of other nineteenth century [[Europe]]an mathematicians including [[Ernst Kummer]], [[Peter Gustav Lejeune Dirichlet]] and [[Richard Dedekind]]. Many of the annotations given by Gauss are in effect announcements of further research of his own, some of which remained unpublished. They must have appeared particularly cryptic to his contemporaries; we can now read them as containing the germs of the theories of [[L-function]]s and [[complex multiplication]], in particular.