Talk:Number theory

Article Checklist for "Number theory"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developing article: beyond a stub, but incomplete
Underlinked article?	Yes
Basic cleanup done?	Yes
Checklist last edited by	--AlekStos 09:45, 26 March 2007 (CDT)

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The introduction is a little too focused on number systems, and then mixes them up with all other things. Perhaps we should start with a historical introduction - then an enumeration of the main areas and problems of study? Harald Helfgott 13:55, 18 June 2007 (CDT)

I'm inclined to agree. The initial comment about C.F. Gauss seems out of place in an encyclopedia but, just as importantly, unrelated to the rest of the article. What follows is basically a hodge-podge of ideas presented without any context. In fact, I think it's probably a good idea to just blank the article and start over. A historical introduction may be the way to go, but there are other possibilities, such as outlining some of the main areas of number theory: algebraic number fields, zeta-functions and analytic methods, quadratic forms and lattices (along the lines of Minkowski), p-adic fields and local methods, algebraic geometry (elliptic curves and abelian varieties), and maybe a bit about the Langlands program. Of course, the approaches aren't mutually exclusive: I think Scharlau and Opolka ("From Fermat to Minkowski") does a masterful job of weaving together a historical account and a cohesive theoretical framework. I completely wore out one copy of the book as a grad student. Greg Woodhouse 14:20, 18 June 2007 (CDT)