
 PlanetMath: number theory 
  Great twentieth century number theorists include Artin, Hardy, Ramanujan, André Weil, Alexandre Grothendieck, JeanPierre Serre, Pierre Deligne, Gerd Faltings, John Tate and Andrew Wiles. 
  Four of the greatest achievements of number theorists in the twentieth century were abelian class field theory (the theory of abelian extensions of number fields, which extends the law of quadratic reciprocity) by Hilbert, Takagi, Artin, Tate and others; the proof of the Weil conjectures (which include the Riemann hypothesis for 
  Arithmetic geometry seeks to bring methods that have been spectacularly successful in “classical” geometric theories (such as complex manifold theory) to have bearing on problems in number theory. 
 planetmath.org /encyclopedia/NumberTheory.html (756 words) 
