TITLE: Who is the "father of number theory"?
QUESTION [15 upvotes]: I noticed that some sources state Fermat as the father of modern number theory while others say Gauss. I am trying to start a paper on the history of number theory for a presentation, but I cannot figure out the fundamental difference between the roles of Fermat and Gauss in founding modern number theory so to speak. What exactly is the difference between them; can they be likened to Newton and Cauchy for example? (Newton founding calculus, Cauchy putting it on a rigorous foundation once and for all.)
Thanks!

REPLY [17 votes]: You can see :

André Weil, Number Theory : An approach through history (1984), Preface, page ix :


Fermat, Euler, Lagrange, Legendre. These are the founders of modern number theory. The greatness of Gauss lies in his having brought to completion what his predecessors had initiated, no less than in his inaugurating a new era in 
  the history of the subject.