Number Theory . I don ' t know what your background is , but the book Rational Point on Elliptic Curves is a nice introduction to things Diophantine . <| sep |> This is the best mental image I ' ve had in a while . Thanks ! P <| sep |> But the guy looks creepy in this one picture with out of context cannibal jokes pasted next to it ! What else evidence do I need ? <| sep |> Whats your username ? Add me foxmulder 0486 <| sep |> Just something I ' ve been thinking about lately . Imo , many Christians who say they are claiming faith based facts are not actually based on faith . I would think faith is a belief without any justification whatsoever . So for example the properly basic beliefs are based on faith . The belief that our memory is somewhat reliable is based on faith because you can ' t use your memory as a justification as that is circular reasoning , so we have nothing else to justify that belief . An example I hear from Christians who claim something is based on faith is the belief that God heals the sick . Whenever I ask Christians obviously not all Christians why they believe God can heal the sick , they usually tell me it ' s because they have seen it before , they have heard it before etc . Those are all justifications right ? Imo bad reasons , but still reasons nonetheless ? But as I type that last sentence . I think I ' m getting confused with what a justification for a belief means and how that relates to having reasons for your beliefs . I . e , you can have reasons for a belief whether good or bad reasons , but just because you have a reason for a belief , that doesn ' t imply your reasons are sufficiently justified to have that belief .