Pythagoras, from what I understand, is considered the origin of
  Geometry and Logic.

  [I should have been specific and said Geometry first and not
  Mathematics.]

  He started the axioms and proofs system, used by both.

  So while Mathematics may have diverged and become impure...
  considering Logic and Geometry are born of the same Father,
  would not a flaw in Geometry also carry directly into being a
  flaw of Logic?

  This would not be a fallacy of composition as they were born
  simultaneously superimposed as one and initially inseparable.