P.S. One "human" remark. Your statement about the
     ancient Greek straightjacket does not apply
     to ancient Greeks. As Archimedes' papers show,
     he used heuristic methods and algorithms to 
     discover his results and only then did he 
     prove them formally. This was also probably
      true of all the other great ancient             
       mathematicians. In fact, Euclid probably
      did not discover what he wrote in his Elements,
      so is not a good example. Basically, judging
      Ancient Greek mathematics from Euclid is like
     judging 20th century math from Bourbaki, or
     from a college Calculus and Analytic Geometry
     textbook.