Where and how did Archimedes get in? Oblique and labyrinthine reflections

This answer to Reviel Netz’s article at first questions his optimism concerning our technological future. After that, it suggests a different role for Archimedes and the other prominent Greek mathematicians than the one claimed by Netz: as providers not of answers but of problems which called for the transformation of the abbacus and cossist algebra tradition, thereby allowing first Viète and then Descartes to create the first level of the new analysis of the seventeenth century (the second level being infinitesimal analysis).