2 - A Less Problematic Miracle: Greek Science

Summary

Early states converge on a similar, number-based, “algorithmic” theoretical science. In Greek mathematics we see a new science, based not on the anonymous teacher but on the named author, seeking fame. Such authors look for new, surprising results, and therefore couch them in the language of proof. The resulting body of knowledge of many surprising proofs has no precedent in previous societies. The generation of Archimedes adds considerable subtlety and brings this to the cusp of modern science. The new Greek departure intertwines with other traditions, especially in the Near East, giving rise to a number-based but also proof-based astronomy (that of Ptolemy) and to the Arabic algebra. In the Renaissance, efforts to creatively engage with this Greek legacy gave rise to the scientific revolution. The science we know is objectively valid, but also historically contingent; one of the contingencies making it possible was the new departure of Greek mathematics.