In Never at Rest, largely regarded as the standard biography of Isaac Newton, Richard Westfall describes the moment in history when Newton and others reached a tipping point for how modern man would evaluate the truth of ideas:
“The antipodes of alchemy with its eternal and exasperating secretiveness was mathematics, the very claim of which to be called knowledge rested on demonstrations open to all. Where the one made its way deviously with allusion and symbolism, the other proceeded in the cold light of rigorous logic. The diversity of the intellectual world of the seventeenth century has perhaps no better illustration than the coexistence of two such antithetical enquiries, both apparently in flourishing condition. Only to later ages would it be clear that seventeenth-century alchemy was the last blossom from a dying plant and seventeenth-century mathematics the first blooming of a hardy perennial. Whatever the state of alchemy, certainly it was manifest in 1661 that mathematics was a flourishing enterprise.”
But clearly, each generation confronts its own ideas which live by “exasperating secretiveness” and “[make their] way deviously with allusion and symbolism.” What was manifest more than 350 years ago must be made clear again and again.