The counterpoint to the conflict bit is that Archimedes was killed during the Roman invasion. We talk a lot about if this or that book hadn't been lost, but if you're gonna take that tack, why not ponder on what would have happened if the man himself had not literally been murdered? If it hadn't been for the Roman invasion, he'd have lived.

Sure, like Da Vinci, military applications was a driver of his patrons and thus his innovations. But war was also the very thing that cut his life -- and thus his innovations -- short.