> To sharpen the point: Archimedes may well have borrowed or inherited some
> algorithms from ancient Egyptian mathematics, as Milo Gardner has claimed.
> But the point is that Archimedes must have recognized the need, and had the
> ability, to validate these algorithms by a general proof.
It seems to me that saying Archimedes recognized 'the need' for proof
supposes that there actually is such a need. Is it not possible that the
inventors of an algorithm took the perfectly reasonable view that a proof
of its correctness didn't make it work any better, and that the lack of a
proof made it work no worse?
Just a thought,
Jeremy Smith