Hello Jeremy.
> 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
>
Of course, having a proof of a valid algorithm does not create its
validity. However, ....
How do we know the algorithm WILL always work? A proof is the
assurance that the algorithm will work. I will call any VALID
assurance that an algorithm will always work a "proof".