"...if we confront Liu Hui's Commentary [on the Nine Mathematical Chapters]
with our comparative issues in mind, we can say this. What he does in the
discussion of the additions of fractions and elsewhere is to show that the
algorithsms used are correct. Now this is as good as a proof of the
procedures as anyone could wish--provided, of course, that we don't limit our
notion of what will count as a proof to the axiomatic-deductive demonstration
in the Euclidean style -- provided, that is, that we do not stipulate that for
a proof to be a proof, it has to be cast in that style. For what more should
we ask of a proof of a procedure than an explanation of how and why it works,
however that explanation proceeds?"
Any comments?
Val Dusek