Re: [HM] Is Greek mathematics the *real* thing?

Roger Cooke (cooke@emba.uvm.edu)
Sat, 7 Nov 1998 16:24:42 -0500 (EST)

I would go one step further. That famous Chinese diagram illustrating the
Pythagorean theorem must count as recognition of the need for proof and
supplying it in one special case. It's impossible to solve any very
complicated problem in mathematics without doing at least parts of proofs.
Another example from Chinese mathematics is the expression for the volume
of a sphere in the 5th or 6th century by Zu Chongzhi and Zu Geng. You
can't just make up a result like that, and it appears they used something
logically equivalent to the "method of indivisibles" commonly known as
Cavalieri's principle.

Roger Cooke

On Sat, 7 Nov 1998, Val Dusek wrote:

> Nathan Sivin and G.E. R. Lloyd in their "Adversaries and Authorities" (a
> comparison of Greek and Chinese science) p. 61-62 say the following:
>
> "...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