Subject: Re: [HM] historiography of mathematics
From: Beatrice Lumpkin (Bealumpkin@aol.com)
Date: Wed Sep 20 2000 - 16:59:32 EDT
Hello all,
I am commenting on a comment:
<< Date: Tue, 19 Sep 2000 11:58:27 +0200 (GMT)
From: Lambrou Michael <lambrou@itia.math.uch.gr>
Subject: Re: [HM] historiography of mathematics
On 16 Sep 2000, Bill Everdell wrote:
> My 6th-graders learning Ancient History, are as fascinated
> with the discovery that sgrt 2 is irrational as they are
> with Pythagoras's attempt to drown the man that showed it
> to him.
> ...
Lambrou Michael goes on to comment:
The only problem is that this is NOT what the sources say!
(They have two different stories, both a variant of the one
mentioned).
The above misconception (a harmless one really) >>
Some aspects of the misconceptions around the right-triangle theorem are
not entirely harmless, especially in mathematics education. Heath says
about the "Theorem of Pythagoras" (Heath's quotation marks):
"...no really trustworthy evidence exists that it was actually discovered
by him. The comparatively late writers who attribute it to him add the
story that he sacrificed an ox to celebrate his discovery."
Among the later writers, Heath mentions Cicero who disbelieved the ox
sacrifice story "because the Pythagorean ritual forbade sacrifices in
which blood was shed." (Thomas Health, A HISTORY OF GREEK MATHEMATICS,
v 1, 144.)
So what is the harm of repeating these stories and naming the right-
triangle theorem after Pythagoras? In my opinion, the harm is extensive.
The Babylonian example of the right-triangle formula over a thousand
years before Pythagoras, the Chinese proof that antedates Pythagoras and
very early Indian writings that use the right triangle theorem, all of
this is hidden by attributing the theorem (without trustworthy evidence)
to Pythagoras. This is but one example, if the most important, of
attributing the mathematical discoveries of earlier people of color to
later Europeans.
The effect is indeed very harmful by inculcating in students of European,
as well as those of African, Asian, Native American, Pacific Islander
descent, the false idea that mathematics is exclusively a European product.
For those who prefer to teach what I believe is a more truthful, balanced
view of the history of mathematics there are many excellent sources. A few
that I have found invaluable are:
Joseph, George G. The Crest of the Peacock - non-European roots of
mathematics.London: Tauris, 1991, Chinese examples, 180 - 187; Indian
examples, 228-31
Gillings, Richard J. Mathematics in the Time of the Pharaohs, Dover
reprint.
J. L. Berggren. Episodes in the Mathematics of Medieval Islam Springer
Verlag 1986.
Li Yan and Du Shuran Chinese Mathematics, A Concise History, Oxford Science
Publications 1987.
This is a very incomplete list and there is excellent material in general
Histories of Mathematics such as Dirk Struik's Concise History, Carl Boyers'
and Victor J. Katz's History of Mathematics. For a taste of many authors
working in the field of ethno mathematics there is the extensive collection
by Arthur B. Powell and Marilyn Frankenstein , Ethnomathematics--Challenging
Eurocentrism in Mathematiacs Education, State University of New York, 1997.
It does make a difference if the Chinese triangle also worked on by Ibn
Haytham, Omar Khayyam and al-Karaji is known to students only as Pascal's
triangle.
I realize that there are many theorems developed by one European but known
by the name of another European. That is not in the same class of wrong
information as the situation in school mathematics where almost NOTHING is
credited to non-Europeans. I must except the practices in Chinese and Indian
school mathematics. Perhaps they do not use the name, Pythagoras, for the
right-triangle theorem.
Anyhow, isn't the "right-triangle theorem" more descriptive and easier for
students to learn?
From a suddenly cool Chicago.
Beatrice Lumpkin
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