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>(2) I am thankful to the listmember who brought up the point on
>history of mathematics for non-mathematicians [ the term
>"mathematician" is used here in a rather wide sense to include anybody
>who studies mathematics, e.g. a school pupil in the mathematics
>classroom ]. It leads me to think about a related question : In the
>ancient world, who were the mathematicians? Unlike in the modern
>world, the mathematicians in the ancient world did not really comprise
>a well-defined group. I do not know enough to speak about what the
>situation was like in the Western world. Let me say a few words about
>what it was like in ancient China to illustrate my point. For the
>past few months I was studying the state curriculum and examination
>in mathematics in the Tang Dynasty (618- 907) in ancient China. In
>connection with this I look into the question : Who were the
>mathematicians? It seems that, besides those "official" mathematicians
>who were employed as imperial astronomers or officials in charge of
>engineering works, or those "unofficial" mathematicians who left us
>with written mathematical classics or commentaries on earlier
>mathematical classics, mathematical activities were also carried out
>among others such as buddhist monks, taoist priests, craftsmen,
>merchants, or even hermits. In this sense, mathematics appeared in the
>full social web. Maybe that is why your friend maintains that history
>of mathematics is closely tied up with the history of the time.
>
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>
>Man-Keung
>
>SIU Man-Keung
>Department of Mathematics
>University of Hong Kong
>Hong Kong SAR, CHINA
>
>
I undertook some time ago to study who the mathematicians were in the
ancient so-called Middle East, i.e. parts of northern Africa and
southwestern Asia such as Egypt and Babylonia, along with "classical"
Greece and Rome -- in short the customary suspects for the rise of
so-called Western civilization. I found that the words we customarily
translate as "mathematician" (in English, and similar words in other modern
languages) were in some regions and times pretty well interchangeable with
the word "astrologer". My study showed further that the kind of
distinction we're accustomed to between "astronomer" and "astrologer"
didn't become common until the 17th or in some cases even 18th century of
the Christian calendars. The two activities, and words used to designate
people who engaged in them, as many people distinguish them today
(especially astronomers), were frequently conflated.
One amusing side-effect of this is that quotations from ancient authors
concerning "mathematicians" (as we customarily translate into English)
which seem to condemn mathematicians or mathematics were actually directed
at what we would call today astrologers.
Historiographically speaking, in my experience it's very hard to avoid
anachronism in discussing who in ancient cultures were the mathematicians,
who were the astronomers, who were the astrologers, who were the priests or
other religious leaders in cultures in which the stars were connected with
religion, and so on. The distinctions many of us are accustomed to didn't
exist yet in many (if not all) times and places. One and the same person
can sometimes be described as being two or three or more of these
simultaneously, or perhaps at different periods in a lifetime.
I suspect that the history of ancient mathematics (where I use "history"
here not in the sense of what happened, but in the sense of what people
have said happened) is imbued with anachronism encouraged by the difficulty
of our overcoming modern changes in meaning of terms which we translate
into modern languages, thereby bringing with the terms all sorts of
associations we've picked up in our lives starting in childhood.
Gordon Fisher gfisher@shentel.net