[ExI] Eurocentric Bias in Human Achievement

[Lee Corbin]

Damien Sullivan writes

> Henrique wrote:
> 
>> The 'arabic' numerals are in fact Indian numerals. Their math knowledge 
>> they took from the Greek. 
> 
> Right, like al-gebra, al-gorithm...

Henrique's two-sentence post contains more truth than
falsehood, I'd say. For example, "al-gebra" and "al-gorithm"
are just Arabic terms for what Diophantus of Alexandria
(for one) knew hundreds of years before.

> http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html

Well, in their enthusiasm, I contend that the authors of those web pages
overstate their case. (I myself did quote from their site last night:
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Arabs.html ).
But the names of those 45 Arabic mathematicians are obtained, as Murray
would say, by relaxing the standards a bit. If you peruse at random in
that list, you'll find a number of entries like

    "Al-Mahani was an Islamic mathematician who tried to
    solve some of Archimedes' problems on cutting up spheres."

If you relax the standards to the same degree, you'll come up 
with hundreds and hundreds of Indian or Chinese mathematicians,
and many thousands of European ones. But!  This is *not* to 
decry the truly remarkable advances that were made; it's just,
like I said, it happened to be *relatively* little in the Arab case,
for reasons we are all too unhappily aware of.

Since you brought up "Algebra" and al-Khwarismi, their greatest
or at least most prominent mathematician, I excerpt from
http://www.uni-essen.de/didmath/texte/jahnke/hnj_pdf/musa.pdf
the following, wherein our hero speaks of himself in the third person:

    IN THE NAME OF GOD, GRACIOUS AND MERCIFUL! This work was
    written by MOHAMMED BEN MUSA, of KHOWAREZM. He commences it
    thus: Praised be God for his bounty towards those who deserve
    it by their virtuous acts: in performing which, as by him
    prescribed to his adoring creatures, we express our thanks,
    and render ourselves worthy of the continuance (of his
    mercy), and preserve ourselves from change: acknowledging his
    might, bending before his power, and revering his greatness!
    He sent MOHAMMED (on whom may the blessing of God repose!)
    with the mission of a prophet...

Oops.  Wrong excerpt.  Looking down further (much further, sigh) one finds

    Squares and Numbers are equal to Roots:

    For instance, "a square and twenty-one in number are equal to
    ten roots of the same square." That is to say, what must be the
    amount of a square, which, when twenty-one dirhems are added to
    it, becomes equal to the equivalent of ten roots of that square?
    Solution: Halve the number of the roots; the moiety is five.
    Multiply this by itself; the product is twenty-five. Subtract
    from this the twenty- one which are connected with the square;
    the remainder is four. Extract its root; it is two. Subtract
    this from the moiety of the roots, which is five; the remainder
    is three. This is the root of the square which you required, and
    the square is nine. Or you may add the root to the moiety of the
    roots; the sum is seven; this is the root of the square which
    you sought for, and the square itself is forty-nine. When you
    meet with an instance which refers you to this case, try its
    solution by addition, and if that do not serve, then subtraction
    certainly will. For in this case both addition and subtraction
    may be employed, which will not answer in any other of the three
    cases in which the number of the roots must be halved.

Diophantus knew how to do this too. But he didn't write up an entire
systematic treatise covering both linear equations and quadratic equations.
See the wikipedia biographical entry on Al-Khwarizmi (which must
have some Arabic in its URL, else I would present it). For this 
reason, Al-Khwarismi along with Diophantus (it says) is 
considered the father of algebra. 

But don't, of course, confuse their achievements with that of
the very minor European mathematician Francois Viete, who
introduced symbols, enabling, for example, Descartes to solve
a long standing problem of Appolonius that nobody, Greek,
Indian, Arab, or Christian had been able to touch. Vieta's
breakthrough makes the above stuff by Al-Khwarizmi look
elementary and easy to the modern reader, but it was *not*
easy before the use of Viete's symbols began.

As you write, the Arabs are credited with

> development of spherical trigonometry, and trigonometry as field
> separate from astronomy.
> modern notation for fractions
> frequency analysis in cryptography
> triangulation
> Omar Khayyam: binomial expansion, roots of non-Euclidean geometry

which evidently is completely correct. But a parallel list of Greek, Indian,
Chinese (I suspect), and European breakthroughs would totally dwarf that.

Lee