Download Overview on mathematics in the medieval Islamic world

Islamic Mathematics, an Overview
MONT 107Q – Thinking About
Mathematics
February 20, 2017
The key role of Baghdad
• The Greek approach to deductive
mathematics (a la Euclid, not so much
Diophantus) has been extremely influential
for later developments in the subject
• But it's not the only important strand
• One reason that things developed this way:
many of the Greek mathematical texts we
have discussed were preserved and studied
in the Bayt-al-Hikma (House of Wisdom) in
Baghdad during the Abbasid period, 750 –
1258 CE
The key role of Baghdad
• Text of works of Euclid obtained about 800
CE by way of Byzantine empire (under caliph
Harun al-Rashid)
• Claudius Ptolemy's Mathematike Syntaxis =
“Almagest” translated into Arabic in 827 CE
• Also translated: Aristotle, Apollonius (conic
sections), Archimedes, Heron, many other
Greek works – some survive only in this form
• In addition, key Indian texts were also
translated into Arabic here
Some key “players” in this story
• Muhammad ibn Musa al-Khwarizmi (ca. 780
– 850 CE)
• Name suggests he or his family came from a
region in current-day Uzbekistan (north-east
of Iran)
• Invited to come to Baghdad about 820 during
reign of caliph al-Mamun
• Spent the rest of his life there under the
patronage of the caliph and his successors
al-Khwarizmi
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Probably his most famous book – Hisab aljabr w'al muqabala – “Compendium on
calculation by restoration and reduction”
Does “al-jabr” sound familiar? (It should, if
you think about it!)
Gave general methods for solving quadratic
equations, other types of solving methods and
manipulations, beyond any previous work we
know of in some cases
Doesn't use symbolic expressions, though –
all expressed verbally and/or geometrically
al-Khwarizmi
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The Hisab al-jabr w'al muqabala was not at all
completely “pure mathematics,” though
Also an extensive section on solving
problems about questions of distribution of
bequests in wills and inheritances (a big
subject in Islamic law)
Involves pretty extensive and intricate
computations with fractions(!)
Thabit ibn-Qurra
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From northern Mesopotamia, lived ca. 836 –
901 CE
Moved to Baghdad as an adult and joined the
translators working on mathematical texts in
the House of Wisdom
Additional works extending some of the
number-theoretic sections of the Elements
Thabit also gave a dissection proof of
the Pythagorean theorem equivalent to
the Chinese “go-gou” construction
Thabit ibn-Qurra
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An interesting question here: Did he have
access to Chinese sources? (Or was
knowledge of the “cut and paste” geometry
from the Babylonian period still preserved?)
Tempting to speculate, but no firm evidence
either way
There were trade and other more or less
indirect contacts between the Islamic
caliphate and China by way of India, so it's
not out of the question.
Omar Khayyam
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Lived ca. 1040 – 1123 CE, in Persia (Iran);
not associated with the House of Wisdom in
Baghdad
Known both as a poet and as a
mathematician, astronomer, and philosopher
Biggest mathematical contribution were
algebraic and geometrical methods for solving
various sorts of cubic and higher-degree
equations
Definitely went beyond the Greeks here
Question: Was the Islamic role just
“transmission?”
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More quotes from our favorite “whipping boy”
Morris Kline from last semester:
“The significant contribution to mathematics
that we owe to the Arabs was to absorb Greek
and Hindu mathematics, preserve it, and
ultimately, … , transmit it to Europe.”
“The Arabs did make critical commentaries of
Euclid's Elements, which is surprising
because it shows appreciation of rigor despite
their usual indifference to it in algebra.”
G. Joseph's model for the history of
math during the “Dark Ages”