Download Historical background

Mathematics in Mesopotamia

MONT 107Q – Thinking about Mathematics

February 8, 2017
Historical Orientation



We are now ready to begin our historical study
of where the mathematics you have learned
originally “came from”
“The past is a foreign country; they do things
differently there” (from a novel by modern
British author L.P. Hartley, The Go-Between)
Today, we'll start that with of orientation (in
location and time) for the Mesopotamian
civilizations
Algebra – the finished product
•
We'll be concentrating on how what we now
call algebra developed over time.
•
Of course it wasn't called that from the start
•
Name comes from the very influential book
by Muhammad Ibn Musa Al Khowarizmi
(about 780 – 850 C.E.) called “Kisab al-jabr
wa-l-muqabala” (“Complete book on
calculation by completion and balancing”)
•
But the story starts much before that …
Ancient Mesopotamia

the ``land between the rivers'' – Tigris and
Euphrates – mostly contained in current
countries of Iraq, Iran, Syria.
A very long history





~5500 BCE -- First village settlements in the
South
~3500 - 2800 BCE -- Sumerian city-state
period, first pictographic texts
~3300 - 3100 BCE -- first cuneiform writing
created with a reed stylus on a wet clay tablet,
then sometimes baked in an oven to set
combined with a pretty dry climate, these
records are very durable!
A tablet with cuneiform writing
Note the limited collection of forms you can make
with a wedge-shaped stylus:
Cuneiform writing



Different combinations of up-down and
sideways wedges were used to represent
syllables
Was used to represent many different spoken
languages over a long period – 1000 years +
Also used to represent numbers, eventually
(and definitely in the period we'll concentrate
on), in a positional, base-60 notation, but
without a zero symbol
Cuneiform number symbols
Concentrate on southern area




~2800 - 2320 BCE -- Early Dynastic Period,
Old Sumerian literature
~2320 - 2180 BCE -- Akkadian (Sumerian)
empire, first real centralized government
~2000 BCE -- collapse of remnant of Sumerian
empire
~2000 - 1600 BCE -- Ammorite kingdom "Old
Babylonian Period"-- Hammurabi Code,
mathematics texts, editing of Sumerian Epic of
Gilgamesh
Later history




This part of the world has been fought over
and conquered repeatedly – most recently, of
course, in the two Iraq wars of the 1990's and
2000's CE – a very complicated story!
Also figures in Biblical history (“Babylonian
captivity” of Jewish people)
612 - 539 BCE -- “New Babylonian” period
(Nebuchadnezzar) height of Babylonian
astronomy
Later we'll see Baghdad was a world center of
learning during “dark ages” in Europe