1. Mathematics in Mesopotamia
MONT 107Q – Thinking about Mathematics
February 8, 2017

2. 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

3. 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 …

4. Ancient Mesopotamia
the ``land between the rivers'' – Tigris and Euphrates – mostly contained in current countries of Iraq, Iran, Syria.

5. A very long history
~5500 BCE -- First village settlements in the South
~ BCE -- Sumerian city-state period, first pictographic texts
~ 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!

6. A tablet with cuneiform writing
Note the limited collection of forms you can make with a wedge-shaped stylus:

7. 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

8. Cuneiform number symbols

9. Concentrate on southern area
~ BCE -- Early Dynastic Period, Old Sumerian literature
~ BCE -- Akkadian (Sumerian) empire, first real centralized government
~2000 BCE -- collapse of remnant of Sumerian empire
~ BCE -- Ammorite kingdom "Old Babylonian Period"-- Hammurabi Code, mathematics texts, editing of Sumerian Epic of Gilgamesh

10. 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)
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