Mathematics in Mesopotamia MONT 107 Q Thinking about

Mathematics in Mesopotamia MONT 107 Q – 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