West Asian Mathematics - History of Math

# West Asian Mathematics

Sumerian multiplication table (2700 BC)

April 2016 - Once people in West Asia figured out how to write down numbers, about 3500 BC, they quickly began to want to use cuneiform to write down other mathematical ideas. The earliest example of this that we have is from about 2700 BC. It shows a multiplication table to help people figure out the area of a space by multiplying width by length. The first column is the width, the second is the length, and the third column is the area. It uses a system for writing down large numbers in base 60 (the way our clocks work today).

Math book (Babylon, about 2000 BC)

This tablet, from about 2000 BC, was a school math book for teaching kids how to calculate inheritance. The problem asks how much each of seven boys would get when their father died, according to Babylonian law. Apparently the law said they should each get a different proportion, with the oldest getting the most and the younger kids less and less. Whoever did the math worked up from the bottom (which was not normal), and also made a mistake in his or her calculations!

Here's a Babylonian math problem you could try to solve yourself. Are you as smart as Babylonian kids?

By the time of the Babylonians, mathematicians were working out quadratic equations like the Pythagorean Theorem, computing square roots and cube roots, and the factors of sixty (because they often worked in base 60).

After the Assyrians formed their empire, mathematical developments seem to have slowed down after this initial rush. But mathematicians continued to work on new ideas. Assyrian mathematicians, working around 1000 BC, first had the idea of dividing the circle into 360 degrees (still working in base 60, so 360=6x60). Thales, working under Lydian political control in Miletus (modern Turkey) in the 630s BC, found ways to calculate when there would be an eclipse of the sun or the moon. Thales also found a way to calculate the height of an Egyptian pyramid by measuring its shadow, and proved various geometrical theorems. Thales' student Anaximander, who was also from Miletus, worked on building a better sundial to measure time. During the Persian Empire, around 500 BC, people first began to use the abacus (nobody knows whether the abacus was invented in Iran or China, or both about the same time, thanks to the beginning of the Silk Road). An abacus is a way of calculating large numbers quickly by moving pebbles along grooves dug into dirt, or beads along wires.

With the development of trade and more travel along the Silk Road between China, India, and West Asia, in the 300s BC, Greek mathematicians were able to talk to Persian and Indian mathematicians more easily than before. A lot of new ideas about infinity, patterns of numbers, and exponents came out of these conversations, but most importantly, from Egypt to India, all across West Asia, mathematicians began to work more on proving that theorems were always true in every case. About 150 BC, Hipparchus (born in Nicaea, now in Turkey) worked on developing trigonometry, making lists of sines and cosines.

Under Parthian and Sassanian rule, scholars continued to bring together knowledge from the countries around them, especially from India. They built a system of math and astronomy based on their Zoroastrian faith, and, like Ptolemy in Egypt and Arya Bhata in India, used trigonometry to make better predictions of the movements of the planets.

Then in the 600s AD, the Arabs conquered West Asia and established the Islamic Empire. Around the same time, Indian numbers revolutionized mathematics. You can read about that here.

## Learn by doing: an abacusA real Babylonian math problemMore about Islamic math

Science in Ancient Mesopotamia, by Carol Moss (1999). Easy reading. On the short side.

## African MathematicsIndian MathematicsGreek mathematicsIslamic MathematicsMore West Asian ScienceAncient West AsiaQuatr.us home

Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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