Pythagoras, a math genius ? Not by Babylonian standards
Pythagoras, a math genius? Not by Babylonian standards
Over 1,000 years before Pythagoras was calculating the length of a hypotenuse, sophisticated scribes in Mesopotamia were working with the same theory to calculate the area of their farmland.
This tablet dating from the Old Babylonian period (2000-1600 BC) illustrates Pythagoras’ theorem and the square root of two. Yale Babylonian Collection.
Working on clay tablets, students would "write" out their math problems in cuneiform script, a method that involved making wedge-shaped impressions in the clay with a blunt reed.
This cuneiform tablet discovered at Nippur, illustrates a multiplication table. University of Pennsylvania Museum.
These tablets bear evidence of practical as well as more advanced theoretical math and show just how sophisticated the ancient Babylonians were with numbers -- more than a millennium before Pythagoras and Euclid were doing the same in ancient Greece.
Pictured is a school tablet, discovered in Nippur, which shows an incomplete calculation. The early training of scribes consisted of copying lists of units of measure and arithmetical tables. University of Pennsylvania Museum.
"They are the most sophisticated mathematics from anywhere in the world at that time," said Alexander Jones, a Professor of the History of the Exact Sciences in Antiquity at New York University.
He is co-curator of "Before Pythagoras: The Culture of Old Babylonian Mathematics," an exhibition at the Institute for the Study of the Ancient World in New York.
They are the most sophisticated mathematics from anywhere in the world at that time
--Curator Alexander Jones
"This is nearly 4,000 years ago and there's no other ancient culture at that time that we know of that is doing anything like that level of work. It seems to be going beyond anything that daily life needs," he said.
Many scribes were trained in the ancient city of Nippur in what is now southern Iraq, where a large number of tablets were discovered between the mid-19th century and the 1920s.
Excavations at Nippur in 1899. Photo : J.H. Haynes / Penn Museum Archives.
Typical problems they worked on involved calculating the area of a given field, or the width of a trench.
These problems, says Jones, required the kind of math training taught to American Grade 10 students, but not in a format we would now recognize.
"It's not like algebra, it's all written out in words and numerals but no symbols and no times signs or equals or anything like that," he said.
This system, and the lack of recognizable Western mathematical symbols such as x and y, meant that it was several years before historians and archaeologists understood just what was represented on these tablets.
It took a young Austrian mathematician in the 1920s, named Otto Neugebauer, to crack the mathematical system and work out what the ancient Babylonians were calculating. But despite his advances, it is only recently that interest in Babylonian math has started to take hold.
Otto Neugebauer (1899-1990). Pictured is Neugebauer’s hand drawing of the last tablet.
"I think that before Neugebauer and even after Neugebauer, there wasn't a lot of attention placed on mathematical training in Babylon even though we have this rich cuneiform history with the tablets," said Jennifer Chi, Associate Director for Exhibitions and Public Programs at Institute for the Study of the Ancient World.
This tablet shows a serie of abstract problems, which Neugebauer was able to work out. Yale Babylonian Collection.
When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid. That shouldn't be the case.
One of the aims of the institute, she says, is to find interconnections between ancient cultures as well as look at what the institute sees as under-represented ancient cultures -- and the culture of ancient Babylonian math, she says, is ripe for popular revision.
"When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid," she said, but that "this shouldn't be the case."
And though ancient Babylonia is often referred to in popular culture as a "lost" world, in fact much more evidence of mathematical learning from the period exists than from ancient Greece, said Chi.
Jones of New York University believes that there is much more that could be excavated but that, of course, current conditions in Iraq are not favorable. Still, there are enough tablets in collections across the world for mathematical historians to get stuck into.
For non-mathematicians, these tablets are a fascinating document of life in Mesopotamia. Most of the problems displayed are grounded in the everyday needs of ancient Babylonians.
But some tablets show the students engaging in what Jones calls "recreational math" -- math for math's sake.
"The only point of learning to do this kind of thing is really as a mental exercise, as a way of showing how smart you are," he said.
And it seems there is still more to learn from the Babylonians. Duncan Melville is a Professor of Mathematics at St. Lawrence University in Canton, New York, whose special interest is Mesopotamian mathematics.
According to Melville, teachers can continue to learn a thing or two about the way math was taught in Mesopotamia.
"You look at the way they set up their sequences of problems and it's all very carefully graduated, from simple problems to more complicated problems," he said.
"As a teacher of mathematics, it's very interesting to see how they organized their material," he continued. "There's still interesting things to learn from cutting-edge pedagogy 4,000 years ago."
With research continuing into this strand of ancient history, it remains to be seen whether Pythagoras's theorem will come to bear the name of an old Babylonian scribe instead.