Ancient Babylonian Mathematics
An Impressive Early Form of Number Usage
The mathematicians of ancient Babylonia were surprisingly sophisticated for their time, coming up with some very clever forms of mathematics.
While theEgyptians may be credited with having the first functional system of numerals and basic mathematics, surely a great amount of credit for modern mathematics should go to the ancient people of the Mesopatamian region (that is Babylonians, located around present-day Iraq).
Beginning as early as the Sumerian period (3000-2400 B.C.), which seems to parallel the introduction of mathematics into the Old Kingdom of Egypt, there is evidence that these early mesopatamian civilizations had developed a system of sexagesimal numerals (base-60, which is still used for modern timekeeping and circle geometry).
The Sumerians were taken over, however, by the Akkadians in 2300 B.C. While their captors also possessed rudimentary mathematical skills (they are credited with the invention of the abacus), the Sumerians were more sophisticated numerologically. Thus, mathematics did not begin to flourish in the region until the Sumerians regained control in 2100 B.C.
A Flood of Sources
Where evidence for actual mathematical workings in ancient Egypt are rather rare, it is remarkable that examples of Babylonian mathematics are actually rather ample, number in the hundreds of clay tablets, especially from the "Old Period" (2100-1600 B.C.), where archaeologists have found examples of some rather advanced mathematics.
Tablets from this period have included examples of multiplication tables, systems of measurements, prime numbers, quadratic formulas, geometry, trigonometry, and many others. They even possessed tables of "Pythagorean Triples," that is, trios of numbers which satisfy the variables A, B, and C in the classic Pythagorean theorem (A squared plus B squared equals C squared).
The system of mathematics developed by the Babylonians was both diverse and highly pragmatic, based almost entirely on a system of fractions.
Babylonian Numerals
Though the Babylonian system used a base-60 system, they did not have to learn sixty different symbols. In fact, all of the numbers between 1 and 59 were based entirely on a complex construction of just two different cuniform (wedge-shaped) symbols. Thus, with just a little practice, any number could be constructed using just these basic symbols.
Legacy of Babylonian Math
The Babylonians in the complexity of their mathematics opened the doors for mathematical exploration throughout the world, demonstrating that complex mathematics could indeed be performed using systems of algorithms and clever tables.
Much of the mathematics of the Mesopatamian world were forgotten, however, with the arrival of the Greeks as the dominant mathematical culture. These new thinkers such as Pythagoras and Euclid were much more focused on the geometrical and analytical side of math, rather than the practical form of math expressed by the Babylonians and the Egyptians (more suitably formed for bookkeeping and counting).
Thus, the focus of mathematics shifted, though to this day there are still elements of mathematics remaining from the Babylonian culture (in the measurements of circles and the counting of time in base-60 units), as well as Greek/Roman/Egyptian culture (base-10 counting systems), and the Arabic culture (modern systems of numerals).
Modern mathematics is a hodge-podge mixture of ancient mathematical cultures. It may not be the perfect way of doing things, but it makes some sense when one considers the origins of today's math.
References:
"An Overview of Babylonian Mathematics."
Fowler, Michael. "Counting in Babylon."
