Ancient Mathematical Origins
From Primitive Counting to Mesopotamian Equations — A History of Mathematics
The History of Mathematics is a fascinating and complex subject that has roots in the Ancient world. The earliest known evidence of the use of Mathematics was found in two small bones from Africa, known as the Lebombo and Ishango bones, which are believed to be 40,000 and 20,000 years old, respectively. They bear engravings that historians believe represent a tally counting system.
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As humans developed more complex societies, the need to measure and keep track of quantities became increasingly important. This led to the development of forms of numeracy, but these were very basic compared to the Mathematics we know today.
One of the most significant early civilisations to develop a sophisticated understanding of Mathematics was the Ancient Mesopotamians.
Mesopotamian Mathematics
Mesopotamian civilisations are those situated in the historical region contained with in the Tigris-Euphrates river system, occupying modern-day Iraq, Kuwait, Iran, Syria and Turkey. From its beginning in Sumer before the 3rd millenium BCE to the eventual fall of Babylon in 539BCE, we see strong evidence for the use of mathematics as a key tenant of society.
The Mesopotamians documents their writings in Cuneiform script, which are clay tablets inscribed while the clay was still pilable. This gives us insight into some of the uses of mathematics that they employed.
Babylonian numerals
They used the sexagesimal (base 60) numeral system, something we can see in modern day with the counting of seconds in a minute, minutes in an hour or the degrees in a full-circle.
The number 60 is a superior highly composite number — which for the purpose of the Babylonians meant it has many divisors (12 in total). This makes calculations, especially with fractions, significantly easier.
Algebra and Arithmetic
The Mesopotamians used pre-calculated tables to assist we calculations. We see two of these found at Senkerah, which give the list of square numbers up to 59. This enabled them to use the mathematical identities to simplify complicated calculations. They also used these pre-calculated tables to solve simple quadratic equations of the form x² + bx = c and cubic equations.
Geometry
Geometry plays a crucial role in construction and city planning, and it is no surprise that these civilisations utilised geometry. However, the complexity of their findings was far beyond historians has previously thought.
We see across two tablets, dated between 1800 and 1600 BCE, exercises by student scribes to calculate the area of different geometric shapes. These includes estimating the area of a circle using π = 3, and the area of a trapezium.
The Pythagorean Theorem
Whilst, we probably attribute the Pythagorean Theorem to its namesake Pythagoras, this is incorrect and we see strong evidence for the knowledge of the theorem in Ancient Mesopotamia. In Plimpton 322 clay tablet written around 1800BCE, we see a table for the calculation of Pythagorean Triples. These are whole numbers that satisfy the equation a² + b² = c² and most impressively, this was seen over 1000 years before Pythagoras was even born.
The Mesopotamians showed a prowess for Mathematics that they are seldom given credit for. Making further contributions to Geometry and even modelling constraint growth.
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