Mathematical Discoveries Made By The Ancient Civilizations And Their Impact On The World

 In the modern era, we heavily rely on calculators and other technological devices as a means to solve the daily problems we face. However, thousands of years ago, long before such technology was available, humans were forced to develop their own methods to solve various mathematical problems. Today, it is difficult for one to imagine what life would be like without the luxury of having our devices constantly alongside us, allowing for instant access to information at the simple click of a button. Without the development of mathematical strategies by the ancient civilizations of the Babylonians, Greeks and Egyptians, we would not be as technologically advanced as we are today.

The Babylonians, who made their debut in 2000 BC, developed a number of mathematical systems, including a numerical system, that were used by many civilizations to follow (James 2016). One well known element of the Babylonian society is an ancient form of writing on cuneiform symbols, in which the symbols were written on wet clay tablets that were hardened in the hot sun (Johnston, 2017). The primary manner in which these tablets were implemented was for making the necessary calculations needed to build their intricate canal system. At the time, the early civilizations of Mesopotamia relied on such canals not for irrigation but were also a vital element in the transport of goods and armies. The government hired Babylonian mathematicians to make the calculations involved with the building of the canal, such as the amount of time needed to build the canal, the number of workers required and the worker’s wages.

Although the mathematics involved in this process are relativity simple, Babylonian society relied on such processes as methods for completing their basic calculations. In addition, the Babylonians utilized a different base-60 number system, or the sexagesimal numeral system, compared to the commonly used base-10 number system (Mastin, 2010_). Although this can be considered more complicated to understand than the current system, it has a number of advantages. For example, it allows for easier calculations and simplifications when fractions are involved as the number 60 has many factors (i.e. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60). The base-60 number system also contributed to the modern measurement of time (i.e. 60 seconds in a minute, 60 minutes in an hour, etc.) (History UK, 2000). Furthermore, civilizations following the Babylonians, including the Egyptians and Greeks, implemented the knowledge and discoveries of the Babylonians as stepping stones for future mathematical advancements.

The ancient Greek’s (800 BC-700 AD) made many significant geometrical discoveries that are still implemented in the present time. One famous and noteworthy Greek figure, Pythagoras, made groundbreaking discoveries that are still recognized today. Pythagoras visited Ionia and watch the Egyptians build pyramids by dividing a rope into twelve equal parts and building triangles by using three parts of the rope on one side, four on the other, and five on the last. Upon viewing this method of building pyramids, Pythagoras recognized that any triangle in this 3:4:5 ratio is a right triangle (Mastin, 2010). He was one of the first individuals to note that a complete system of mathematics could developed where geometric elements correspond to numbers. As a result, the Pythagorean Theorem was born, which is now one of the most well-known mathematical theorems to date. It states that the square of the length of the hypotenuse is equal to the sum of the square each of the other two sides for any right angle triangle, or a2 + b2 = c2.

In addition, the Greeks made a number of other large contributions to geometry. Thales, who is one of the Seven Sages of Ancient Greece, developed what is now known as the Thales Theorem. The theorem indicates the ratios of the line segments created when if two intersecting lines cross a set of parallel lines (Mastin, 2010). According to legends, Thales theorem was used to calculate the height of the Great Pyramids in Egypt and the Tower of the Wends in Athens using the surrounding shadows (Violatti, 2019). In addition, another notable Greek geometrical discovery is referred to as the three classical problems, which were all attempted to be solved by geometric means, a straight edge, and a compass.

The first problem is called the “squaring (quadrature) of a circle,” which asked for one to construct a square with the same area as a given circle. The second is the “doubling of a cube,” which entailed constructing a cube with exactly twice the volume of a given cube. The last problem is the “trisection of an angle,” which asked to construct an angle that is exactly one-third of any given angle. These three problems were had a great impact on future geometry and led to many other “accidental” discoveries in the attempt to solve them, despite the fact that they were later proven to be impossible. In sum, the mathematical discoveries in ancient Greece, including the Pythagorean theorem, Thales theorem, and the three classical problems, set a foundation for geometry, thus allowing it to flourish and for other breakthroughs to be made.

The application of ancient Egyptian mathematics was predominantly used for the engineering behind the building of the great pyramids and other renowned monuments. The pyramids themselves indicate the sophistication of the mathematics in ancient Egypt. They are the first known structure to obtain the golden ratio of 1: 1.618 (Mastin, 2010). Also, there is evidence to show that the Egyptians knew the formula for the volume of a pyramid: ⅓ times the height times the width times the length. In addition, they were utilizing the right triangle ratio of 3:4:5 to build their pyramids by using rope knotted at these intervals to ensure the pyramid had right angles. However, Pythagoras, the previously discussed Greek philosopher, was the one to realize the significance of the ratio and apply the Egyptian’s methods of building pyramids to the revelation of new mathematical concepts (Mastin, 2010).

Also, the famous ancient scroll referred to as “The Rhind Papyrus” acts as an instruction manual for arithmetic and geometry and dates back to 1650 BCE (Mastin, 2010). The document illustrates the manner in which the ancient Egyptians carried out multiplication and division as well as evidence of knowledge of unit factors, composite and prime numbers, arithmetic, geometric and harmonic means, and solving first and second order equations (Britannica, 2008). Additionally, the Egyptians developed the decimal, or base-ten, numerical system that is used today in modern society. Although the number ten has fewer divisors than the number sixty does in the babylonian developed sexagesimal numeral system, a base-ten system allows for easier counting on our ten fingers (Mastin, 2010). Overall, even though the numerous discoveries made by the ancient Egyptian mathematicians can be viewed as seemingly insignificant, the discoveries are a vital component of architecture and the concepts are still applicable in the engineering of structures.

Ultimately, the brilliant and curious minds of the past in ancient Babylon, Greece, and Egypt can be thanked for the numerous breakthroughs made that helped set a foundation for the mathematics that we rely on in society today. Moreover, as technology begins to advance and we continue to rely on the internet and computers for not only our primary source of information but also to complete our daily tasks, in factories, and to essentially replace human labour, the depth of our mathematical knowledge will continue to rapidly progress. With the exponential nature of the development of mathematical knowledge, who knows where our discoveries will lead humanity and it’s advancement in years to come.