# Ancient Mathematics

## A Blast From the Past

In modern day, we have an entire subject of our school day dedicated to mathematics. We find it normal to solve many mathematical equations in our everyday lives. However, we most likely do not often think about how the study of mathematics came to be. The study of mathematics started thousands of years ago, and it started with the people of ancient civilizations.

Below is a photo of the Rhind Mathematical Papyrus of Ancient Egypt. It is considered to be one of the most important documents of the Ancient World. This Ancient Egyptian document dates back from almost 40000 years ago. It was written as a kind of math textbook, containing 84 practical problems in Egyptian life. The problems range from finding the area of a circle to finding the slope of a pyramid. The mathematical knowledge of the Ancient Egyptians that this represents is astounding. I have included this to give you a quick preview of the Ancient Mathematics. Later on, I will get more into detail on Ancient Egyptian Math.

## Prehistoric Mathematics

Mathematics initially started as a result to the need to measure plots of land in the Sumerian and Babylonian civilizations of Mesopotamia and in ancient Egypt. In addition, there is evidence of basic arithmetic and geometric notations on burial mounds in Ireland dating from about 3500-3200 BCE [Before the Common Era]. Another monument in England arguably displays use of 60 and 360 in circle measurements, a practice developed by the Sumerians and Babylonians. Math has therefore existed over 20,000 years ago.

Below is a picture of Ishango bones, tally sticks found in Africa dating over 20,000 years ago. Although tallying is not considered true mathematics, it does represent a form of knowledge of amounts. People knew the difference between 1 or 2 animals 20,000 years ago.

## Sumerian/Babylonian Mathematics

The Sumerians initially began work with mathematics as a response to the need to measure plots of land, tax people, and chart the night sky. The Sumerians/Babylonians also needed to describe large numbers as they began charting the night sky and creating their sophisticated lunar calendar. Therefore, there were perhaps the first people to assign symbols to groups of objects in an attempt to make the description of large numbers easier. They started out using coins or symbols to represent a certain amount of specific objects [jars of oil, shaves of wheat, etc.]. Then, the Sumerian/Babylonians began to develop symbols for a certain number of anything. Over time, the Sumerians and Babylonians based their mathematics on a numeric system, where the numbers represented a true place-value system, much like today´s decimal system.

The idea of square numbers and quadratic equations arose in the process of measuring land. Babylonian mathematical tablets give the first ever evidence of solutions to quadratic equations. The Babylonian approach to solving these types of problems usually revolved around a kind of geometric game of slicing up and rearranging shapes, although the use of algebra and quadratic equations also appears.

Below: Babylonian clay tablets show the solving of quadratic equations and the area of an irregular shape from c. 2100 BCE.

## Egyptian Mathematics

Ancient Egyptians began recording patterns of lunar phases and the seasons very early in history both for agricultural and religious reasons. Not long after, they, like the Sumerians/Babylonians, began to develop a system for measuring plots of land. The Pharoh´s surveyors would measure land and buildings based on measurements of body parts [like the palm of a hand or the length of a wrist to an elbow] very early in Ancient Egyptian history. The Egyptians also developed a decimal numeric system based on our ten fingers.

The oldest mathematical text discovered from Ancient Egypt so far is the Moscow Papyrus. The Moscow Papyrus dates back from the Egyptian Middle Kingdom, from around 2000 to 1800 BCE. Below is a photo of the Moscow Papyrus.

The Egyptians were perhaps the first people to carry out a sophisticated decimal numeric system with a base of ten. They accomplished many great mathematical advancements that we still use today, such as multiplication and division. Ancient Egyptian documents, such as the Rhind Papyrus and the Berlin Papyrus, show us that the Ancient Egyptians figured out very early in time how to add, subtract, multiply, divide, and even solve second-order algebraic equations from as early as 1650 BCE.

## Greek Mathematics

The Greeks were smart enough to adapt useful elements from societies they conquered. Because of this, Greek mathematics shows elements and techniques of the Babylonians and the Egyptians. However, the Greeks did make their own important contributions to the mathematical world. The created a numeral system at around 650 BCE that used the numbers: 1, 5, 10, 50, 100, 500, and 1000 as many times as needed to represent the desired number. With their simple, yet advanced, revolutionary numeric system, they designed a simplified way of addition, subtraction, multiplication, and division that we use everyday.

Not only did the Greeks revolutionize the numeric system and function, but they also made major contributions to the world of geometry. Thales, a Greek mathematician, developed the most basic ways of geometry that now seem quite simple, but led the way to major mathematical advancements. Thales created the Thales´ Theorem, where if a triangle is drawn inside a circle with the long side as the diameter of the circle, then the opposite angle will be a right angle. Thales also created another theorem, known as the Intercept Theorem, about ratios of line segments that are created if two intercepting lines are intercepted by a pair of parallels [and, by extension, the ratios of the sides are similar triangles].

Below: This is a picture of what Thales' Intercept Theorem represents. Although this seems like a very simple equation, this was one of the basic building blocks of geometry contributed by the Ancient Greeks.

## Conclusion

In conclusion, what I believe I have made quite clear in this presentation is that mathematics has been around for over 20,000 years, and without math, our world as we know it would not be the same. We have the Prehistoric people, the Sumerians/Babylonians, the Ancient Egyptians, the Ancient Greeks, and many more people to thank for the great advancements in math they have contributed. I have merely touched base on the history of math, but it should be clear that mathś colorful history will always be remembered.

Please watch the following short video of the history of mathematics summarized. This video includes subjects I have already covered and touches base on other information, too.

History of Mathematics