The Mathematics of Ancient Egypt

The Impressive Numerical History of an Ancient Civilization

Mar 31, 2008

The ancient Egyptians possessed one of the earliest forms of mathematics, inspiring all mathematcal traditions that would follow in history.

Among the first civilizations in the world to begin to take advantage the benefits of numbers and mathematics, the work of the Ancient Egyptians truly stands out, especially considering the fact that many of the results of this early math are still visible today in the form of the vast architectural achievements of these "primitive" people.

At the beginning of what is now known as the "Old Kingdom" of Egypt, somewhere around 3,000 B.C., when the previously separate nations in the lower Nile valley formed into a single nation under one ruler (or Pharoah, the first being Djoser), the Egyptians already possessed a system of counting using hieroglyphics.

Formulation of the Egyptian Numerals

The Egyptian numerals are actually very similar in principle to the familiar "Roman numerals" (which evolved out of Etruscan numerals used around 800 or 700 B.C.), where specific symbols representing particular units are added together.

A vertical dash, to the Egyptians, stood for one. An upside-down horseshoe shape stood for ten. A coil of rope was 100. A lotus plant was 1000. A single finger pointed to the sky, 10,000. A frog, 100,000. A god with his arms raised, 1,000,000. How these numbers combined to make larger numbers should be readily obvious.

Limitations of Egyptian Numerals

Like most of the world's cultures throughout the next four thousand years, the system of Egyptian numerals possessed both strengths and weaknesses.

In keeping with early numerical systems, such as the Hebrew and Greek systems (which used specific combinations of letters to stand for numerical ideas) or the Roman system of numerals, the Egyptian system was rather simple to understand and to use for simple addition and subtraction, but it made advanced mathematics such as multiplication and division nearly impossible.

Mathematical Applications

What is impressive, though, is just how effectively the Egyptians even during these ancient times were able to use this rather limited form of arithmetic to accomplish all that they did. Any examination of the architecture of this time (this is the beginning of the age of the pyramids - absolutely famous for their attention to geometrical detail).

Like many other aspects of this era, however, while it is clear that there was certainly a high level of mathematical achievement at least on some level, it is not quite clear exactly what this entailed, though surely the Egyptians had developed a strong system of applied geometry used in sophisticated surveying.

The Egyptians were also able to formulate methods of using their system of numerals to denote fractions. To do this, they used a system called the "Eye of Horus," in which different portions of this single glyph represented different fractions with a numerator of one and a denominator of powers of two (i.e. 1/2, 1/4, 1/8, 1/16...). They were also able to perform multiplication and division using only addition and subtraction.

The Evolution of Egyptian Mathematics

This ancient form of Egyptian math, based on heiroglyphics (which was the dominant form of writing at the time), did not remain stagnant throughout the history of this great empire (which would last for more than three thousand years - a considerable period of time), but would grow and evolve along with the Empire, surely inspiring the mathematics of other cultures, such as the Greeks, Romans and Middle Eastern peoples.

As the Egyptian language evolved from Hieroglyphic to Hieratic form of scripts (see the Suite101 article on Egyptian Languages for more information), the common numerals changed as well, to a sort of "cursive" form of the original

While the earliest forms of Egyptian math may still remain a mystery to this day, it was inarguably effective in serving their purposes, and while much of it has been lost, other elements surely survived and were adopted by other cultures. Greeks such as Euclid in the third century (the famous "inventor" of modern geometry) spent their time in Egyptian cities such as Alexandria during the Ptolemaic period, when the library at Alexandria was perhaps the most important center of knowledge in the world.

The Egyptians, by virtue of their ultimate successes at applied mathematics and the fact that they were the first culture known to possess mathematics, were vitally important to the later evolution of mathematics, and should be given great credit for their remarkable achievements.

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