Mathematics and Numerology
For the Ancient Egyptians, the two primary numbers in the universe are 2 and 3. All phenomena, without exception, are polar in nature and treble in principle. As such, the numbers 2 and 3 are the only primary numbers from which other numbers are derived.
Two symbolizes the power of multiplicity—the female, mutable receptacle – while Three symbolizes the male. This was the music of the spheres—the universal harmonies played out between these two primal female and male universal symbols of Isis and Osiris, whose heavenly marriage produced the child Horus. Plutarch confirmed this Egyptian knowledge in Moralia Vol. V:
“Three (Osiris) is the first perfect odd number: four is a square whose side is the even number two (Isis); but five (Horus) is in some ways like to its father, and in some ways like to its mother, being made up of three and two…”
The significance of the two primary numbers 2 and 3 (as represented by Isis and Osiris was made very clear by Diodorus of Sicily [Book I, 11. 5]:
“These two neteru (gods), they hold, regulate the entire universe, giving both nourishment and increase to all things…”
In the animated world of Ancient Egypt, numbers did not simply designate quantities but instead were considered to be concrete definitions of energetic formative principles of nature. The Egyptians called these energetic principles neteru (gods, goddesses).
To Egyptians, numbers were not just odd and even. These animated numbers in Ancient Egypt were referred to by Plutarch in Moralia, Vol. V, when he described the Egyptian 3-4-5 triangle:
“The upright, therefore, may be likened to the male, the base to the female, and the hypotenuse to the child of both, and so Osiris may be regarded as the origin, Isis as the recipient, and Horus as perfected result.”
The vitality and the interactions between these numbers shows how they are male and female, active and passive, vertical and horizontal, etc. The divine significance of numbers is personified in Ancient Egyptian traditions by Seshat, The Enumerator. The netert (goddess) Seshat is also described as: Lady of Writing(s), Scribe, Head of the House of the Divine Books (Archives), and the Lady of Builders.
Seshat is closely associated with Thoth(Tehuti), and is considered to be his female counterpart.
The Egyptian concept of number symbolism was subsequently popularized in the West by and through Pythagoras [ca. 580–500 BCE]. It is a known fact that Pythagoras studied for about 20 years in Egypt, in the 6th century BCE.
Pythagoras and his immediate followers left nothing of their own writing. Yet, Western academia attributed an open-ended list of major achievements to him and the so-called Pythagoreans. They were issued a blank check by Western academia.
Pythagoras and his followers are said to view numbers as divine concepts; ideas of the God who created a universe of infinite variety and gave satisfying order to a numerical pattern. The same principles were stated more than 13 centuries before Pythagoras’ birth in the heading of the Egyptian’s Papyrus known as the Rhind Mathematical Papyrus [1848–1801 BCE], which promises:
“Rules for inquiring into nature and for knowing all that exists, every mystery, every secret.”
The intent is very clear: Ancient Egyptians believed in and set the rules for numbers and their interactions (so-called mathematics) as the basis for “all that exists”.
All the design elements in Egyptian art and buildings (dimensions, proportions, numbers, etc.) were based on the Egyptian number symbolism, such as the Ancient Egyptian name for the largest temple in Egypt, the Karnak Temple Complex, which is Apet-sut, meaning Enumerator of the Places. The temple’s name speaks for itself. This temple started in the Middle Kingdom in ca. 1971 BCE and was added to continuously for the next 1,500 years. [For more information about numbers and their significance, see Egyptian Cosmology: The Animated Universe & The Ancient Egyptian Metaphysical Architecture by Moustafa Gadalla.]
Regarding the present-day narrow application of the subject of “mathematics”, the perfection of the Ancient Egyptian monuments attests to their superior knowledge. For starters, the Egyptians had a system of decimal numbering, with a sign for 1, another for 10, 100, 1,000, and so on. The evidence at the beginning of the 1st Dynasty (2575 BCE) shows that the system of notation was known up to the sign for 1,000,000. They used addition and subtraction. Multiplication, except for the simplest cases in which a number had either to be doubled or multiplied by ten, involved a process of doubling and adding (which is, by the way, how the computer process works). Our multiplication tables rely totally on memorization and nothing more, and can by no means be considered a human achievement. The computer process is easier, more accurate, and faster, as we all know.
Academicians ignore the knowledge embedded in the numerous Ancient Egyptian works. They want to only refer to a few recovered Ancient Egyptian papyri that come from a Middle Kingdom papyrus and a few fragments of other texts of a similar nature. The study of mathematics began long before the found “mathematical” papyri were written. These found papyri do not represent a mathematical treatise in the modern sense – that is to say, they do not contain a series of rules for dealing with problems of different kinds, but merely present a series of tables and examples worked out with the aid of the tables. The four most referred to papyri are:
- The Rhind “Mathematical” Papyrus (now in the British Museum), a copy of an older document during King Nemara (1849–1801 BCE), 12th Dynasty. It contains a number of examples to which academic Egyptologists have given the serial numbers 1-84.
- The Moscow “Mathematical” Papyrus (in the Museum of Fine Arts of Moscow) also dates from the 12th Dynasty. It contains a number of examples to which academic Egyptologists have given the serial numbers 1-19. Four examples are geometrical ones.
- The Kahun fragments.
- The Berlin Papyrus 6619, which consists of four fragments reproduced under the numbers 1-4.
Here is a synopsis of the contents of the Rhind “Mathematical” Papyrus:
– Division of various numbers.
– Multiplication of fractions.
– Solutions of equations of the first degree.
– Division of items in unequal proportions.
– Volumes and cubic content of cylindrical containers and rectangular parallelopi pectal
- Areas of:
– truncated triangle
- Batter or angle of a slope of a pyramid and of a cone.
- Miscellaneous problems:
– Divisions into shares in arithmetical progression.
– Geometrical progression.
Other Mathematical Processes known from other Papyri include:
- Square and square root of quantities involving simple fractions [Berlin 6619].
- Solution of equations of the second degree [Berlin Papyrus 6619].
- It must be noted that the Rhind Papyrus shows that the calculation of the slope of the pyramid [Rhind Nos. 56-60] employs the principles of a quadrangle triangle, which is called the Pythagoras Theorem. This Egyptian Papyrus is dated thousands of years before Pythagoras ever walked this earth.
This theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Plutarch explained the relationship between the three sides of the right angle triangle 3:4:5, which he (like all the people of his time) called the “Osiris” Triangle.
[An excerpt from Ancient Egyptian Culture Revealed , 2nd edition by Moustafa Gadalla]