An Ancient Egyptian Mathematical Photo Album – Hieroglyph Numerals and More

The Louvre, the most well-known art museum in the world, houses one of the largest collections of ancient Egyptian artifacts and art. Hieroglyphs appear on several of the objects, and by looking carefully one can find Egyptian numerals. In this section we present a photo album of hieroglyphic numerals from the Annals of Thutmose III, a cubit rod showing fractions, and art and instruments of Egyptian scribes, who would have been transcribing and working with the numbers.

The first group of photos from the Louvre show the Annals of Thutmose III on a sandstone wall that was originally in Karnak in Egypt. The first four pictures show larger sections of the wall. These are followed by a selection of photos of specific numerals found on the wall to demonstrate various ways the digits of the numerals are aligned. More numerals can be found by zooming in on the first four photos.

Figure 28. Part of the left side of the Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 29. More of the left side of the Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 30. The middle portion of the Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 31. The right side of the Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 32. 4,622 and possibly 5,428 (damaged) in Egyptian hieroglyphsfrom Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 33. Possibly 329 (damaged) and 470 in Egyptian hieroglyphsfrom Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 34. 276 and 618 in Egyptian hieroglyphsfrom Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

Figure 35. 1200 in Egyptian hieroglyphsfrom Annals of Thutmose III (1479–1425 BCE, Karnak Temple) in the Louvre.

A fascinating mathematical object in the Egyptian collection in the Louvre is a cubit rod that was found in the tomb of Maya in Saqqara. Maya was an important official who held several positions, including the Minister of Finance, for the pharaoh Tutankhamun.

Figure 36. The cubit rod (1327–1295 BCE) of Maya in the Louvre.

A cubit, the length from the elbow to the tip of the middle finger, was the basic unit of measure in ancient Egypt. A cubit was divided into seven palms and each palm was divided into four fingers. The finger hieroglyph (which is also used to represent 10,000) is used to represent the length, 1 finger. If we look at the far left of the above cubit (see Figure 37), in the middle row, we see 1 finger, 2 fingers, and 3 fingers marked off. Continuing on in the middle row, we have a palm, 1 palm and 1 finger, 1 palm and 2 fingers, etc. The middle row (and the top row with other hieroglyphs) is partitioned into a total of 28 fingers.

Figure 37. The left end of the cubit rod (1327–1295 BCE) of Maya in the Louvre.

The right end of the cubit has fingers marked into parts from one-half up to sixteenths. Above the markings are the labels in Egyptian fractions, starting with the special hieroglyph for (frac{1}{2}) and then using the mouth symbol to denote fraction for (frac{1}{3}) to (frac{1}{16}). Figure 38 shows a close-up of the right end with the markings from (frac{1}{2}) to (frac{1}{14}).

Figure 38. The right end of the cubit rod (1327–1295 BCE) of Maya in the Louvre.

Egyptian scribes, some of the few literate people in ancient Egypt, were responsible for keeping records and accounts, writing letters, and recording events. According to The Teaching of Khety, an ancient Egyptian text of a father’s advice to his son, the vocation of scribe was a desirable one and “there is no job without a boss except for the scribe” [Wilkinson 2017, pp. 289–299]. Khety explained that being a scribe had advantages over other professions, such as not smelling like the smith (“who stinks more than fish roe”) and the stoker (“his fingers are putrid and smell of corpses”); not having to watch out for crocodiles like the fisherman and washerman (who also “handles the clothes of menstruating women”); not having to be out in the weather like the reed cutter, arrow maker, and messenger; and not having to do back-breaking work like the gardener, mason, and farmer. Photos of several examples of scribes at work and scribal tools are given below.

Figure 39. Representations of various scribes and their tools in the Louvre collections.

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