An Ancient Egyptian Mathematical Photo Album – Hieroglyph Numerals and More

Author(s):
Cynthia J. Huffman (Pittsburg State University)

The Egyptian hieroglyph numeration system is studied in many mathematics courses for pre-service elementary education students as well as in history of mathematics courses. Starting with the 2009 MAA Study Tour to Egypt, the author began collecting photographs of authentic hieroglyphs to show students during presentations on numeration systems and ancient Egyptian mathematics. Students are fascinated to see the actual hieroglyphs, rather than just drawings or typeset characters. The purpose of this article is to share some of these images, so that others may also use them in their classrooms. The article contains a sampling of photographs (taken by the author unless otherwise noted) that can be used (with attribution, CC BY 4.0) in classrooms to illustrate the genuine use of hieroglyphic numerals in ancient Egypt. After a brief overview of Egyptian hieroglyphic numerals and their uses, the sections of this article are organized by location of the hieroglyphs. (Note: For more details on Egyptian mathematics and recent scholarly theories in Egyptology, see [Imhausen 2016].)

Hieroglyphs were used on temple walls, stelae, and early papyri in ancient Egypt. The term “hieroglyph” comes from Greek for “sacred carvings.” “Hieroglyph” is a noun and “hieroglyphic” is the corresponding adjective. As time passed, a cursive style of writing, called hieratic, was developed for writing on papyrus. In this article, we will focus on hieroglyphs. So, we will not be including images from the two classic sources on Egyptian mathematics, the Rhind Mathematical Papyrus or the Moscow Mathematical Papyrus, since both of these papyri are in hieratic script.

In classrooms, the Egyptian hieroglyph numeration system is often presented, possibly with other numeration systems, as a comparison to the base ten, place-value, Hindu-Arabic numeration system that we use today. The hieroglyphic system is also base ten, with special hieroglyphs for the powers of ten from 0 to 6 (ones to millions). However, it is not a place-value system. Instead, it is additive, like early Roman numerals, in which a specific numeric hieroglyph can be repeated from one to nine times. To write counting numbers, the symbols are written in decreasing order, with like symbols grouped together and sometimes stacked. Egyptian hieroglyphs may be written to be read from right to left, left to right, or top to bottom. To determine whether one reads from right to left or left to right, the rule is to read toward any faces in the hieroglyphs. Whenever the hieroglyphs are in columns, they are always read from top to bottom. In Figure 1, which is from the Edfu Temple, we can see six of the seven hieroglyphs that are used in creating natural numbers.

Figure 1. 1,333,330 in Egyptian hieroglyphs from the Edfu Temple (237–57 BCE) in Egypt.
All photos in this article—except for Figures 2–4, 15, and 40—were taken by the author
and can be used with attribution under a CC BY 4.0 license.

The hieroglyph on the left is the Egyptian god Heh (chaos or infinity), representing one million. Next, a tadpole hieroglyph represents 100,000. The bent finger hieroglyph is 10,000; the lotus flower is 1000; the coil of rope is 100; and the hobble (used for cattle and missing the crossbar) is 10. Reading from left to right, the hieroglyph number is 1,333,330. The one missing numeric hieroglyph symbol in the photo is the stroke or tally mark for 1.

Cynthia J. Huffman (Pittsburg State University), "An Ancient Egyptian Mathematical Photo Album – Hieroglyph Numerals and More," Convergence (April 2022), DOI:10.4169/convergence20220409