Mathematics and the establishment of normative orders in ancient cultures: Egypt and Mesopotamia in comparison

Project leader: Prof. Dr. Annette Warner (Imhausen)

Mathematics played a decisive role in the establishment of the normative order of ruling systems in Egypt and Mesopotamia. In both Mesopotamia and Egypt, the establishment of the ruling systems was accompanied by the development of writing and number systems, as well as the development of meteorological systems. In the following, parallel developments in the interlocking of rule and the development of mathematical techniques can be observed in Egypt and Mesopotamia, as well as culture-specific differences.

Mathematical quantities were defined to control the available resources (materials and people), which created the basis for administration in both cultures. In order to manage people’s work performance, for example, a quantity of the respective work product was defined, which had to be produced within a certain time frame (daily or weekly). Mathematical task texts from Egypt and Mesopotamia, as well as coefficient lists from Mesopotamia, describe the mathematical techniques with which the work norms set by the rulers were made mathematically controllable. This mathematical control of the prescribed norms can also be documented from corresponding administrative sources. By examining the relationship between the theory (i.e. the procedures conveyed by the school texts) and the practice of this implementation of labor norms, an insight was to be gained into the interactions between mathematical practices and the normative orders of the rulers.

Another aspect of this project was the intercultural comparison between Egypt and Mesopotamia. The comparative study of the mathematics of these two cultures is particularly interesting, as similar tasks were accomplished in them to some extent and comparable sources are therefore available. The most extensive corpus of mathematical texts in Egypt comes from the Middle Kingdom period (2000-1800 BC, around half a dozen sources), in Mesopotamia from the Old Babylonian period (1800-1600 BC, thousands of sources). However, the two cultures differ significantly not only in the number of sources due to the choice of writing medium, but also in the fundamental structures of their mathematical systems, such as the number system and the arithmetic based on it.

While the monograph “Mathematics in Ancient Iraq. A social history” by Eleanor Robson provides a comprehensive analysis of the role of mathematics in Mesopotamia, there has been no such study for Egypt until now. This was compiled as part of the project and published by Princeton University Press in 2016 as “Mathematics in Ancient Egypt. A contextual history”. The book by the project leader describes the development of mathematics in Pharaonic Egypt from the invention of writing and the number system at the beginning of the unification of the empire around 3000 BC to the end of the indigenous Egyptian mathematical tradition in the Greco-Roman period. The difficulty to be overcome in such an overview (in contrast to Mesopotamia!) lies in the source situation. Due to the choice of writing medium and the geographical conditions, sources from Egypt are primarily from the funerary and religious fields. Mathematical texts have only survived in exceptional cases – although it is perhaps no coincidence that the two surviving groups of texts are concentrated on two specific periods of Egyptian history (a similar phenomenon exists here in the concentration of sources at certain times in Mesopotamia). Consequently, textual sources from administrative and literary contexts were also used in the work in order to be able to trace a development over the entire period of Pharaonic history.
These publications then lay the foundation for a comprehensive comparison of the two cultures over their several thousand years of existence.

In both Egypt and Mesopotamia, mathematics played a decisive role in the implementation of rulership requirements by ensuring (sometimes implicitly and unchallenged) their “legality” and/or “justice”. Here again, a fundamentally different attitude can be observed in Egypt and Mesopotamia. While the Mesopotamian ruler explicitly represents the justice of his rule to the outside world through mathematical symbols, mathematics in Egypt is primarily used to exercise power through control, and no justification is provided. In collaboration with other researchers in the cluster, this has given rise to the question of a further project in which the connection between mathematics and legal orders in ancient cultures is to be investigated.

The first cluster term also focused on the mathematization of work performance in Egypt. Three tasks in the Egyptian mathematical texts are available for this purpose, as well as a large number of sources from the administrative texts from Lahun and above all from Deir el-Medina. The evaluation of the Egyptian material for this area has been completed. The results were published in the anthology of the research field.
Another aspect of the project is the way in which mathematical and scientific knowledge was preserved, developed and exchanged between cultures.

The following publications resulted from this research project:
Warner (Imhausen), Annette (2016): Mathematics in Ancient Egypt. A contextual history , Princeton: University Press
Warner (Imhausen), Annette (2015): “Traditions/Norms in the structure of ancient Egyptian mathematical texts”, in: Daliah Bawanypeck/Annette Warner (Imhausen) (eds.), Traditions of Written Knowledge in Ancient Egypt and Mesopotamia (Alter Orient und Altes Testamen 403) Münster: Ugarit Verlag
Warner (Imhausen), Annette (2013): “Experten und die Umsetzung normativer Ordnungen im Alten Ägypten: Theorie und historisch fassbare Praxis”, in: Andreas Fahrmeir/Annette Imhausen (eds.): The diversity of normative orders. Conflicts and dynamics from a historical and ethnological perspective (Series: Normative Orders Vol. 8). Frankfurt/M.: Campus, 49-77
Annette Warner (Imhausen) and Tanja Pommerening (eds.) (2010): Writings of Early Scholars in the Ancient Near East, Egypt, Rome, and Greece, (Beiträge zur Altertumskunde; 286), Berlin/New York: De Gruyter; therein: Annette Warner (Imhausen) and Tanja Pommerening: “Introduction: Translating ancient scientific texts.” 1-10; and Annette Warner (Imhausen): “From the cave into reality: Mathematics and cultures”, 333-347
Annette Warner (Imhausen) (2009): “Traditions and myths in the historiography of Egyptian mathematics”, in: Eleanor Robson/ Jacqueline Stedall (eds.), The Oxford Handbook of the History of Mathematics, Oxford: Oxford University Press.

Among the most important events of the project were two workshops for the compilation of the anthology “Die Vielfalt normativer Ordnungen” (April 29-30, 2011, and September 9, 2011, Bockenheim).