Recent research suggests that ancient pottery designs may represent the earliest evidence of mathematical thought among humans. A study conducted by researchers from the Hebrew University of Jerusalem examined pottery created by the Halafian people of northern Mesopotamia, dating back as far as 8,000 years ago. The findings, published last month in the Journal of World Prehistory, reveal that many pottery bowls feature floral designs with petals in numbers that follow a geometric sequence: four, eight, 16, 32, or 64.
The research team, led by Yosef Garfinkel, a professor of archaeology, along with Sarah Krulwich, a research assistant and MA student, analyzed pottery fragments from 29 Halafian sites over a century of excavations. They discovered that of the total 375 fragments displaying floral motifs, nearly all adhered to this doubling sequence, indicating a possible early form of mathematical reasoning linked to symmetry and repetition.
Strong evidence supports the notion that this method of representing numbers was intentional, as Garfinkel emphasized, stating, “The strict adherence to these numbers, which are repeated in examples from different sites over hundreds of kilometers, cannot be accidental.” This suggests a level of sophistication in the Halafians’ understanding of mathematical concepts, potentially developed to manage increasingly complex village communities in the Near East.
The researchers propose that the ability to divide space evenly, as reflected in these floral motifs, may have practical roots in daily life, including activities such as sharing harvests or allocating communal fields. Garfinkel noted that the Halafians’ mathematical reasoning predates documented systems that emerged in the third millennium BC, such as the Sumerians’ base-60 numerical system.
While the Sumerians utilized a more complex mathematical framework, the Halafian numerical representation of four, eight, 16, and 32 may signify a simpler, earlier level of mathematical thought. Krulwich remarked, “These patterns show that mathematical thinking began long before writing. People visualized divisions, sequences, and balance through their art.”
Additionally, the study contributes to the academic field of ethnomathematics, which investigates mathematical knowledge embedded in prehistoric or non-literate communities’ cultural expressions. This is not the first instance where artifacts have suggested early mathematical understanding; some experts argue that evidence of string-making by Neanderthals over 40,000 years ago indicates that these ancient humans had basic numeracy skills.
Garfinkel describes this discovery as a foundational step in the evolution of human thought, asserting that basic division capabilities were essential for the later development of more intricate mathematical systems. He and Krulwich highlighted the uniqueness of Halafian pottery as an early example of humans applying an understanding of symmetry to art, emphasizing that the depictions are not of edible crops, suggesting that their purpose was aesthetic rather than agricultural or ritualistic.
“This reflects a cognitive shift tied to village life and a growing awareness of symmetry and aesthetics,” they stated.
Despite the compelling nature of these findings, not all experts agree on the implications of the evidence. Jens Høyrup, a Senior Associate Professor Emeritus at Roskilde University in Denmark, expressed skepticism regarding the researchers’ conclusions. He characterized the symmetry observed in the Halafians’ floral designs as an isolated mathematical technique rather than a reflection of a broader mathematical system.
Høyrup clarified, “If you have to divide a circle nicely, at first you make a diameter — then it’s two. Then you divide the other way, so you have four. It doesn’t amount to any search for a geometric ascending sequence; it’s simply halving.” He acknowledged the presence of symmetry but cautioned against inferring a comprehensive mathematical system from it, asserting that it represents the simplest method for making divisions rather than a sophisticated understanding of mathematics.
The ongoing debate surrounding these findings highlights the complexities of understanding early human cognition and the development of mathematical thought. As researchers continue to explore these ancient artifacts, they contribute significantly to our understanding of the cognitive and cultural advancements of early societies.
