Ancient pottery reveals potential early mathematical thought
Pottery adorned with floral designs from as long as 8,000 years ago may represent the earliest known instance of mathematical thought by humans, according to a recent study. Researchers from the Hebrew University of Jerusalem analyzed artifacts produced by the Halafian people, who inhabited northern Mesopotamia between 6200 BC and 5500 BC, reports BritPanorama.
The research highlighted that many bowls featured flowers illustrated with petal counts of four, eight, 16, 32, or 64. This consistent use of numbers suggests a “geometric sequence,” indicative of mathematical reasoning centered on symmetry and repetition. The findings were published last month in the Journal of World Prehistory.
Study authors Yosef Garfinkel, an archaeology professor at the Hebrew University, and research assistant Sarah Krulwich examined pottery fragments from 29 Halafian sites. These artifacts were excavated over a century, beginning in 1899. Nearly every one of the 375 fragments depicting flowers adhered to this doubling sequence, reflecting a division of circles into symmetrical units.
“The strict adherence to these numbers, which are repeated in examples from different sites over hundreds of kilometers, cannot be accidental and indicates that it was done intentionally,” Garfinkel stated. The researchers further suggested that this mathematical reasoning may have evolved in response to the complexity of managing village communities that had existed in the Near East for approximately 4,000 years.
The ability to evenly divide space, as shown in these floral motifs, likely had practical roots in day-to-day life, facilitating functions such as the equitable distribution of agricultural harvests. The study notes that undisputed records of mathematical systems only appear in texts from the third millennium BC, with the Sumerians utilizing a base-60 numerical system. The Halafian numerical progression does not align with either known system, hinting at an earlier form of mathematical thinking.
“These patterns show that mathematical thinking began long before writing,” Krulwich remarked. “People visualized divisions, sequences, and balance through their art.” The study contributes to the academic discipline of ethnomathematics, which uncovers mathematical knowledge embedded in the cultural expressions of prehistoric societies.
While the findings indicate a cognitive and symbolic shift in the Halafian community, critiques have emerged regarding the implications of their artistry. Jens Høyrup, a senior associate professor at Roskilde University, viewed the symmetry observed in the floral depictions as an isolated instance rather than evidence of complex mathematical reasoning. He characterised it merely as an early method of dividing circles.
Overall, this discovery offers insight into early human cognitive development and the sophistication of artistic expressions tied to practical needs. The narrative surrounding the origins of mathematical reasoning continues to unfold, underscoring the inherent complexity of human history.
