Recent research has uncovered what may be the earliest evidence of mathematical thought among humans, originating from pottery crafted up to 8,000 years ago. A team of archaeologists from the Hebrew University of Jerusalem scrutinized artifacts produced by the Halafian people, who inhabited northern Mesopotamia between 6200 BC and 5500 BC. Their study, published in the Journal of World Prehistory, highlights floral designs on pottery that reflect a sophisticated understanding of numerical patterns.
The researchers examined pottery fragments from 29 Halafian sites, excavated over a century, revealing that many bowls featured flowers depicted with four, eight, 16, 32, or 64 petals. This consistent use of numbers forms a “geometric sequence,” suggesting an intentional mathematical reasoning based on symmetry and repetition. According to lead study author Yosef Garfinkel, a professor in archaeology, the patterns found across these artifacts indicate a deliberate choice rather than mere coincidence.
Garfinkel, along with research assistant Sarah Krulwich, highlighted that nearly all 375 fragments examined showed this doubling sequence. They propose that the Halafians may have developed this mathematical reasoning to better manage their increasingly complex village communities, which had thrived in the Near East for approximately 4,000 years. Garfinkel explained that the ability to divide space evenly, as illustrated by these floral motifs, likely had practical applications in daily activities, such as sharing harvests or organizing communal fields.
The authors noted that clear mathematical records did not emerge until the third millennium BC, when the Sumerians, located in present-day Iraq, utilized a numerical system based on 60. There is speculation of a pre-Sumerian system based on 10, but the Halafian numerical patterns do not align with either system. Instead, they may represent a more primitive form of mathematical thought prevalent in the region during the 6th and 5th millennia BC.
In Krulwich’s words, “These patterns show that mathematical thinking began long before writing. People visualized divisions, sequences, and balance through their art.” This study contributes to the field of ethnomathematics, which identifies mathematical concepts embedded within the cultural expressions of prehistoric or non-literate communities.
While the findings are significant, some experts urge caution. Jens Høyrup, a Senior Associate Professor Emeritus at Roskilde University in Denmark, expressed skepticism about the interpretation of these designs as evidence of broader mathematical reasoning. He described the symmetrical floral depictions as “an isolated incident of mathematical technique,” emphasizing that the act of dividing a circle does not indicate a pursuit of geometric sequences but rather a basic method of halving.
Høyrup acknowledged the Halafians’ sense of symmetry but contended that this does not confirm the existence of a mathematical system. “There’s no higher mathematics; it’s just the simplest way to make divisions,” he noted.
As the research team continues to explore the implications of their findings, Garfinkel believes this discovery marks a foundational step in the evolution of human thought. Understanding basic division would have been essential for the development of more complex mathematical systems in the future.
The Halafian pottery stands out as an early example of humans applying their understanding of symmetry to artistic expression. The absence of depictions of edible crops suggests a focus on aesthetic rather than agricultural or ritualistic purposes. “These vessels represent the first moment in history when people chose to portray the botanical world as a subject worthy of artistic expression,” Garfinkel and Krulwich stated, indicating a cognitive shift tied to the advent of village life and an increasing awareness of aesthetics.
This groundbreaking research not only sheds light on the cognitive capabilities of early humans but also invites further exploration into how early mathematical concepts have shaped human societies throughout history.
