Analysis of samples from the Khalafite culture in northern Mesopotamia found symmetrical divisions of the numbers 4, 8, 16, 32 and even 64 – a hint at quantitative thinking before the emergence of written numbers
Paintings of flowers, shrubs, branches and trees on pottery from the Halafian culture in northern Mesopotamia – in present-day Iraq, Syria and Turkey – may be the earliest evidence of systematic “ancient botanical art”, and also hint at practical mathematical thinking even before the appearance of written numbers. This is what Prof. Joseph Garfinkel and Sarah Karolovich of the Hebrew University claim, in an article published on 05-12-2025 in the journal Journal of World Prehistorysystem. (link.springer.com)
Their claim also ties in with the “Research Highlight” review of Nature from 14-01-2026, which highlights the gap between the appearance of the first written numbers in the region (around 3400 BC) and the earlier visual evidence for the division of space into symmetrical “units.” (Nature)
Flowers, shrubs and trees: a change in the world of images
The article argues that early prehistoric art tended to focus mainly on animals and human figures, while plant motifs appear systematically and in large numbers only in the Chalcolithic period (c. 6200–5500 BCE). The researchers classify the motifs into four main categories: flowers, shrubs, branches, and trees, and emphasize that the variety is wide – from relatively “natural” imitations to very schematic images.
They relied on data collection from a large number of sites and excavation reports, and claim that only when the findings from many places are combined does the “big picture” of the use of plant motifs become clear. However, they also admit in advance: it is sometimes difficult to distinguish between a flower and a schematic “star”, or between a branch and a geometric pattern of lines. Often only part of the painting was preserved on broken pottery, so the identification is not always clear.
The mathematical sequence: 4, 8, 16, 32 and also 64
The core of the story is the numerical order. In the flower patterns on the vessels, numbers of petals or divisions of the circle into symmetrical units of 4, 8, 16, and 32 appear repeatedly, and sometimes compositions reaching 64 flowers on one vessel. The researchers claim that the repetition is not accidental, because it is a geometric sequence of doubling, and not other “convenient divisions” (such as 3, 6, 12, 24) that do not form the same sequence.
From here they offer a broad interpretation: the ability to divide space in a consistent and symmetrical manner reflects practical quantitative thinking. In their opinion, this is the same cognitive ability that was required in early agricultural village life: dividing up land, dividing crops, and managing shared resources.
The researchers present these motifs as early evidence for:Ancient botanical art And also as a hint to “mathematics before written numbers.”
What does this mean, and what is still open to debate?
The argument is intriguing, but it is important to note the caveats that the article itself notes: the iconographic identification is not always certain, some of the potsherds are small and broken, and sometimes the same potter's wheel was published in more than one source – which may result in double counting in a few cases.
Additionally, even if it is indeed a mathematical intention, it is difficult to know “what the actual implementation was.” This is still an interpretation: was the numerical order born from the needs of fair distribution, or was it an aesthetic tradition of craftsmen that developed on its own? Nature presents this as evidence of “structured” mathematical thinking long before writing, but does not claim that it is a complete number system. (Nature)
Israel has an interesting, albeit secondary, connection here: the article notes that plant motifs rarely appeared outside the core Halafi region, and among other things mentions examples of branches engraved on artefacts from the Gushrim and Neve Yam sites in Israel.
More of the topic in Hayadan:
