The study examined 375 pottery fragments collected from 29 different Halafian sites over more than a century of excavations. Despite the distance between these sites and the long span of time involved, the same patterns kept appearing. The researchers found that almost every flower followed this same sequence, strongly pointing to deliberate design choices rather than coincidence.

According to the researchers, this repeated use of doubling numbers shows an early form of mathematical thinking that existed long before people began writing numbers or equations. The ability to divide a circle evenly into matching parts reflects a practical understanding of space and proportion. This kind of thinking may have been useful in everyday village life, such as sharing food, dividing land, or organising community resources.

This is also pointed out by the researchers, as such number patterns do not match with better-known counting systems that were developed thousands of years later. Rather, they see in this evidence of a more primitive period of mathematical thinking, one based on visual patterns rather than symbols or formulas.

Purpose of artwork

One other interesting observation is that the paintings of the flowers in the pottery are not of edible flowers. This shows that the purpose of their artwork was solely for aesthetics and not for any practical purpose of growing the said things. One of the arguments presented in the study is that this could be the first time in history that humans considered nature as a subject of purely artistic endeavour, appreciating increased symmetry and design.

Not all scholars are fully satisfied with this explanation. Some specialists suggest that, while there is undoubtedly a balance evident in the artwork, it may not demonstrate a deeper mathematical system. The division of the circle into equal parts may merely have been the easiest and most natural way to ornament a round surface, not evidence of deeper numerical thinking.

Despite this, the scientists think that such discoveries mark a significant milestone within the historical context of understanding the evolution of human cognition as regards mathematical thinking and its applications. Such scholars point out that conceptual understanding of division and balance might have paved the way for advanced mathematical concepts that would not emerge until many centuries later.

This research contributes to a growing literature that finds early humans conveyed their mathematical understanding through art and artefacts. Well before the written representation of numbers, humans had their minds on patterns, symmetry, and structure, leaving these in clay forms behind.