December 15, 2025 – Some of humanity’s earliest artistic representations of botanical figures display sophisticated mathematical thinking, according to a new study by researchers at the Hebrew University of Jerusalem. 

According to findings in the Journal of World Prehistory, the Halafian culture of northern Mesopotamia (c. 6200–5500 BCE) produced the earliest systematic plant imagery in prehistoric art, flowers, shrubs, branches, and trees painted on fine pottery, arranged with precise symmetry and numerical sequences, especially petal and flower counts of 4, 8, 16, 32, and 64. This suggests that these farming villages in the Near East already possessed sophisticated, practical mathematical thinking about dividing space and quantities, likely tied to everyday needs such as fairly sharing crops from collectively worked fields, long before writing or formal number systems existed. 

In an extensive analysis of ancient pottery, Prof. Yosef Garfinkel and Sarah Krulwich of the Hebrew University Institute of Archaeology documented hundreds of carefully rendered vegetal motifs, some naturalistic, others abstract, all reflecting conscious artistic choice across 29 archaeological sites.

Earlier prehistoric art focused primarily on humans and animals. Halafian pottery, however, marks the moment when the plant world entered human artistic expression in a systematic and visually sophisticated way. 

“These patterns show that mathematical thinking began long before writing,” Prof. Krulwich says. “People visualized divisions, sequences, and balance through their art.” 

These sequences, the researchers argue, are intentional and demonstrate a sophisticated grasp of spatial division long before the appearance of written numbers. 

This work contributes to the field of ethnomathematics, which identifies mathematical knowledge embedded in cultural expression. 

The motifs documented span the full botanical spectrum: 

• Flowers with meticulously balanced petals 

• Seedlings and shrubs, rendered with botanical clarity 

• Branches, arranged in rhythmic, repeating bands 

• Tall, imposing trees, sometimes shown alongside animals or architecture 

Notably, none of the images depict edible crops, suggesting that the purpose was aesthetic rather than agricultural or ritualistic. Flowers, the authors note, are associated with positive emotional responses, which may explain their prominence.  

Revising the History of Mathematics 

While written mathematical texts appear millennia later in Sumer, Halafian pottery reveals an earlier, intuitive form of mathematical reasoning, rooted in symmetry, repetition, and geometric organization. 

By cataloguing these vegetal motifs and revealing their mathematical foundations, the study offers a new perspective on how early communities understood the natural world, organized their environments, and expressed cognitive complexity. 

“These vessels represent the first moment in history when people chose to portray the botanical world as a subject worthy of artistic attention,” the authors note. “It reflects a cognitive shift tied to village life and a growing awareness of symmetry and aesthetics.”  

The research paper titled “The Earliest Vegetal Motifs in Prehistoric Art: Painted Halafian Pottery of Mesopotamia and Prehistoric Mathematical Thinking” is now available in Journal of World Prehistory and can be accessed here.

Researchers: 

Yosef Garfinkel, Sarah Krulwich 

Institutions: 

Institute of Archaeology, The Hebrew University of Jerusalem