Tech News, 16 January, 2026: Long before the invention of the first written numeral systems or the famous Sumerian base-60 math, prehistoric farmers were already using complex geometric sequences. Archaeologists from the Hebrew University of Jerusalem, led by Prof. Yosef Garfinkel and Sarah Krulwich, recently analyzed over 700 pottery fragments from 29 different sites.
The “Powers of Two” in Flowers
The study, published in the Journal of World Prehistory, found that the Halafian people (c. 6200–5500 BCE) decorated their ceramic bowls with floral motifs that weren’t just random art. The number of petals followed a strict mathematical progression:
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Geometric Sequences: Flowers were meticulously painted with 4, 8, 16, 32, and even 64 petals.
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Doubling Logic: This constant doubling suggests an intuitive understanding of arithmetic and the “powers of two” thousands of years before formal math existed.
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Spatial Division: To paint a flower with exactly 64 symmetrical petals on a curved bowl, the artist had to understand how to divide a circular space into equal, precise fractions.
Why Math on Pottery?
Researchers believe this wasn’t just for beauty. The ability to divide space and count in sequences likely had practical roots in early village life:
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Land Division: As humans settled into farming, they needed to divide communal fields into equal shares.
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Resource Sharing: Calculating harvest portions for a growing population required a system of proportional order.
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Symmetry as Cognitive Growth: The shift from drawing animals and humans to drawing perfectly symmetrical, geometric plants marks a “cognitive shift” in how humans organized their world.
“These patterns show that mathematical thinking began long before writing. People visualized divisions, sequences, and balance through their art.” — Sarah Krulwich, Hebrew University
Comparison of Early Mathematical Evidence
| Period | Evidence Type | Mathematical Concept |
| 6200 BCE | Halafian Pottery | Doubling sequences (4, 8, 16…), Symmetry, Spatial division |
| 4000 BCE | Mesopotamian Tokens | Concrete counting of goods (grain, livestock) |
| 3200 BCE | Sumerian Tablets | Base-60 system (Sexagesimal), First written numbers |
