8,200-year-old calculations: Ancient humans knew geometry and long division way before numbers were invented

Scientists have found proof of mathematics being used by a society long before formal numbers were invented. The Halafian culture of northern Mesopotamia painted floral patterns on pottery that follow mathematical systems, such as geometry, symmetry, and spatial long division. A new study published in the Journal of World Prehistory reveals how mathematics was known even during prehistoric times, without even the existence of numbers. Archaeologists from the Hebrew University of Jerusalem came across pottery from a prehistoric culture known as the Halafian. This society lived in northern Mesopotamia from 6200 to 5500 BCE, that is 8,200 to 7,500 years ago. Analysis of the flower motifs on them showed that they were placed in a pattern. Around 700 fragments with such depictions were found.

The researchers put them under the scanner and found that they followed a geometrical pattern. Study authors Yosef Garfinkel and Sarah Krulwich found that the petals were arranged in a geometric sequence: 4, 8, 16, 32, and 64. This was a time when the formal number system did not exist. This means that the scientists have found proof of mathematics being used even when it wasn't a thing. The flower motifs on the pottery showed the Halafian people knew about spatial long division before the invention of numbers. The mathematical concepts on these pottery are years older than the first written mathematical texts from Sumer in southern Mesopotamia.

Divisions and sequence through art

The study authors said that it is hard to know how much mathematical ability prehistoric communities had without the existence of written evidence. But the discovery and analysis of the vegetal decoration of Halafian pottery vessels "enables some understanding of these aspects." Krulwich said in a statement, "These patterns show that mathematical thinking began long before writing. People visualised divisions, sequences, and balance through their art." Garfinkel believes the Halafians were using these concepts in their daily lives, such as for "sharing harvests or allocating communal fields."

The other thing about the discovery is the use of flowers in an artistic medium. The pieces discovered from the time of ancient humans till now only had animals and humans on them. Plants only appeared after early Homo sapiens were already using them for various uses. The latest finding shows the time when flowers became a part of human artistic expression.