These ancient designs may be the first evidence of humans doing math

Pictured is Halafian pottery from an excavation at Arpachiyah, Iraq. (Yosef Garfinkel via CNN Newsource)

Images of plants painted on pottery made up to 8,000 years ago may be the earliest example of humans’ mathematical thought, a study has found.

Researchers from the Hebrew University of Jerusalem examined pottery produced by the Halafian people of northern Mesopotamia, who lived between 6200 BC and 5500 BC.

Many bowls featured flowers that have been depicted with four, eight, 16, 32 or 64 petals. The use of these numbers forms a “geometric sequence” that implies a form of mathematical reasoning rooted in symmetry and repetition, the researchers said in the study published last month in the Journal of World Prehistory.

Study authors Yosef Garfinkel, a professor in archaeology at the Hebrew University of Jerusalem, and Sarah Krulwich, a research assistant and MA student at the university’s archaeology department, examined pottery fragments from 29 Halafian sites, excavated over a 100-year period from 1899.

They found that in nearly every one of the 375 fragments that depict flowers, the number of petals is determined by this doubling sequence, which divides a circle into symmetrical units.

“The strict adherence to these numbers, which are repeated in examples from different sites over hundreds of kilometers, cannot be accidental, and indicates that it was done intentionally,” Garfinkel told CNN.

The Halafians may have developed this form of mathematical reasoning — based on the progressive doubling of numbers — in response to managing village communities that had existed in the Near East for some 4,000 years and had become economically complex, the researchers said.

“The ability to divide space evenly, reflected in these floral motifs, likely had practical roots in daily life, such as sharing harvests or allocating communal fields,” Garfinkel said in a press statement.

In the study, the authors note that it wasn’t until the third millennium BC that texts supply undisputed data on various mathematical systems. The Sumerians, in what is now Iraq, used a numerical system based on the number 60 — of the kind still used in timekeeping — and it has been suggested that a pre-Sumerian system existed, which used the number 10 as the base.

But the researchers said the Halafian use of the numbers four, eight, 16 and 32 does not fit either of these systems and “may reflect an earlier and simpler level of mathematical thinking that was in use in the Near East in the 6th and 5th millennia BC.”

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

The study contributes to the academic field of ethnomathematics, which identifies mathematical knowledge embedded in cultural expression by prehistoric or non-literate communities.

This is not the first time it has been suggested that artifacts other than written documents may indicate early mathematical thinking.

Some experts believe that evidence of string-making by Neanderthals more than 40,000 years ago indicates that our Stone Age ancestors had an understanding of mathematical concepts like pairs and sets, as well as other basic numeracy skills.

Garfinkel said his team’s discovery constitutes a foundational step in the maturation of human thought, and that understanding how to do basic division would have been necessary for the later emergence of more complex mathematics.

“Like everything in human development, aspects of mathematics also developed in an evolutionary way from the simple to the more complex,” he said.

He and Krulwich also said in the statement that the Halafian pottery is unique in being an early instance of humans applying an understanding of symmetry to art. None of the images depicts edible crops, implying their purpose was aesthetic rather than agricultural or ritualistic.

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

However, Jens Høyrup, Senior Associate Professor Emeritus at Roskilde University, Denmark, who specializes in Mesopotamian mathematics and was not involved in the study, is less convinced by the archaeologists’ argument.

He described the symmetry of the Halafians’ floral depictions as “an isolated incident of mathematical technique” rather than evidence of broader mathematical reasoning.

“If you have to divide a circle nicely, at first you make a diameter — then it’s two. Then you divide the other way, so you have four,” he told CNN. “It doesn’t amount to any search for a geometric ascending sequence, it’s simply halving.”

“They have a sense of symmetry, that’s clear. But we cannot decide from there that they had a mathematical system,” he adds. “There’s no higher mathematics; it’s just the simplest way to make divisions.”

By Jasmin Sykes