What is the Ishango bone?

The Ishango bone is a roughly 20,000-year-old carved bone unearthed in what is now the Democratic Republic of Congo, and it is one of the oldest mathematical objects ever found, evidence that abstract numerical thinking began in Africa long before Greece, Rome or any civilization the standard curriculum treats as the origin of mathematics.

Background

The Ishango bone was discovered at the "Fisherman Settlement" of Ishango in the Democratic Republic of the Congo, and is a bone tool and possible mathematical device that dates to the Upper Paleolithic era. The Upper Paleolithic is the later part of the Old Stone Age, roughly 50,000 to 10,000 years ago, before farming, cities or writing. The bone was found in 1950 by Belgian geologist Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo, discovered in the area of Ishango near the Semliki River. Part of Lake Edward empties into the Semliki, which forms part of the headwaters of the Nile River, on the border between modern-day Uganda and Congo. The bone was found among the remains of a small community that fished and gathered in that area of Africa, a settlement that had been buried in a volcanic eruption.

What it actually is

The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of quartz affixed to one end, perhaps for engraving. That is roughly the length of your index finger. The bone carries 167 or 168 notches distributed in three columns along its length. It was first thought to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool. More scientists have suggested that the groupings of notches indicate a mathematical understanding beyond counting.

Look more closely at those groupings and the picture gets striking. On one side, for example, there are groups of three and six (2 x 3), four and eight (2 x 4), and five and ten (2 x 5) notches, a pattern that looks a lot like deliberate doubling. The numbers on the left and right columns are odd, specifically 9, 11, 13, 17, 19, and 21, with those in the left column being all prime numbers between 10 and 20, forming a prime quadruplet, while those in the right column consist of 10 + 1, 10 − 1, 20 + 1, and 20 − 1. A prime number, to be clear, is a whole number greater than 1 that cannot be produced by multiplying two smaller whole numbers together: 2, 3, 5, 7, 11, 13 and so on. The Greeks are usually given credit for formalizing the study of primes.

What scholars debate

Various hypotheses about the bone's function include tally marks, a mathematical device, a series of prime numbers, or a lunar calendar. Alexander Marshack, who examined it microscopically, concluded that it represented a six-month lunar calendar. Other researchers argue the notch patterns are too structured to be simple tallying. The artifact displays sixteen groups of notches organized into three distinct columns, and a recent study identified previously undescribed mathematical patterns across all three: two columns comprise all prime and odd numbers between 9 and 21, with the sole exception of 15, itself the arithmetic mean of that set, and each column sums to 60 and subdivides into two internal groupings each summing to 30. That level of internal structure is hard to explain as accident.

Dating the bone has proven difficult because volcanic activity disrupted the ratio of isotopes at the site, but the consensus places it between approximately 18,000 and 20,000 years before the present.

Why it matters for the history we have been tracing

Every civilization we have walked through together, from the pharaohs of Egypt to the gold routes of Mali to the stone courts of Great Zimbabwe, rested on systems of counting, measurement and record-keeping. The Ishango bone pushes that intellectual tradition back far further than any of them, into the deep African past, to a fishing community on the edge of a volcanic lake.

Our current mainstream knowledge indicates that primes were first conceived almost 20,000 years later by a Greek scholar in Egypt. If the Ishango bone's notches do represent prime numbers, that timeline collapses. Many scholars assumed that African peoples living 22,000 years ago were too far behind to have understood mathematics in this way, and those assumptions may have prevented scholars from investigating the opposite hypothesis: that these people may have been so mathematically inclined that they could have been the first to discover prime numbers. That bias in the assumptions, not the evidence, is what kept the bone out of the standard story of mathematics.

The Ishango bone is now housed at the Museum of Natural Sciences in Brussels, Belgium. It sits there, in a Belgian museum, taken from the country that made it, which is itself a whole other conversation about who owns the artifacts that tell Africa's story.

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