Prehistoric mathematics

The Ishango bone, found in what is today part of the Democratic Republic of the Congo and dating back 20,000 years, may contain some of the earliest evidence of mathematical thought.

Ishango Bone
Ben2, CC BY-SA 3.0, via Wikimedia Commons

It’s really difficult to find evidence of mathematics prior to the invention of writing systems – but it’s not impossible. Tally sticks are relatively common in the archaeological record, so we know that people were counting things at least – but what about more complex processes? We have Babylonian tablets with multiplication tables, and Egyptian tablets and papyrus with fractions, but even by then mathematics was in a reasonably advanced state.

One possible piece of evidence for prehistoric mathematics is the Ishango bone. It was dug up by a Belgian geologist in the 1950s in Ishango, in what is today the Democratic Republic of the Congo (near the border with Uganda); the bone had been buried in a volcanic eruption some 20,000 years ago.

This piece of animal bone looks like a tally stick, with notches carved across its length, but it also has a piece of quartz embedded in the top – potentially turning it into some kind of writing tool. And the notches themselves follow an intriguing pattern. They hint at an intentional order and structure.

There are three columns of notches, and each column groups the notches into smaller sets:

7, 5, 5, 10, 8, 4, 6, 3
9, 19, 21, 11
19, 17, 13, 11

There are quite a few interesting features here. The first column seems to imply doubling: 5 to 10, 4 to 8, and 3 to 6. The second column follows the pattern 10-1, 20-1, 20+1, 10+1. The third column contains all of the prime numbers between 10 and 20. And both the second and third columns add up to the same amount: 60.

Is this evidence of early mathematics? Well, we’re not sure. The first part of the first column (7, 5) is confusing, the groupings of notches are disputed, the appearance of prime numbers could be a complete coincidence, and some people believe that these notches hold no meaning whatsoever – it’s just a grip pattern that has been enthusiastically over-interpreted. It could also be a lunar calendar, which has led some to suggest that its actual purpose is tracking menstrual cycles. In any case, it’s one of the most tantalising pieces of evidence for the earliest pre-history of mathematics.

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